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Discrete Mathematics DSBA 2022/2023

2023-03-11T15:47:05Z

Nasta.trofimova: /* Assignment deadlines */

== Instructors ==

=== The lecturer ===
My name is Evgeny Dashkov. Feel free to contact me via email: edashkov@gmail.com, [https://t.me/edashkov Telegram], or [https://vk.com/evgeny.v.dashkov VK].

=== Seminar instructors ===
{| class="wikitable" style="text-align:center"
|-
! Group !! 221 !! 222 !! 223 !! 224
|-
|| Teachers || Evgeny Dashkov ||colspan="2"| Boris Danilov [https://t.me/brdann Telegram]|| Trofimova Anastasia [https://t.me/AnastasiiaTrofimova Telegram]
|-
|| Teaching Assistants || Arseny Bolotnikov [https://t.me/l0i4b Telegram] ||Daria Ivanova [https://t.me/ivanovskayaaaaa Telegram]|| Egor Kornelyuk [https://t.me/feddes5 Telegram] || Marianna Kouis [https://t.me/mariannakouis Telegram]
|-
|| Lecturer’s Assistant || colspan="4"| Alena Chislova [https://t.me/alenka_chislova Telegram]
|}

== Current performance ==

[https://docs.google.com/spreadsheets/d/1KoXyABY4alQu-Gw3HsYy3Vco9rfvHdYQZuUjE_ERJB8/edit?usp=sharing The Table]

== Homework ==
The homework includes a few problem sets, one in a fortnight or so (the deadlines are announced on giving each set). Every problem set consists of about 10 – 15 problems, some of which are labeled as ‘bonus’ while all the remaining are considered ‘ordinary’. One can get either 0, ½, or 1 point for each problem. For the entire homework, two values are computed:

HW = (the sum of points given for ordinary problems) / #(ordinary problems);

HW* = (the sum of points given for bonus problems) / #(bonus problems).

The value HW1 is similar to HW but restricted to the problem sets given in Module 1.

A student may be required to explain orally his written solution to any problem. His grade for the problem may be decreased if he fails to do so properly.

== Exam 1 ==
A written examination is held past Module 1. Students may not consult any sources during the exam. Some problems of the exam are labeled as ‘bonus’; the others are ‘ordinary’. Each problem solution is graded with either 0, ¼, ½, ¾, or 1 point, and the entire exam with two values:

Exam1 = (the sum of points given for ordinary problems) / #(ordinary problems);

Exam1* = (the sum of points given for bonus problems) / #(bonus problems)

== Colloquium ==
An oral colloquium is held at the beginning of Module 3. Each student is given two questions concerning statements and definitions as well as one question requiring a proof. After no less than 45 minutes of preparation (when using any literature is allowed), the student is required to answer ‘from scratch’, that is, with no recourse to any materials. The examiner may pose additional questions as he sees fit. The student may get from 0 to 10 integer points for his answer; the value Colloq is just this score.

Please find the question list and rules [https://drive.google.com/file/d/13gNFBATQ6V3lieUj8vym8OXC2RXmbdt4/view?usp=share_link here].

== Exam 2 ==
A written examination is held at the end of the Course. Students may not consult any sources during the exam. The examination takes about 120 minutes. Some problems of the exam are labeled as ‘bonus’; the others are ‘ordinary’. Each problem solution is graded with either 0, ¼, ½, ¾, or 1 point; finally, two values are computed:

Exam2 = (the sum of points given for ordinary problems) / #(ordinary problems);

Exam2* = (the sum of points given for bonus problems) / #(bonus problems).

== Bonus activities ==
The students may be graded for a variety of ‘bonus activities’ (like quizzes, etc.) with an overall integer value Bonus from 0 to 25.

== Exam retaking ==
Examinations 1 and 2 are subject to be retaken if Module 1 grade or Final grade (see below), respectively, is unsatisfactory. Retaking the exam is similar to the regular examination. The resulting grade is substituted for that of the latter. The last try Commission retaking is held for those whose final grade is still unsatisfactory after the retaking. A designated Commission carefully examines the student’s performance and gives him a final mark not better than ‘satisfactory’; at that the Commission is not bound by the grading formulas herein.

== Course materials ==

[https://t.me/joinchat/T_YTN4IG1vAJNWT9 Course chat].

=== Lecture notes ===

https://drive.google.com/file/d/1mmNLLQ0--EDihGNRKwSyXLOA1KL7A0lD/view?usp=sharing

=== Classes recordings ===

https://disk.yandex.ru/d/enYKJ6O8NN_3lQ

=== Lecture video archive ===

https://youtube.com/playlist?list=PLEwK9wdS5g0pk-1YWDc3hezRt_rNpQDf8

=== Compensatory lecture video ===

https://youtu.be/SBH4lou-awE

=== Other resources ===
* [https://tinyurl.com/rwky5vmk The Course's Google Directory]

* [https://www.youtube.com/playlist?list=PL1Uob8iPTHGTidrmrqEHTJ96Pt3-PmML4 Past years' videos]

* We have a [https://meet.edashkov.net.ru dedicated server] to hold an online meeting if we need one.

== Problem sets ==

=== Class problems ===

* [https://drive.google.com/file/d/1EP-diSuOTn9f0ryg18Z2w0xjEp8j0bnl/view?usp=sharing Problem set 1]

* [https://drive.google.com/file/d/12ct99-ORd7A94Gh5g4Nf9riv7UqNMSRc/view?usp=sharing Problem set 2]

* [https://drive.google.com/file/d/1yKKqLsS99V4AhCYqbjafuav2CMCdQTOQ/view?usp=sharing Problem set 3]

* [https://drive.google.com/file/d/1YgH_AdCk4GcKC0KH7xBA4-sUnOYkUvUK/view?usp=share_link Problem set 4]

* [https://drive.google.com/file/d/1M556PSgTJOo5W-AxYEXjFu94VfledpF5/view?usp=share_link Problem set 5]

* [https://drive.google.com/file/d/1-ylVViaBgzxEM-M7Rvrz2iggtK6UiJTY/view?usp=share_link Problem set 6]

* [https://drive.google.com/file/d/15tcTNLW-uFqT2xPJn1imOnEzaGwlaZAq/view?usp=share_link Problem set 7]

* [https://drive.google.com/file/d/1N1EuCCe7NIiEa69nXHwncfQG2IOTyzLi/view?usp=share_link Problem set 8]

* [https://drive.google.com/file/d/1PmlR2bysnKSZrJle9Dwa4KiB23G5ORdZ/view?usp=share_link Problem set 9]

=== Homework problems ===

* [https://drive.google.com/file/d/1A8lFPdI3ZvC1vOgz2KEpYcuWOFlsQvb1/view?usp=sharing Homework 1]

* [https://drive.google.com/file/d/1LOPPwGjyVleR_mclxTKUJ_bxFrxt44sW/view?usp=sharing Homework 2a]

* [https://drive.google.com/file/d/1W7k1OTiIMlPOpo-2mwmGegrc4RDHz5_j/view?usp=share_link Homework 2b]

* [https://drive.google.com/file/d/1UvF-3gRwMrnsDAT9H4KDpoUafhrthKPw/view?usp=share_link Homework 3]

* [https://drive.google.com/file/d/1I25qKW9F_ZJi8akim-X8Op17VTLnZznJ/view?usp=share_link Homework 4]

=== Assignment deadlines ===

{| class="wikitable"
|-
! Home problem set !! colspan="11" | Deadline
|-
| || 221 || 222 || 223 || 224
|-
| HW 1 №1-3 || || 22.IX || 22.IX || 22.IX
|-
| HW 1 || October 6 || October 6 || October 6 || October 6
|-
| HW 2a №1-3 || || October 20 || October 20 ||
|-
| HW 2a || October 24 || October 27 || October 27 || October 27
|-
| HW 2b №1-7 || November 30 || November 20 || November 20 || November 20
|-
| HW 2b №8-14 || December 14 || December 4 || December 4 || December 4
|-
| HW 3 №1-3 || December 22 || December 22 || December 22 || December 24
|-
| HW 3 №4-12 || February 11 || February 11 || February 11 || February 11
|-
| HW 4 || March 16 || March 18 || March 18 || March 19
|}

'''Each deadline is set by the respective group's instructor.'''

== Grading system ==
For the final grading, we compute the following values:

Module 1 grade = round ((50*HW1 + 50*Exam1)/100);

basic = (21*Exam1 + 21*Colloq + 28*HW + 30*Exam2)/100;

adv = (30*Exam1* + Bonus + 35*HW* + 35*Exam2*)/100;

Final grade = round(min(10, 8 * basic + 2 * adv)).

The final grade is rounded half up to an integer. All the other values are reported with the greatest precision available.

== Recommended reading ==
''Please notice that '''The Book''' for our Course does not exist. The latter is based on many sources.''

# Anderson J. A., Discrete Mathematics With Combinatorics. Prentice Hall, 2003.
# Biggs N. L., Discrete mathematics. 2nd ed., New York; Oxford: Oxford University Press, 2004.
# Gavrilov G. P., Sapozhenko A. A. Problems and Exercises in Discrete Mathematics. Kluwer Texts in the Mathematical Sciences 14. Springer, 1996.
# [http://courses.csail.mit.edu/6.042/spring17/mcs.pdf Lehman E., Thomson Leighton F., Meyer A. R. Mathematics for Computer Science, 2017.]
# [http://www.cs.elte.hu/~lovasz/dmbook.ps Lovasz L., Vesztergombi K. Discrete Mathematics. Lecture Notes; Yale University, 1999.]
# Melnikov O., Sarvanov V., Tyshkevich R., Yemelichev V., Zverovich I. Exercises in Graph Theory. Kluwer Texts in the Mathematical Sciences 19. Springer, 1998.
# Rosen K. H. Discrete Mathematics and Its Applications. McGraw-Hill, 1999.
# Stein C., Drysdale R. L., Bogart K. Discrete mathematics for computer scientists. Addison-Wesley, 2010.
# Vinogradov I. M. Elements of number theory. Dover, 1954.

=== In Russian ===
''If you understand Russian (by any chance), you will probably benefit from reading the following books.''

# Виноградов И. М. Основы теории чисел. 9-е изд., М.: Наука, 1981.
# [http://rubtsov.su/public/DM-HSE-Draft.pdf Вялый М., Подольский В., Рубцов А., Шварц Д., Шень А. Лекции по дискретной математике.]
# Гаврилов Г. П., Сапоженко А. А. Задачи и упражнения по дискретной математике. 3-е изд., М.: ФИЗМАТЛИТ, 2004.
# [https://drive.google.com/file/d/1RM6KX_reBFwUXesWGUEu0sFn2NCaBgvz/view?usp=sharing Дашков Е. В. Введение в математическую логику. Множества и отношения. М.: МФТИ, 2019.]
# Зубков А. М., Севастьянов Б. А., Чистяков В. П. Сборник задач по теории вероятностей. 2-е изд., М.: Наука, 1989.
# Мельников О. И. Теория графов в занимательных задачах. 5-е изд., М.: Книжный дом "ЛИБРОКОМ", 2013.
# [http://www.mccme.ru/free-books/shen/shen-induction.pdf Шень А., Математическая индукция. 5-е изд, М.: МЦНМО, 2016.]

Adaptation course in Discrete Math (факультатив)

2023-02-17T13:26:56Z

Nasta.trofimova: /* Course materials */

== General Information ==
The main goal of the Discrete Mathematics Adaptation Course is to help students keep up with the course curriculum by discussing the most important and challenging topics in detail. The second very important goal of the course is to teach students to work competently with mathematical definitions and proofs, correctly logically build solutions to problems and prove statements. The topics of the course are coordinated with the "basic" course of the DSBA and SE program, but its study will also be useful for the direction of AMI. The approximate order of topics is sets and logic, functions and relations, the beginning of number theory, combinatorics, graphs, the foundations of probability theory, generating functions.

== Schedule ==

The classes are organised on Saturdays at 16:20.

== Course materials ==

[https://t.me/+113aheknlsxmYzVi Chat in Telegram]

'''First semester'''

{| class="wikitable"
|-
! Date !! Topic !! Problem Set !! Class note !! Video
|-
|| 21.09.22 || Statements, connectives, quantifiers || [https://drive.google.com/file/d/1kbtRp8c79zE2AspfVb4ZfGZLJRy9Z5j2/view?usp=drivesdk Problem Set 1]|| - ||
|-
|| 28.09.22 || Validity of statements, types of proof|| [https://drive.google.com/file/d/1Q2OlmVzXf4P0ocd3eBet4ktoJ1h1DZyn/view?usp=sharing Problem Set 2] || [https://drive.google.com/file/d/11pdljFmpW57o5OqBH40YwioTW_Ebs_gK/view?usp=sharing Solutions] || -
|-
|| 7.10.22 || Three types of mathematical induction || [https://drive.google.com/file/d/14h2jy4W7KgxBffxE8TKh_13rSG3Wy_Ll/view?usp=sharing Problem Set 3] ||[https://drive.google.com/file/d/1yFnH5QBNxM-1ajoA5y7w9wV_31XeBwWp/view?usp=sharing Solutions] || [https://youtu.be/nljNhVjlnXg Video 3]
|-
|| 14.10.22 || Proofs with induction || [https://drive.google.com/file/d/13vsHkpBV8riwyKOTCh1v1heuAqf0L9nK/view?usp=sharing Problem Set 4] ||[https://drive.google.com/file/d/1PZD-YWikatG9jCbcc1r_Eo5t0y-kdcpj/view?usp=sharing Solutions] || -
|-
|| 21.10.22 || Divisibility. Calculation of remainders. Direct proofs. || [https://drive.google.com/file/d/1rHfC1WRv4IB8kNRMynVWv0C26PXGi137/view?usp=sharing Problem Set 5] ||[https://drive.google.com/file/d/1CvWAD5pDmMB8JFWSFNxOrrT7-Jfp_0Wd/view?usp=sharing Solutions] ||
[https://youtu.be/-OIYkDOkLyk Video 5]
|-
|| 11.11.22 || Great commod divider, the main thorem of arithmetic, direct proofs. || [https://drive.google.com/file/d/1CrF9W2rXFiTMKFoxZO-PJDmhYAx6Ql84/view?usp=share_link Problem Set 6] ||[https://drive.google.com/file/d/1TWSgbLrRtZWRrbneebExE4BPoDzLU4-b/view?usp=share_link Solutions] ||
[https://youtu.be/_2RRlq21gqM Video 6]
|-
|| 19.11.22 || Fermat's Little theorem, inverse elements in groups $\mathbb{Z}_p$, congruences. || [https://drive.google.com/file/d/1IF6rqwLN0Bq8n07mxQ3CAmoMfWplJ3OR/view?usp=share_link Problem Set 7] ||[https://drive.google.com/file/d/1FZevxpUjcPrrtCbxHn-HRh1odDamJqlq/view?usp=share_link Solutions] ||
[https://youtu.be/peuzIDzh1bE Video 7]
|-
|| 25.11.22 || Fermat's Little theorem, inverse elements in groups $\mathbb{Z}_p$, congruences. || [https://drive.google.com/file/d/1CYGJ7B5d426ChuZBozzsLKwMVZeVPgQJ/view?usp=share_link Problem Set 8] ||[https://drive.google.com/file/d/1_PCu2dDhIgN7uE1ijLGLH1USapPskGWH/view?usp=share_link Solutions] ||
[ -]
|-
|| 2.12.22 || Application of Euler's theorem and Euclidean algorithm, cryptography || [https://drive.google.com/file/d/1Oq3grvUbG-yBBbrHqhK_4Ylz4Io-D1Lw/view?usp=share_link Problem Set 9] ||[https://drive.google.com/file/d/1BFDh6-6KVmb65w7qDEQprP6BYUMUW6AQ/view?usp=share_link Solutions] ||
[https://youtu.be/HPpI7VpHrWY Video 9]
|-
|| 9.12.22 || Sets, direct proofs of set identities || [https://drive.google.com/file/d/1C6I_cviJwznCLZ5BKtxUtlUrjpp4Kegw/view?usp=share_link Problem Set 10] ||[https://drive.google.com/file/d/179jjcjhdU0LschqhPEFMPJylunwRiofA/view?usp=share_link Solutions] || [https://youtu.be/7Gk3JxRpeWU Video 10]
|-
|| 16.12.22 || Operations with sets, cardinality and power set || [https://drive.google.com/file/d/1D9A7QTq-7dPN8Xz_jQhsYIknX8cukhZD/view?usp=share_link Problem Set 11] ||[https://drive.google.com/file/d/1B1snvrzqMgUMDEEQqOHVzomfWVwf2t07/view?usp=share_link Solutions] ||
[https://youtu.be/TK4BNYF4vEU Video 11]
|-
|| 21.01.23 || Sets once again, proofs that a statement is wrong|| [https://drive.google.com/file/d/15hSnMr1jVCSJ6boGK5KuEUldlx3-8Pvv/view?usp=share_link Problem Set 12] ||[https://drive.google.com/file/d/1PDsR6DjO_K9-XfoqprA0UsYWh-2fSb8T/view?usp=share_link Solutions] ||
[https://youtu.be/2J8qDgwpivU Video 12]
|-
|| 28.01.23 || Relations, main definitions || [https://drive.google.com/file/d/1IJAqHsXCQaSFlzZFaH5TpfnNdibKAzen/view?usp=share_link Problem Set 13] ||[https://drive.google.com/file/d/188uRSv9ALwy4IsPreEbS8J61PDMw9uVw/view?usp=share_link Solutions] ||
[ Video 13]
|-
|| 11.02.23 || Relations, proofs of inclisions and construction of counterexamples. || [https://drive.google.com/file/d/1BL5L3ZneQh61HWjLcok0iDMIR3IMjFbA/view?usp=share_link Problem Set 14] ||[https://drive.google.com/file/d/1aC59jPGQT3e_RBrbar_Z1hgdabfqojG0/view?usp=share_link Solutions] ||
[https://youtu.be/KrKWF381vtc Video 14]
|-
|| 17.02.23 || Functions and their properties. || [https://drive.google.com/file/d/1ONrAr-5rX6T_2vGTPJ63AJmanSh_H-bP/view?usp=share_link Problem Set 15] ||[Solutions] ||
[ Video 15]
|}

[https://drive.google.com/file/d/163PgGw33FTt3PUVdVBYCjIHluftfZVol/view?usp=sharing Last year retake]

[https://drive.google.com/file/d/1bljTOb3x0kvYy7cslTOC4B3StYOHi3CX/view Last year test 1]

== Homeworks ==
[https://forms.gle/TAgL2eUkhSyhZKLD9 Homework 1 (Logics)], Deadline 31st October

[https://forms.gle/pVA1a8xbeP54RqAQ7 Homework 2 (Induction)], Deadline 31st November, better to complete before the November Test

Hint🦉 in Problem 5: Do not try to prove P(n) out of P(n-1). Assume that P(1), P(2), ...P(n-1) are all true. For proving P(n) say: lets find the biggest Fibonacci number F_i<n. Then, n = F_i + k. For the k apply your assumption😉😉

[https://drive.google.com/file/d/1k8SKmN9J_DdSs8ibP_9b52n8LxiPf_8U/view?usp=share_link Homework 3]: write down solutions to exam 1 in a perfect manner (like you you are going to print a book of your solutions), Deadline 25th November. You can pass them written or orally on Fridays evenings. Do it if you want to have MAX in the retake(if so happened) and in the exam in the end of the course.

[https://forms.gle/DQUEyuh1vuXgdtr6A Homework 4 (Number theory)], Deadline with bonus 29th December

==Semester 1 ==

[https://docs.google.com/spreadsheets/d/1YHhkk8TCm_qPF0tXyGe7rc-DzubrgSESZUoW6fHMLZA/edit?usp=sharing Current grades and comments]

== References ==

1. [http://discrete.openmathbooks.org/dmoi3.html Discrete Mathematics (An Open Introduction) by Oscar Levin,] p. 197 Logics. Many simple problems with solution to feel the topic.

2. [https://drive.google.com/file/d/1mmNLLQ0--EDihGNRKwSyXLOA1KL7A0lD/view?usp=sharing Lecture notes by Evgeny Dashkov]

PLUS: there is a [https://youtube.com/playlist?list=PLEwK9wdS5g0pk-1YWDc3hezRt_rNpQDf8 folder with records on wikipage ]

3. [http://www.mccme.ru/free-books/shen/shen-induction.pdf Шень А., Математическая индукция. 5-е изд, М.: МЦНМО, 2016.] Many problems to work with three different versions of induction.

== Grading and Results ==

'''Final grade''' = Average(HWs)+ Bonus points

Bonus point number is between 0 to 20. Such points may be given for a variety of auxiliary activities.

Adaptation course in Discrete Math (факультатив)

2023-02-17T13:25:42Z

Nasta.trofimova: /* Course materials */

== General Information ==
The main goal of the Discrete Mathematics Adaptation Course is to help students keep up with the course curriculum by discussing the most important and challenging topics in detail. The second very important goal of the course is to teach students to work competently with mathematical definitions and proofs, correctly logically build solutions to problems and prove statements. The topics of the course are coordinated with the "basic" course of the DSBA and SE program, but its study will also be useful for the direction of AMI. The approximate order of topics is sets and logic, functions and relations, the beginning of number theory, combinatorics, graphs, the foundations of probability theory, generating functions.

== Schedule ==

The classes are organised on Saturdays at 16:20.

== Course materials ==

[https://t.me/+113aheknlsxmYzVi Chat in Telegram]

'''First semester'''

{| class="wikitable"
|-
! Date !! Topic !! Problem Set !! Class note !! Video
|-
|| 21.09.22 || Statements, connectives, quantifiers || [https://drive.google.com/file/d/1kbtRp8c79zE2AspfVb4ZfGZLJRy9Z5j2/view?usp=drivesdk Problem Set 1]|| - ||
|-
|| 28.09.22 || Validity of statements, types of proof|| [https://drive.google.com/file/d/1Q2OlmVzXf4P0ocd3eBet4ktoJ1h1DZyn/view?usp=sharing Problem Set 2] || [https://drive.google.com/file/d/11pdljFmpW57o5OqBH40YwioTW_Ebs_gK/view?usp=sharing Solutions] || -
|-
|| 7.10.22 || Three types of mathematical induction || [https://drive.google.com/file/d/14h2jy4W7KgxBffxE8TKh_13rSG3Wy_Ll/view?usp=sharing Problem Set 3] ||[https://drive.google.com/file/d/1yFnH5QBNxM-1ajoA5y7w9wV_31XeBwWp/view?usp=sharing Solutions] || [https://youtu.be/nljNhVjlnXg Video 3]
|-
|| 14.10.22 || Proofs with induction || [https://drive.google.com/file/d/13vsHkpBV8riwyKOTCh1v1heuAqf0L9nK/view?usp=sharing Problem Set 4] ||[https://drive.google.com/file/d/1PZD-YWikatG9jCbcc1r_Eo5t0y-kdcpj/view?usp=sharing Solutions] || -
|-
|| 21.10.22 || Divisibility. Calculation of remainders. Direct proofs. || [https://drive.google.com/file/d/1rHfC1WRv4IB8kNRMynVWv0C26PXGi137/view?usp=sharing Problem Set 5] ||[https://drive.google.com/file/d/1CvWAD5pDmMB8JFWSFNxOrrT7-Jfp_0Wd/view?usp=sharing Solutions] ||
[https://youtu.be/-OIYkDOkLyk Video 5]
|-
|| 11.11.22 || Great commod divider, the main thorem of arithmetic, direct proofs. || [https://drive.google.com/file/d/1CrF9W2rXFiTMKFoxZO-PJDmhYAx6Ql84/view?usp=share_link Problem Set 6] ||[https://drive.google.com/file/d/1TWSgbLrRtZWRrbneebExE4BPoDzLU4-b/view?usp=share_link Solutions] ||
[https://youtu.be/_2RRlq21gqM Video 6]
|-
|| 19.11.22 || Fermat's Little theorem, inverse elements in groups $\mathbb{Z}_p$, congruences. || [https://drive.google.com/file/d/1IF6rqwLN0Bq8n07mxQ3CAmoMfWplJ3OR/view?usp=share_link Problem Set 7] ||[https://drive.google.com/file/d/1FZevxpUjcPrrtCbxHn-HRh1odDamJqlq/view?usp=share_link Solutions] ||
[https://youtu.be/peuzIDzh1bE Video 7]
|-
|| 25.11.22 || Fermat's Little theorem, inverse elements in groups $\mathbb{Z}_p$, congruences. || [https://drive.google.com/file/d/1CYGJ7B5d426ChuZBozzsLKwMVZeVPgQJ/view?usp=share_link Problem Set 8] ||[https://drive.google.com/file/d/1_PCu2dDhIgN7uE1ijLGLH1USapPskGWH/view?usp=share_link Solutions] ||
[ -]
|-
|| 2.12.22 || Application of Euler's theorem and Euclidean algorithm, cryptography || [https://drive.google.com/file/d/1Oq3grvUbG-yBBbrHqhK_4Ylz4Io-D1Lw/view?usp=share_link Problem Set 9] ||[https://drive.google.com/file/d/1BFDh6-6KVmb65w7qDEQprP6BYUMUW6AQ/view?usp=share_link Solutions] ||
[https://youtu.be/HPpI7VpHrWY Video 9]
|-
|| 9.12.22 || Sets, direct proofs of set identities || [https://drive.google.com/file/d/1C6I_cviJwznCLZ5BKtxUtlUrjpp4Kegw/view?usp=share_link Problem Set 10] ||[https://drive.google.com/file/d/179jjcjhdU0LschqhPEFMPJylunwRiofA/view?usp=share_link Solutions] || [https://youtu.be/7Gk3JxRpeWU Video 10]
|-
|| 16.12.22 || Operations with sets, cardinality and power set || [https://drive.google.com/file/d/1D9A7QTq-7dPN8Xz_jQhsYIknX8cukhZD/view?usp=share_link Problem Set 11] ||[https://drive.google.com/file/d/1B1snvrzqMgUMDEEQqOHVzomfWVwf2t07/view?usp=share_link Solutions] ||
[https://youtu.be/TK4BNYF4vEU Video 11]
|-
|| 21.01.23 || Sets once again, proofs that a statement is wrong|| [https://drive.google.com/file/d/15hSnMr1jVCSJ6boGK5KuEUldlx3-8Pvv/view?usp=share_link Problem Set 12] ||[https://drive.google.com/file/d/1PDsR6DjO_K9-XfoqprA0UsYWh-2fSb8T/view?usp=share_link Solutions] ||
[https://youtu.be/2J8qDgwpivU Video 12]
|-
|| 28.01.23 || Relations, main definitions || [https://drive.google.com/file/d/1IJAqHsXCQaSFlzZFaH5TpfnNdibKAzen/view?usp=share_link Problem Set 13] ||[https://drive.google.com/file/d/188uRSv9ALwy4IsPreEbS8J61PDMw9uVw/view?usp=share_link Solutions] ||
[ Video 13]
|-
|| 11.02.23 || || [https://drive.google.com/file/d/1BL5L3ZneQh61HWjLcok0iDMIR3IMjFbA/view?usp=share_link Problem Set 14] ||[https://drive.google.com/file/d/1aC59jPGQT3e_RBrbar_Z1hgdabfqojG0/view?usp=share_link Solutions] ||
[https://youtu.be/KrKWF381vtc Video 14]
|-
|| 17.02.23 || || [https://drive.google.com/file/d/1ONrAr-5rX6T_2vGTPJ63AJmanSh_H-bP/view?usp=share_link Problem Set 15] ||[Solutions] ||
[ Video 15]
|}

[https://drive.google.com/file/d/163PgGw33FTt3PUVdVBYCjIHluftfZVol/view?usp=sharing Last year retake]

[https://drive.google.com/file/d/1bljTOb3x0kvYy7cslTOC4B3StYOHi3CX/view Last year test 1]

== Homeworks ==
[https://forms.gle/TAgL2eUkhSyhZKLD9 Homework 1 (Logics)], Deadline 31st October

[https://forms.gle/pVA1a8xbeP54RqAQ7 Homework 2 (Induction)], Deadline 31st November, better to complete before the November Test

Hint🦉 in Problem 5: Do not try to prove P(n) out of P(n-1). Assume that P(1), P(2), ...P(n-1) are all true. For proving P(n) say: lets find the biggest Fibonacci number F_i<n. Then, n = F_i + k. For the k apply your assumption😉😉

[https://drive.google.com/file/d/1k8SKmN9J_DdSs8ibP_9b52n8LxiPf_8U/view?usp=share_link Homework 3]: write down solutions to exam 1 in a perfect manner (like you you are going to print a book of your solutions), Deadline 25th November. You can pass them written or orally on Fridays evenings. Do it if you want to have MAX in the retake(if so happened) and in the exam in the end of the course.

[https://forms.gle/DQUEyuh1vuXgdtr6A Homework 4 (Number theory)], Deadline with bonus 29th December

==Semester 1 ==

[https://docs.google.com/spreadsheets/d/1YHhkk8TCm_qPF0tXyGe7rc-DzubrgSESZUoW6fHMLZA/edit?usp=sharing Current grades and comments]

== References ==

1. [http://discrete.openmathbooks.org/dmoi3.html Discrete Mathematics (An Open Introduction) by Oscar Levin,] p. 197 Logics. Many simple problems with solution to feel the topic.

2. [https://drive.google.com/file/d/1mmNLLQ0--EDihGNRKwSyXLOA1KL7A0lD/view?usp=sharing Lecture notes by Evgeny Dashkov]

PLUS: there is a [https://youtube.com/playlist?list=PLEwK9wdS5g0pk-1YWDc3hezRt_rNpQDf8 folder with records on wikipage ]

3. [http://www.mccme.ru/free-books/shen/shen-induction.pdf Шень А., Математическая индукция. 5-е изд, М.: МЦНМО, 2016.] Many problems to work with three different versions of induction.

== Grading and Results ==

'''Final grade''' = Average(HWs)+ Bonus points

Bonus point number is between 0 to 20. Such points may be given for a variety of auxiliary activities.

Discrete Mathematics DSBA 2022/2023

2023-02-10T17:00:17Z

Nasta.trofimova:

== Instructors ==

=== The lecturer ===
My name is Evgeny Dashkov. Feel free to contact me via email: edashkov@gmail.com, [https://t.me/edashkov Telegram], or [https://vk.com/evgeny.v.dashkov VK].

=== Seminar instructors ===
{| class="wikitable" style="text-align:center"
|-
! Group !! 221 !! 222 !! 223 !! 224
|-
|| Teachers || Evgeny Dashkov ||colspan="2"| Boris Danilov [https://t.me/brdann Telegram]|| Trofimova Anastasia [https://t.me/AnastasiiaTrofimova Telegram]
|-
|| Teaching Assistants || Arseny Bolotnikov [https://t.me/l0i4b Telegram] ||Daria Ivanova [https://t.me/ivanovskayaaaaa Telegram]|| Egor Kornelyuk [https://t.me/feddes5 Telegram] || Marianna Kouis [https://t.me/mariannakouis Telegram]
|-
|| Lecturer’s Assistant || colspan="4"| Alena Chislova [https://t.me/alenka_chislova Telegram]
|}

== Current performance ==

[https://docs.google.com/spreadsheets/d/1KoXyABY4alQu-Gw3HsYy3Vco9rfvHdYQZuUjE_ERJB8/edit?usp=sharing The Table]

== Homework ==
The homework includes a few problem sets, one in a fortnight or so (the deadlines are announced on giving each set). Every problem set consists of about 10 – 15 problems, some of which are labeled as ‘bonus’ while all the remaining are considered ‘ordinary’. One can get either 0, ½, or 1 point for each problem. For the entire homework, two values are computed:

HW = (the sum of points given for ordinary problems) / #(ordinary problems);

HW* = (the sum of points given for bonus problems) / #(bonus problems).

The value HW1 is similar to HW but restricted to the problem sets given in Module 1.

A student may be required to explain orally his written solution to any problem. His grade for the problem may be decreased if he fails to do so properly.

== Exam 1 ==
A written examination is held past Module 1. Students may not consult any sources during the exam. Some problems of the exam are labeled as ‘bonus’; the others are ‘ordinary’. Each problem solution is graded with either 0, ¼, ½, ¾, or 1 point, and the entire exam with two values:

Exam1 = (the sum of points given for ordinary problems) / #(ordinary problems);

Exam1* = (the sum of points given for bonus problems) / #(bonus problems)

== Colloquium ==
An oral colloquium is held at the beginning of Module 3. Each student is given two questions concerning statements and definitions as well as one question requiring a proof. After no less than 45 minutes of preparation (when using any literature is allowed), the student is required to answer ‘from scratch’, that is, with no recourse to any materials. The examiner may pose additional questions as he sees fit. The student may get from 0 to 10 integer points for his answer; the value Colloq is just this score.

Please find the question list and rules [https://drive.google.com/file/d/13gNFBATQ6V3lieUj8vym8OXC2RXmbdt4/view?usp=share_link here].

== Exam 2 ==
A written examination is held at the end of the Course. Students may not consult any sources during the exam. The examination takes about 120 minutes. Some problems of the exam are labeled as ‘bonus’; the others are ‘ordinary’. Each problem solution is graded with either 0, ¼, ½, ¾, or 1 point; finally, two values are computed:

Exam2 = (the sum of points given for ordinary problems) / #(ordinary problems);

Exam2* = (the sum of points given for bonus problems) / #(bonus problems).

== Bonus activities ==
The students may be graded for a variety of ‘bonus activities’ (like quizzes, etc.) with an overall integer value Bonus from 0 to 25.

== Exam retaking ==
Examinations 1 and 2 are subject to be retaken if Module 1 grade or Final grade (see below), respectively, is unsatisfactory. Retaking the exam is similar to the regular examination. The resulting grade is substituted for that of the latter. The last try Commission retaking is held for those whose final grade is still unsatisfactory after the retaking. A designated Commission carefully examines the student’s performance and gives him a final mark not better than ‘satisfactory’; at that the Commission is not bound by the grading formulas herein.

== Course materials ==

[https://t.me/joinchat/T_YTN4IG1vAJNWT9 Course chat].

=== Lecture notes ===

https://drive.google.com/file/d/1mmNLLQ0--EDihGNRKwSyXLOA1KL7A0lD/view?usp=sharing

=== Classes recordings ===

https://disk.yandex.ru/d/enYKJ6O8NN_3lQ

=== Lecture video archive ===

https://youtube.com/playlist?list=PLEwK9wdS5g0pk-1YWDc3hezRt_rNpQDf8

=== Other resources ===
* [https://tinyurl.com/rwky5vmk The Course's Google Directory]

* [https://www.youtube.com/playlist?list=PL1Uob8iPTHGTidrmrqEHTJ96Pt3-PmML4 Past years' videos]

* We have a [https://meet.edashkov.net.ru dedicated server] to hold an online meeting if we need one.

== Problem sets ==

=== Class problems ===

* [https://drive.google.com/file/d/1EP-diSuOTn9f0ryg18Z2w0xjEp8j0bnl/view?usp=sharing Problem set 1]

* [https://drive.google.com/file/d/12ct99-ORd7A94Gh5g4Nf9riv7UqNMSRc/view?usp=sharing Problem set 2]

* [https://drive.google.com/file/d/1yKKqLsS99V4AhCYqbjafuav2CMCdQTOQ/view?usp=sharing Problem set 3]

* [https://drive.google.com/file/d/1YgH_AdCk4GcKC0KH7xBA4-sUnOYkUvUK/view?usp=share_link Problem set 4]

* [https://drive.google.com/file/d/1M556PSgTJOo5W-AxYEXjFu94VfledpF5/view?usp=share_link Problem set 5]

* [https://drive.google.com/file/d/1-ylVViaBgzxEM-M7Rvrz2iggtK6UiJTY/view?usp=share_link Problem set 6]

* [https://drive.google.com/file/d/15tcTNLW-uFqT2xPJn1imOnEzaGwlaZAq/view?usp=share_link Problem set 7]

* [https://drive.google.com/file/d/1N1EuCCe7NIiEa69nXHwncfQG2IOTyzLi/view?usp=share_link Problem set 8]

=== Homework problems ===

* [https://drive.google.com/file/d/1A8lFPdI3ZvC1vOgz2KEpYcuWOFlsQvb1/view?usp=sharing Homework 1]

* [https://drive.google.com/file/d/1LOPPwGjyVleR_mclxTKUJ_bxFrxt44sW/view?usp=sharing Homework 2a]

* [https://drive.google.com/file/d/1W7k1OTiIMlPOpo-2mwmGegrc4RDHz5_j/view?usp=share_link Homework 2b]

* [https://drive.google.com/file/d/1UvF-3gRwMrnsDAT9H4KDpoUafhrthKPw/view?usp=share_link Homework 3]

=== Assignment deadlines ===

{| class="wikitable"
|-
! Home problem set !! colspan="11" | Deadline
|-
| || 221 || 222 || 223 || 224
|-
| HW 1 №1-3 || || 22.IX || 22.IX || 22.IX
|-
| HW 1 || October 6 || October 6 || October 6 || October 6
|-
| HW 2a №1-3 || || October 20 || October 20 ||
|-
| HW 2a || October 24 || October 27 || October 27 || October 27
|-
| HW 2b №1-7 || November 30 || November 20 || November 20 || November 20
|-
| HW 2b №8-14 || December 14 || December 4 || December 4 || December 4
|-
| HW 3 №1-3 || December 22 || December 22 || December 22 || December 24
|-
| HW 3 №4-12 || February 11 || February 11 || February 11 || February 11
|}

'''Each deadline is set by the respective group's instructor.'''

== Grading system ==
For the final grading, we compute the following values:

Module 1 grade = round ((50*HW1 + 50*Exam1)/100);

basic = (21*Exam1 + 21*Colloq + 28*HW + 30*Exam2)/100;

adv = (30*Exam1* + Bonus + 35*HW* + 35*Exam2*)/100;

Final grade = round(min(10, 8 * basic + 2 * adv)).

The final grade is rounded half up to an integer. All the other values are reported with the greatest precision available.

== Recommended reading ==
''Please notice that '''The Book''' for our Course does not exist. The latter is based on many sources.''

# Anderson J. A., Discrete Mathematics With Combinatorics. Prentice Hall, 2003.
# Biggs N. L., Discrete mathematics. 2nd ed., New York; Oxford: Oxford University Press, 2004.
# Gavrilov G. P., Sapozhenko A. A. Problems and Exercises in Discrete Mathematics. Kluwer Texts in the Mathematical Sciences 14. Springer, 1996.
# [http://courses.csail.mit.edu/6.042/spring17/mcs.pdf Lehman E., Thomson Leighton F., Meyer A. R. Mathematics for Computer Science, 2017.]
# [http://www.cs.elte.hu/~lovasz/dmbook.ps Lovasz L., Vesztergombi K. Discrete Mathematics. Lecture Notes; Yale University, 1999.]
# Melnikov O., Sarvanov V., Tyshkevich R., Yemelichev V., Zverovich I. Exercises in Graph Theory. Kluwer Texts in the Mathematical Sciences 19. Springer, 1998.
# Rosen K. H. Discrete Mathematics and Its Applications. McGraw-Hill, 1999.
# Stein C., Drysdale R. L., Bogart K. Discrete mathematics for computer scientists. Addison-Wesley, 2010.
# Vinogradov I. M. Elements of number theory. Dover, 1954.

=== In Russian ===
''If you understand Russian (by any chance), you will probably benefit from reading the following books.''

# Виноградов И. М. Основы теории чисел. 9-е изд., М.: Наука, 1981.
# [http://rubtsov.su/public/DM-HSE-Draft.pdf Вялый М., Подольский В., Рубцов А., Шварц Д., Шень А. Лекции по дискретной математике.]
# Гаврилов Г. П., Сапоженко А. А. Задачи и упражнения по дискретной математике. 3-е изд., М.: ФИЗМАТЛИТ, 2004.
# [https://drive.google.com/file/d/1RM6KX_reBFwUXesWGUEu0sFn2NCaBgvz/view?usp=sharing Дашков Е. В. Введение в математическую логику. Множества и отношения. М.: МФТИ, 2019.]
# Зубков А. М., Севастьянов Б. А., Чистяков В. П. Сборник задач по теории вероятностей. 2-е изд., М.: Наука, 1989.
# Мельников О. И. Теория графов в занимательных задачах. 5-е изд., М.: Книжный дом "ЛИБРОКОМ", 2013.
# [http://www.mccme.ru/free-books/shen/shen-induction.pdf Шень А., Математическая индукция. 5-е изд, М.: МЦНМО, 2016.]

Discrete Mathematics DSBA 2022/2023

2023-02-10T16:59:56Z

Nasta.trofimova: /* Assignment deadlines */

== Instructors ==

=== The lecturer ===
My name is Evgeny Dashkov. Feel free to contact me via email: edashkov@gmail.com, [https://t.me/edashkov Telegram], or [https://vk.com/evgeny.v.dashkov VK].

=== Seminar instructors ===
{| class="wikitable" style="text-align:center"
|-
! Group !! 221 !! 222 !! 223 !! 224
|-
|| Teachers || Evgeny Dashkov ||colspan="2"| Boris Danilov [https://t.me/brdann Telegram]|| Trofimova Anastasia [https://t.me/AnastasiiaTrofimova Telegram]
|-
|| Teaching Assistants || Arseny Bolotnikov [https://t.me/l0i4b Telegram] ||Daria Ivanova [https://t.me/ivanovskayaaaaa Telegram]|| Egor Kornelyuk [https://t.me/feddes5 Telegram] || Marianna Kouis [https://t.me/mariannakouis Telegram]
|-
|| Lecturer’s Assistant || colspan="4"| Alena Chislova [https://t.me/alenka_chislova Telegram]
|}

== Current performance ==

[https://docs.google.com/spreadsheets/d/1KoXyABY4alQu-Gw3HsYy3Vco9rfvHdYQZuUjE_ERJB8/edit?usp=sharing The Table]

== Homework ==
The homework includes a few problem sets, one in a fortnight or so (the deadlines are announced on giving each set). Every problem set consists of about 10 – 15 problems, some of which are labeled as ‘bonus’ while all the remaining are considered ‘ordinary’. One can get either 0, ½, or 1 point for each problem. For the entire homework, two values are computed:

HW = (the sum of points given for ordinary problems) / #(ordinary problems);

HW* = (the sum of points given for bonus problems) / #(bonus problems).

The value HW1 is similar to HW but restricted to the problem sets given in Module 1.

A student may be required to explain orally his written solution to any problem. His grade for the problem may be decreased if he fails to do so properly.

== Exam 1 ==
A written examination is held past Module 1. Students may not consult any sources during the exam. Some problems of the exam are labeled as ‘bonus’; the others are ‘ordinary’. Each problem solution is graded with either 0, ¼, ½, ¾, or 1 point, and the entire exam with two values:

Exam1 = (the sum of points given for ordinary problems) / #(ordinary problems);

Exam1* = (the sum of points given for bonus problems) / #(bonus problems)

== Colloquium ==
An oral colloquium is held at the beginning of Module 3. Each student is given two questions concerning statements and definitions as well as one question requiring a proof. After no less than 45 minutes of preparation (when using any literature is allowed), the student is required to answer ‘from scratch’, that is, with no recourse to any materials. The examiner may pose additional questions as he sees fit. The student may get from 0 to 10 integer points for his answer; the value Colloq is just this score.

Please find the question list and rules [https://drive.google.com/file/d/13gNFBATQ6V3lieUj8vym8OXC2RXmbdt4/view?usp=share_link here].

== Exam 2 ==
A written examination is held at the end of the Course. Students may not consult any sources during the exam. The examination takes about 120 minutes. Some problems of the exam are labeled as ‘bonus’; the others are ‘ordinary’. Each problem solution is graded with either 0, ¼, ½, ¾, or 1 point; finally, two values are computed:

Exam2 = (the sum of points given for ordinary problems) / #(ordinary problems);

Exam2* = (the sum of points given for bonus problems) / #(bonus problems).

== Bonus activities ==
The students may be graded for a variety of ‘bonus activities’ (like quizzes, etc.) with an overall integer value Bonus from 0 to 25.

== Exam retaking ==
Examinations 1 and 2 are subject to be retaken if Module 1 grade or Final grade (see below), respectively, is unsatisfactory. Retaking the exam is similar to the regular examination. The resulting grade is substituted for that of the latter. The last try Commission retaking is held for those whose final grade is still unsatisfactory after the retaking. A designated Commission carefully examines the student’s performance and gives him a final mark not better than ‘satisfactory’; at that the Commission is not bound by the grading formulas herein.

== Course materials ==

[https://t.me/joinchat/T_YTN4IG1vAJNWT9 Course chat].

=== Lecture notes ===

https://drive.google.com/file/d/1mmNLLQ0--EDihGNRKwSyXLOA1KL7A0lD/view?usp=sharing

=== Classes recordings ===

https://disk.yandex.ru/d/enYKJ6O8NN_3lQ

=== Lecture video archive ===

https://youtube.com/playlist?list=PLEwK9wdS5g0pk-1YWDc3hezRt_rNpQDf8

=== Other resources ===
* [https://tinyurl.com/rwky5vmk The Course's Google Directory]

* [https://www.youtube.com/playlist?list=PL1Uob8iPTHGTidrmrqEHTJ96Pt3-PmML4 Past years' videos]

* We have a [https://meet.edashkov.net.ru dedicated server] to hold an online meeting if we need one.

== Problem sets ==

=== Class problems ===

* [https://drive.google.com/file/d/1EP-diSuOTn9f0ryg18Z2w0xjEp8j0bnl/view?usp=sharing Problem set 1]

* [https://drive.google.com/file/d/12ct99-ORd7A94Gh5g4Nf9riv7UqNMSRc/view?usp=sharing Problem set 2]

* [https://drive.google.com/file/d/1yKKqLsS99V4AhCYqbjafuav2CMCdQTOQ/view?usp=sharing Problem set 3]

* [https://drive.google.com/file/d/1YgH_AdCk4GcKC0KH7xBA4-sUnOYkUvUK/view?usp=share_link Problem set 4]

* [https://drive.google.com/file/d/1M556PSgTJOo5W-AxYEXjFu94VfledpF5/view?usp=share_link Problem set 5]

* [https://drive.google.com/file/d/1-ylVViaBgzxEM-M7Rvrz2iggtK6UiJTY/view?usp=share_link Problem set 6]

* [https://drive.google.com/file/d/15tcTNLW-uFqT2xPJn1imOnEzaGwlaZAq/view?usp=share_link Problem set 7]

* [https://drive.google.com/file/d/1N1EuCCe7NIiEa69nXHwncfQG2IOTyzLi/view?usp=share_link Problem set 8]

=== Homework problems ===

* [https://drive.google.com/file/d/1A8lFPdI3ZvC1vOgz2KEpYcuWOFlsQvb1/view?usp=sharing Homework 1]

* [https://drive.google.com/file/d/1LOPPwGjyVleR_mclxTKUJ_bxFrxt44sW/view?usp=sharing Homework 2a]

* [https://drive.google.com/file/d/1W7k1OTiIMlPOpo-2mwmGegrc4RDHz5_j/view?usp=share_link Homework 2b]

* [https://drive.google.com/file/d/1UvF-3gRwMrnsDAT9H4KDpoUafhrthKPw/view?usp=share_link Homework 3]

=== Assignment deadlines ===

{| class="wikitable"
|-
! Home problem set !! colspan="11" | Deadline
|-
| || 221 || 222 || 223 || 224
|-
| HW 1 №1-3 || || 22.IX || 22.IX || 22.IX
|-
| HW 1 || October 6 || October 6 || October 6 || October 6
|-
| HW 2a №1-3 || || October 20 || October 20 ||
|-
| HW 2a || October 24 || October 27 || October 27 || October 27
|-
| HW 2b №1-7 || November 30 || November 20 || November 20 || November 20
|-
| HW 2b №8-14 || December 14 || December 4 || December 4 || December 4
|-
| HW 3 №1-3 || December 22 || December 22 || December 22 || December 24
|-
| HW 3 №4-12 || February 10 || February 10 || February 10 || February 10
|}

'''Each deadline is set by the respective group's instructor.'''

== Grading system ==
For the final grading, we compute the following values:

Module 1 grade = round ((50*HW1 + 50*Exam1)/100);

basic = (21*Exam1 + 21*Colloq + 28*HW + 30*Exam2)/100;

adv = (30*Exam1* + Bonus + 35*HW* + 35*Exam2*)/100;

Final grade = round(min(10, 8 * basic + 2 * adv)).

The final grade is rounded half up to an integer. All the other values are reported with the greatest precision available.

== Recommended reading ==
''Please notice that '''The Book''' for our Course does not exist. The latter is based on many sources.''

# Anderson J. A., Discrete Mathematics With Combinatorics. Prentice Hall, 2003.
# Biggs N. L., Discrete mathematics. 2nd ed., New York; Oxford: Oxford University Press, 2004.
# Gavrilov G. P., Sapozhenko A. A. Problems and Exercises in Discrete Mathematics. Kluwer Texts in the Mathematical Sciences 14. Springer, 1996.
# [http://courses.csail.mit.edu/6.042/spring17/mcs.pdf Lehman E., Thomson Leighton F., Meyer A. R. Mathematics for Computer Science, 2017.]
# [http://www.cs.elte.hu/~lovasz/dmbook.ps Lovasz L., Vesztergombi K. Discrete Mathematics. Lecture Notes; Yale University, 1999.]
# Melnikov O., Sarvanov V., Tyshkevich R., Yemelichev V., Zverovich I. Exercises in Graph Theory. Kluwer Texts in the Mathematical Sciences 19. Springer, 1998.
# Rosen K. H. Discrete Mathematics and Its Applications. McGraw-Hill, 1999.
# Stein C., Drysdale R. L., Bogart K. Discrete mathematics for computer scientists. Addison-Wesley, 2010.
# Vinogradov I. M. Elements of number theory. Dover, 1954.

=== In Russian ===
''If you understand Russian (by any chance), you will probably benefit from reading the following books.''

# Виноградов И. М. Основы теории чисел. 9-е изд., М.: Наука, 1981.
# [http://rubtsov.su/public/DM-HSE-Draft.pdf Вялый М., Подольский В., Рубцов А., Шварц Д., Шень А. Лекции по дискретной математике.]
# Гаврилов Г. П., Сапоженко А. А. Задачи и упражнения по дискретной математике. 3-е изд., М.: ФИЗМАТЛИТ, 2004.
# [https://drive.google.com/file/d/1RM6KX_reBFwUXesWGUEu0sFn2NCaBgvz/view?usp=sharing Дашков Е. В. Введение в математическую логику. Множества и отношения. М.: МФТИ, 2019.]
# Зубков А. М., Севастьянов Б. А., Чистяков В. П. Сборник задач по теории вероятностей. 2-е изд., М.: Наука, 1989.
# Мельников О. И. Теория графов в занимательных задачах. 5-е изд., М.: Книжный дом "ЛИБРОКОМ", 2013.
# [http://www.mccme.ru/free-books/shen/shen-induction.pdf Шень А., Математическая индукция. 5-е изд, М.: МЦНМО, 2016.]

Adaptation course in Discrete Math (факультатив)

2023-01-31T17:30:21Z

Nasta.trofimova:

== General Information ==
The main goal of the Discrete Mathematics Adaptation Course is to help students keep up with the course curriculum by discussing the most important and challenging topics in detail. The second very important goal of the course is to teach students to work competently with mathematical definitions and proofs, correctly logically build solutions to problems and prove statements. The topics of the course are coordinated with the "basic" course of the DSBA and SE program, but its study will also be useful for the direction of AMI. The approximate order of topics is sets and logic, functions and relations, the beginning of number theory, combinatorics, graphs, the foundations of probability theory, generating functions.

== Schedule ==

The classes are organised on Saturdays at 16:20.

== Course materials ==

[https://t.me/+113aheknlsxmYzVi Chat in Telegram]

'''First semester'''

{| class="wikitable"
|-
! Date !! Topic !! Problem Set !! Class note !! Video
|-
|| 21.09.22 || Statements, connectives, quantifiers || [https://drive.google.com/file/d/1kbtRp8c79zE2AspfVb4ZfGZLJRy9Z5j2/view?usp=drivesdk Problem Set 1]|| - ||
|-
|| 28.09.22 || Validity of statements, types of proof|| [https://drive.google.com/file/d/1Q2OlmVzXf4P0ocd3eBet4ktoJ1h1DZyn/view?usp=sharing Problem Set 2] || [https://drive.google.com/file/d/11pdljFmpW57o5OqBH40YwioTW_Ebs_gK/view?usp=sharing Solutions] || -
|-
|| 7.10.22 || Three types of mathematical induction || [https://drive.google.com/file/d/14h2jy4W7KgxBffxE8TKh_13rSG3Wy_Ll/view?usp=sharing Problem Set 3] ||[https://drive.google.com/file/d/1yFnH5QBNxM-1ajoA5y7w9wV_31XeBwWp/view?usp=sharing Solutions] || [https://youtu.be/nljNhVjlnXg Video 3]
|-
|| 14.10.22 || Proofs with induction || [https://drive.google.com/file/d/13vsHkpBV8riwyKOTCh1v1heuAqf0L9nK/view?usp=sharing Problem Set 4] ||[https://drive.google.com/file/d/1PZD-YWikatG9jCbcc1r_Eo5t0y-kdcpj/view?usp=sharing Solutions] || -
|-
|| 21.10.22 || Divisibility. Calculation of remainders. Direct proofs. || [https://drive.google.com/file/d/1rHfC1WRv4IB8kNRMynVWv0C26PXGi137/view?usp=sharing Problem Set 5] ||[https://drive.google.com/file/d/1CvWAD5pDmMB8JFWSFNxOrrT7-Jfp_0Wd/view?usp=sharing Solutions] ||
[https://youtu.be/-OIYkDOkLyk Video 5]
|-
|| 11.11.22 || Great commod divider, the main thorem of arithmetic, direct proofs. || [https://drive.google.com/file/d/1CrF9W2rXFiTMKFoxZO-PJDmhYAx6Ql84/view?usp=share_link Problem Set 6] ||[https://drive.google.com/file/d/1TWSgbLrRtZWRrbneebExE4BPoDzLU4-b/view?usp=share_link Solutions] ||
[https://youtu.be/_2RRlq21gqM Video 6]
|-
|| 19.11.22 || Fermat's Little theorem, inverse elements in groups $\mathbb{Z}_p$, congruences. || [https://drive.google.com/file/d/1IF6rqwLN0Bq8n07mxQ3CAmoMfWplJ3OR/view?usp=share_link Problem Set 7] ||[https://drive.google.com/file/d/1FZevxpUjcPrrtCbxHn-HRh1odDamJqlq/view?usp=share_link Solutions] ||
[https://youtu.be/peuzIDzh1bE Video 7]
|-
|| 25.11.22 || Fermat's Little theorem, inverse elements in groups $\mathbb{Z}_p$, congruences. || [https://drive.google.com/file/d/1CYGJ7B5d426ChuZBozzsLKwMVZeVPgQJ/view?usp=share_link Problem Set 8] ||[https://drive.google.com/file/d/1_PCu2dDhIgN7uE1ijLGLH1USapPskGWH/view?usp=share_link Solutions] ||
[ -]
|-
|| 2.12.22 || Application of Euler's theorem and Euclidean algorithm, cryptography || [https://drive.google.com/file/d/1Oq3grvUbG-yBBbrHqhK_4Ylz4Io-D1Lw/view?usp=share_link Problem Set 9] ||[https://drive.google.com/file/d/1BFDh6-6KVmb65w7qDEQprP6BYUMUW6AQ/view?usp=share_link Solutions] ||
[https://youtu.be/HPpI7VpHrWY Video 9]
|-
|| 9.12.22 || Sets, direct proofs of set identities || [https://drive.google.com/file/d/1C6I_cviJwznCLZ5BKtxUtlUrjpp4Kegw/view?usp=share_link Problem Set 10] ||[https://drive.google.com/file/d/179jjcjhdU0LschqhPEFMPJylunwRiofA/view?usp=share_link Solutions] || [https://youtu.be/7Gk3JxRpeWU Video 10]
|-
|| 16.12.22 || Operations with sets, cardinality and power set || [https://drive.google.com/file/d/1D9A7QTq-7dPN8Xz_jQhsYIknX8cukhZD/view?usp=share_link Problem Set 11] ||[https://drive.google.com/file/d/1B1snvrzqMgUMDEEQqOHVzomfWVwf2t07/view?usp=share_link Solutions] ||
[https://youtu.be/TK4BNYF4vEU Video 11]
|-
|| 21.01.23 || Sets once again, proofs that a statement is wrong|| [https://drive.google.com/file/d/15hSnMr1jVCSJ6boGK5KuEUldlx3-8Pvv/view?usp=share_link Problem Set 12] ||[https://drive.google.com/file/d/1PDsR6DjO_K9-XfoqprA0UsYWh-2fSb8T/view?usp=share_link Solutions] ||
[https://youtu.be/2J8qDgwpivU Video 12]
|-
|| 28.01.23 || Relatins, main definitions || [https://drive.google.com/file/d/1IJAqHsXCQaSFlzZFaH5TpfnNdibKAzen/view?usp=share_link Problem Set 13] ||[https://drive.google.com/file/d/188uRSv9ALwy4IsPreEbS8J61PDMw9uVw/view?usp=share_link Solutions] ||
[ Video 13]
|}

[https://drive.google.com/file/d/163PgGw33FTt3PUVdVBYCjIHluftfZVol/view?usp=sharing Last year retake]

[https://drive.google.com/file/d/1bljTOb3x0kvYy7cslTOC4B3StYOHi3CX/view Last year test 1]

== Homeworks ==
[https://forms.gle/TAgL2eUkhSyhZKLD9 Homework 1 (Logics)], Deadline 31st October

[https://forms.gle/pVA1a8xbeP54RqAQ7 Homework 2 (Induction)], Deadline 31st November, better to complete before the November Test

Hint🦉 in Problem 5: Do not try to prove P(n) out of P(n-1). Assume that P(1), P(2), ...P(n-1) are all true. For proving P(n) say: lets find the biggest Fibonacci number F_i<n. Then, n = F_i + k. For the k apply your assumption😉😉

[https://drive.google.com/file/d/1k8SKmN9J_DdSs8ibP_9b52n8LxiPf_8U/view?usp=share_link Homework 3]: write down solutions to exam 1 in a perfect manner (like you you are going to print a book of your solutions), Deadline 25th November. You can pass them written or orally on Fridays evenings. Do it if you want to have MAX in the retake(if so happened) and in the exam in the end of the course.

[https://forms.gle/DQUEyuh1vuXgdtr6A Homework 4 (Number theory)], Deadline with bonus 29th December

==Semester 1 ==

[https://docs.google.com/spreadsheets/d/1YHhkk8TCm_qPF0tXyGe7rc-DzubrgSESZUoW6fHMLZA/edit?usp=sharing Current grades and comments]

== References ==

1. [http://discrete.openmathbooks.org/dmoi3.html Discrete Mathematics (An Open Introduction) by Oscar Levin,] p. 197 Logics. Many simple problems with solution to feel the topic.

2. [https://drive.google.com/file/d/1mmNLLQ0--EDihGNRKwSyXLOA1KL7A0lD/view?usp=sharing Lecture notes by Evgeny Dashkov]

PLUS: there is a [https://youtube.com/playlist?list=PLEwK9wdS5g0pk-1YWDc3hezRt_rNpQDf8 folder with records on wikipage ]

3. [http://www.mccme.ru/free-books/shen/shen-induction.pdf Шень А., Математическая индукция. 5-е изд, М.: МЦНМО, 2016.] Many problems to work with three different versions of induction.

== Grading and Results ==

'''Final grade''' = Average(HWs)+ Bonus points

Bonus point number is between 0 to 20. Such points may be given for a variety of auxiliary activities.

Adaptation course in Discrete Math (факультатив)

2023-01-31T17:28:10Z

Nasta.trofimova:

== General Information ==
The main goal of the Discrete Mathematics Adaptation Course is to help students keep up with the course curriculum by discussing the most important and challenging topics in detail. The second very important goal of the course is to teach students to work competently with mathematical definitions and proofs, correctly logically build solutions to problems and prove statements. The topics of the course are coordinated with the "basic" course of the DSBA and SE program, but its study will also be useful for the direction of AMI. The approximate order of topics is sets and logic, functions and relations, the beginning of number theory, combinatorics, graphs, the foundations of probability theory, generating functions.

== Schedule ==

The classes are organised on Saturdays at 16:20.

== Course materials ==

[https://t.me/+113aheknlsxmYzVi Chat in Telegram]

'''First semester'''

{| class="wikitable"
|-
! Date !! Topic !! Problem Set !! Class note !! Video
|-
|| 21.09.22 || Statements, connectives, quantifiers || [https://drive.google.com/file/d/1kbtRp8c79zE2AspfVb4ZfGZLJRy9Z5j2/view?usp=drivesdk Problem Set 1]|| - ||
|-
|| 28.09.22 || Validity of statements, types of proof|| [https://drive.google.com/file/d/1Q2OlmVzXf4P0ocd3eBet4ktoJ1h1DZyn/view?usp=sharing Problem Set 2] || [https://drive.google.com/file/d/11pdljFmpW57o5OqBH40YwioTW_Ebs_gK/view?usp=sharing Solutions] || -
|-
|| 7.10.22 || Three types of mathematical induction || [https://drive.google.com/file/d/14h2jy4W7KgxBffxE8TKh_13rSG3Wy_Ll/view?usp=sharing Problem Set 3] ||[https://drive.google.com/file/d/1yFnH5QBNxM-1ajoA5y7w9wV_31XeBwWp/view?usp=sharing Solutions] || [https://youtu.be/nljNhVjlnXg Video 3]
|-
|| 14.10.22 || Proofs with induction || [https://drive.google.com/file/d/13vsHkpBV8riwyKOTCh1v1heuAqf0L9nK/view?usp=sharing Problem Set 4] ||[https://drive.google.com/file/d/1PZD-YWikatG9jCbcc1r_Eo5t0y-kdcpj/view?usp=sharing Solutions] || -
|-
|| 21.10.22 || Divisibility. Calculation of remainders. Direct proofs. || [https://drive.google.com/file/d/1rHfC1WRv4IB8kNRMynVWv0C26PXGi137/view?usp=sharing Problem Set 5] ||[https://drive.google.com/file/d/1CvWAD5pDmMB8JFWSFNxOrrT7-Jfp_0Wd/view?usp=sharing Solutions] ||
[https://youtu.be/-OIYkDOkLyk Video 5]
|-
|| 11.11.22 || Great commod divider, the main thorem of arithmetic, direct proofs. || [https://drive.google.com/file/d/1CrF9W2rXFiTMKFoxZO-PJDmhYAx6Ql84/view?usp=share_link Problem Set 6] ||[https://drive.google.com/file/d/1TWSgbLrRtZWRrbneebExE4BPoDzLU4-b/view?usp=share_link Solutions] ||
[https://youtu.be/_2RRlq21gqM Video 6]
|-
|| 19.11.22 || Fermat's Little theorem, inverse elements in groups $\mathbb{Z}_p$, congruences. || [https://drive.google.com/file/d/1IF6rqwLN0Bq8n07mxQ3CAmoMfWplJ3OR/view?usp=share_link Problem Set 7] ||[https://drive.google.com/file/d/1FZevxpUjcPrrtCbxHn-HRh1odDamJqlq/view?usp=share_link Solutions] ||
[https://youtu.be/peuzIDzh1bE Video 7]
|-
|| 25.11.22 || Fermat's Little theorem, inverse elements in groups $\mathbb{Z}_p$, congruences. || [https://drive.google.com/file/d/1CYGJ7B5d426ChuZBozzsLKwMVZeVPgQJ/view?usp=share_link Problem Set 8] ||[https://drive.google.com/file/d/1_PCu2dDhIgN7uE1ijLGLH1USapPskGWH/view?usp=share_link Solutions] ||
[ -]
|-
|| 2.12.22 || Application of Euler's theorem and Euclidean algorithm, cryptography || [https://drive.google.com/file/d/1Oq3grvUbG-yBBbrHqhK_4Ylz4Io-D1Lw/view?usp=share_link Problem Set 9] ||[https://drive.google.com/file/d/1BFDh6-6KVmb65w7qDEQprP6BYUMUW6AQ/view?usp=share_link Solutions] ||
[https://youtu.be/HPpI7VpHrWY Video 9]
|-
|| 9.12.22 || Sets, direct proofs of set identities || [https://drive.google.com/file/d/1C6I_cviJwznCLZ5BKtxUtlUrjpp4Kegw/view?usp=share_link Problem Set 10] ||[https://drive.google.com/file/d/179jjcjhdU0LschqhPEFMPJylunwRiofA/view?usp=share_link Solutions] || [https://youtu.be/7Gk3JxRpeWU Video 10]
|-
|| 16.12.22 || Operations with sets, cardinality and power set || [https://drive.google.com/file/d/1D9A7QTq-7dPN8Xz_jQhsYIknX8cukhZD/view?usp=share_link Problem Set 11] ||[https://drive.google.com/file/d/1B1snvrzqMgUMDEEQqOHVzomfWVwf2t07/view?usp=share_link Solutions] ||
[https://youtu.be/TK4BNYF4vEU Video 11]
|}

[https://drive.google.com/file/d/163PgGw33FTt3PUVdVBYCjIHluftfZVol/view?usp=sharing Last year retake]

[https://drive.google.com/file/d/1bljTOb3x0kvYy7cslTOC4B3StYOHi3CX/view Last year test 1]

== Homeworks ==
[https://forms.gle/TAgL2eUkhSyhZKLD9 Homework 1 (Logics)], Deadline 31st October

[https://forms.gle/pVA1a8xbeP54RqAQ7 Homework 2 (Induction)], Deadline 31st November, better to complete before the November Test

Hint🦉 in Problem 5: Do not try to prove P(n) out of P(n-1). Assume that P(1), P(2), ...P(n-1) are all true. For proving P(n) say: lets find the biggest Fibonacci number F_i<n. Then, n = F_i + k. For the k apply your assumption😉😉

[https://drive.google.com/file/d/1k8SKmN9J_DdSs8ibP_9b52n8LxiPf_8U/view?usp=share_link Homework 3]: write down solutions to exam 1 in a perfect manner (like you you are going to print a book of your solutions), Deadline 25th November. You can pass them written or orally on Fridays evenings. Do it if you want to have MAX in the retake(if so happened) and in the exam in the end of the course.

[https://forms.gle/DQUEyuh1vuXgdtr6A Homework 4 (Number theory)], Deadline with bonus 29th December

==Semester 1 ==

[https://docs.google.com/spreadsheets/d/1YHhkk8TCm_qPF0tXyGe7rc-DzubrgSESZUoW6fHMLZA/edit?usp=sharing Current grades and comments]

== References ==

1. [http://discrete.openmathbooks.org/dmoi3.html Discrete Mathematics (An Open Introduction) by Oscar Levin,] p. 197 Logics. Many simple problems with solution to feel the topic.

2. [https://drive.google.com/file/d/1mmNLLQ0--EDihGNRKwSyXLOA1KL7A0lD/view?usp=sharing Lecture notes by Evgeny Dashkov]

PLUS: there is a [https://youtube.com/playlist?list=PLEwK9wdS5g0pk-1YWDc3hezRt_rNpQDf8 folder with records on wikipage ]

3. [http://www.mccme.ru/free-books/shen/shen-induction.pdf Шень А., Математическая индукция. 5-е изд, М.: МЦНМО, 2016.] Many problems to work with three different versions of induction.

== Grading and Results ==

'''Final grade''' = Average(HWs)+ Bonus points

Bonus point number is between 0 to 20. Such points may be given for a variety of auxiliary activities.

Adaptation course in Discrete Math (факультатив)

2023-01-31T17:18:50Z

Nasta.trofimova: /* Course materials */

== General Information ==
The main goal of the Discrete Mathematics Adaptation Course is to help students keep up with the course curriculum by discussing the most important and challenging topics in detail. The second very important goal of the course is to teach students to work competently with mathematical definitions and proofs, correctly logically build solutions to problems and prove statements. The topics of the course are coordinated with the "basic" course of the DSBA and SE program, but its study will also be useful for the direction of AMI. The approximate order of topics is sets and logic, functions and relations, the beginning of number theory, combinatorics, graphs, the foundations of probability theory, generating functions.

== Schedule ==

The classes are organised on Saturdays at 16:20.

== Course materials ==

[https://t.me/+113aheknlsxmYzVi Chat in Telegram]

'''First semester'''

{| class="wikitable"
|-
! Date !! Topic !! Problem Set !! Class note !! Video
|-
|| 21.09.22 || Statements, connectives, quantifiers || [https://drive.google.com/file/d/1kbtRp8c79zE2AspfVb4ZfGZLJRy9Z5j2/view?usp=drivesdk Problem Set 1]|| - ||
|-
|| 28.09.22 || Validity of statements, types of proof|| [https://drive.google.com/file/d/1Q2OlmVzXf4P0ocd3eBet4ktoJ1h1DZyn/view?usp=sharing Problem Set 2] || [https://drive.google.com/file/d/11pdljFmpW57o5OqBH40YwioTW_Ebs_gK/view?usp=sharing Solutions] || -
|-
|| 7.10.22 || Three types of mathematical induction || [https://drive.google.com/file/d/14h2jy4W7KgxBffxE8TKh_13rSG3Wy_Ll/view?usp=sharing Problem Set 3] ||[https://drive.google.com/file/d/1yFnH5QBNxM-1ajoA5y7w9wV_31XeBwWp/view?usp=sharing Solutions] || [https://youtu.be/nljNhVjlnXg Video 3]
|-
|| 14.10.22 || Proofs with induction || [https://drive.google.com/file/d/13vsHkpBV8riwyKOTCh1v1heuAqf0L9nK/view?usp=sharing Problem Set 4] ||[https://drive.google.com/file/d/1PZD-YWikatG9jCbcc1r_Eo5t0y-kdcpj/view?usp=sharing Solutions] || -
|-
|| 21.10.22 || Divisibility. Calculation of remainders. Direct proofs. || [https://drive.google.com/file/d/1rHfC1WRv4IB8kNRMynVWv0C26PXGi137/view?usp=sharing Problem Set 5] ||[https://drive.google.com/file/d/1CvWAD5pDmMB8JFWSFNxOrrT7-Jfp_0Wd/view?usp=sharing Solutions] ||
[https://youtu.be/-OIYkDOkLyk Video 5]
|-
|| 11.11.22 || Great commod divider, the main thorem of arithmetic, direct proofs. || [https://drive.google.com/file/d/1CrF9W2rXFiTMKFoxZO-PJDmhYAx6Ql84/view?usp=share_link Problem Set 6] ||[https://drive.google.com/file/d/1TWSgbLrRtZWRrbneebExE4BPoDzLU4-b/view?usp=share_link Solutions] ||
[https://youtu.be/_2RRlq21gqM Video 6]
|-
|| 19.11.22 || Fermat's Little theorem, inverse elements in groups $\mathbb{Z}_p$, congruences. || [https://drive.google.com/file/d/1IF6rqwLN0Bq8n07mxQ3CAmoMfWplJ3OR/view?usp=share_link Problem Set 7] ||[https://drive.google.com/file/d/1FZevxpUjcPrrtCbxHn-HRh1odDamJqlq/view?usp=share_link Solutions] ||
[https://youtu.be/peuzIDzh1bE Video 7]
|-
|| 25.11.22 || Fermat's Little theorem, inverse elements in groups $\mathbb{Z}_p$, congruences. || [https://drive.google.com/file/d/1CYGJ7B5d426ChuZBozzsLKwMVZeVPgQJ/view?usp=share_link Problem Set 8] ||[https://drive.google.com/file/d/1_PCu2dDhIgN7uE1ijLGLH1USapPskGWH/view?usp=share_link Solutions] ||
[ -]
|-
|| 2.12.22 || Application of Euler's theorem and Euclidean algorithm, cryptography || [https://drive.google.com/file/d/1Oq3grvUbG-yBBbrHqhK_4Ylz4Io-D1Lw/view?usp=share_link Problem Set 9] ||[https://drive.google.com/file/d/1BFDh6-6KVmb65w7qDEQprP6BYUMUW6AQ/view?usp=share_link Solutions] ||
[https://youtu.be/HPpI7VpHrWY Video 9]
|-
|| 9.12.22 || Sets, direct proofs of set identities || [https://drive.google.com/file/d/1C6I_cviJwznCLZ5BKtxUtlUrjpp4Kegw/view?usp=share_link Problem Set 10] ||[https://drive.google.com/file/d/179jjcjhdU0LschqhPEFMPJylunwRiofA/view?usp=share_link Solutions] || [https://youtu.be/7Gk3JxRpeWU Video 10]
|-
|| 16.12.22 || Operations with sets, cardinality and power set || [https://drive.google.com/file/d/1D9A7QTq-7dPN8Xz_jQhsYIknX8cukhZD/view?usp=share_link Problem Set 11] ||[https://drive.google.com/file/d/1B1snvrzqMgUMDEEQqOHVzomfWVwf2t07/view?usp=share_link Solutions] ||
[https://youtu.be/TK4BNYF4vEU Video 11]
|-
|| 21.01.23 || Sets once again, proofs that a statement is wrong|| [https://drive.google.com/file/d/15hSnMr1jVCSJ6boGK5KuEUldlx3-8Pvv/view?usp=share_link Problem Set 12] ||[https://drive.google.com/file/d/1PDsR6DjO_K9-XfoqprA0UsYWh-2fSb8T/view?usp=share_link Solutions] ||
[https://youtu.be/2J8qDgwpivU Video 12]
|-
|| 28.01.23 || Relatins, main definitions || [https://drive.google.com/file/d/1IJAqHsXCQaSFlzZFaH5TpfnNdibKAzen/view?usp=share_link Problem Set 13] ||[https://drive.google.com/file/d/188uRSv9ALwy4IsPreEbS8J61PDMw9uVw/view?usp=share_link Solutions] ||
[ Video 13]
|}

[https://drive.google.com/file/d/163PgGw33FTt3PUVdVBYCjIHluftfZVol/view?usp=sharing Last year retake]

[https://drive.google.com/file/d/1bljTOb3x0kvYy7cslTOC4B3StYOHi3CX/view Last year test 1]

== Homeworks ==
[https://forms.gle/TAgL2eUkhSyhZKLD9 Homework 1 (Logics)], Deadline 31st October

[https://forms.gle/pVA1a8xbeP54RqAQ7 Homework 2 (Induction)], Deadline 31st November, better to complete before the November Test

Hint🦉 in Problem 5: Do not try to prove P(n) out of P(n-1). Assume that P(1), P(2), ...P(n-1) are all true. For proving P(n) say: lets find the biggest Fibonacci number F_i<n. Then, n = F_i + k. For the k apply your assumption😉😉

[https://drive.google.com/file/d/1k8SKmN9J_DdSs8ibP_9b52n8LxiPf_8U/view?usp=share_link Homework 3]: write down solutions to exam 1 in a perfect manner (like you you are going to print a book of your solutions), Deadline 25th November. You can pass them written or orally on Fridays evenings. Do it if you want to have MAX in the retake(if so happened) and in the exam in the end of the course.

[https://forms.gle/DQUEyuh1vuXgdtr6A Homework 4 (Number theory)], Deadline with bonus 29th December

==Semester 1 ==

[https://docs.google.com/spreadsheets/d/1YHhkk8TCm_qPF0tXyGe7rc-DzubrgSESZUoW6fHMLZA/edit?usp=sharing Current grades and comments]

== References ==

1. [http://discrete.openmathbooks.org/dmoi3.html Discrete Mathematics (An Open Introduction) by Oscar Levin,] p. 197 Logics. Many simple problems with solution to feel the topic.

2. [https://drive.google.com/file/d/1mmNLLQ0--EDihGNRKwSyXLOA1KL7A0lD/view?usp=sharing Lecture notes by Evgeny Dashkov]

PLUS: there is a [https://youtube.com/playlist?list=PLEwK9wdS5g0pk-1YWDc3hezRt_rNpQDf8 folder with records on wikipage ]

3. [http://www.mccme.ru/free-books/shen/shen-induction.pdf Шень А., Математическая индукция. 5-е изд, М.: МЦНМО, 2016.] Many problems to work with three different versions of induction.

== Grading and Results ==

'''Final grade''' = Average(HWs)+ Bonus points

Bonus point number is between 0 to 20. Such points may be given for a variety of auxiliary activities.

Adaptation course in Discrete Math (факультатив)

2023-01-31T17:18:17Z

Nasta.trofimova:

== General Information ==
The main goal of the Discrete Mathematics Adaptation Course is to help students keep up with the course curriculum by discussing the most important and challenging topics in detail. The second very important goal of the course is to teach students to work competently with mathematical definitions and proofs, correctly logically build solutions to problems and prove statements. The topics of the course are coordinated with the "basic" course of the DSBA and SE program, but its study will also be useful for the direction of AMI. The approximate order of topics is sets and logic, functions and relations, the beginning of number theory, combinatorics, graphs, the foundations of probability theory, generating functions.

== Schedule ==

The classes are organised on Saturdays at 16:20.

== Course materials ==

[https://t.me/+113aheknlsxmYzVi Chat in Telegram]

'''First semester'''

{| class="wikitable"
|-
! Date !! Topic !! Problem Set !! Class note !! Video
|-
|| 21.09.22 || Statements, connectives, quantifiers || [https://drive.google.com/file/d/1kbtRp8c79zE2AspfVb4ZfGZLJRy9Z5j2/view?usp=drivesdk Problem Set 1]|| - ||
|-
|| 28.09.22 || Validity of statements, types of proof|| [https://drive.google.com/file/d/1Q2OlmVzXf4P0ocd3eBet4ktoJ1h1DZyn/view?usp=sharing Problem Set 2] || [https://drive.google.com/file/d/11pdljFmpW57o5OqBH40YwioTW_Ebs_gK/view?usp=sharing Solutions] || -
|-
|| 7.10.22 || Three types of mathematical induction || [https://drive.google.com/file/d/14h2jy4W7KgxBffxE8TKh_13rSG3Wy_Ll/view?usp=sharing Problem Set 3] ||[https://drive.google.com/file/d/1yFnH5QBNxM-1ajoA5y7w9wV_31XeBwWp/view?usp=sharing Solutions] || [https://youtu.be/nljNhVjlnXg Video 3]
|-
|| 14.10.22 || Proofs with induction || [https://drive.google.com/file/d/13vsHkpBV8riwyKOTCh1v1heuAqf0L9nK/view?usp=sharing Problem Set 4] ||[https://drive.google.com/file/d/1PZD-YWikatG9jCbcc1r_Eo5t0y-kdcpj/view?usp=sharing Solutions] || -
|-
|| 21.10.22 || Divisibility. Calculation of remainders. Direct proofs. || [https://drive.google.com/file/d/1rHfC1WRv4IB8kNRMynVWv0C26PXGi137/view?usp=sharing Problem Set 5] ||[https://drive.google.com/file/d/1CvWAD5pDmMB8JFWSFNxOrrT7-Jfp_0Wd/view?usp=sharing Solutions] ||
[https://youtu.be/-OIYkDOkLyk Video 5]
|-
|| 11.11.22 || Great commod divider, the main thorem of arithmetic, direct proofs. || [https://drive.google.com/file/d/1CrF9W2rXFiTMKFoxZO-PJDmhYAx6Ql84/view?usp=share_link Problem Set 6] ||[https://drive.google.com/file/d/1TWSgbLrRtZWRrbneebExE4BPoDzLU4-b/view?usp=share_link Solutions] ||
[https://youtu.be/_2RRlq21gqM Video 6]
|-
|| 19.11.22 || Fermat's Little theorem, inverse elements in groups $\mathbb{Z}_p$, congruences. || [https://drive.google.com/file/d/1IF6rqwLN0Bq8n07mxQ3CAmoMfWplJ3OR/view?usp=share_link Problem Set 7] ||[https://drive.google.com/file/d/1FZevxpUjcPrrtCbxHn-HRh1odDamJqlq/view?usp=share_link Solutions] ||
[https://youtu.be/peuzIDzh1bE Video 7]
|-
|| 25.11.22 || Fermat's Little theorem, inverse elements in groups $\mathbb{Z}_p$, congruences. || [https://drive.google.com/file/d/1CYGJ7B5d426ChuZBozzsLKwMVZeVPgQJ/view?usp=share_link Problem Set 8] ||[https://drive.google.com/file/d/1_PCu2dDhIgN7uE1ijLGLH1USapPskGWH/view?usp=share_link Solutions] ||
[ -]
|-
|| 2.12.22 || Application of Euler's theorem and Euclidean algorithm, cryptography || [https://drive.google.com/file/d/1Oq3grvUbG-yBBbrHqhK_4Ylz4Io-D1Lw/view?usp=share_link Problem Set 9] ||[https://drive.google.com/file/d/1BFDh6-6KVmb65w7qDEQprP6BYUMUW6AQ/view?usp=share_link Solutions] ||
[https://youtu.be/HPpI7VpHrWY Video 9]
|-
|| 9.12.22 || Sets, direct proofs of set identities || [https://drive.google.com/file/d/1C6I_cviJwznCLZ5BKtxUtlUrjpp4Kegw/view?usp=share_link Problem Set 10] ||[https://drive.google.com/file/d/179jjcjhdU0LschqhPEFMPJylunwRiofA/view?usp=share_link Solutions] || [https://youtu.be/7Gk3JxRpeWU Video 10]
|-
|| 16.12.22 || Operations with sets, cardinality and power set || [https://drive.google.com/file/d/1D9A7QTq-7dPN8Xz_jQhsYIknX8cukhZD/view?usp=share_link Problem Set 11] ||[https://drive.google.com/file/d/1B1snvrzqMgUMDEEQqOHVzomfWVwf2t07/view?usp=share_link Solutions] ||
[https://youtu.be/TK4BNYF4vEU Video 11]
|-
|| 21.01.23 || Sets once again, proofs that a statement is wrong|| [https://drive.google.com/file/d/15hSnMr1jVCSJ6boGK5KuEUldlx3-8Pvv/view?usp=share_link Problem Set 12] ||[https://drive.google.com/file/d/1PDsR6DjO_K9-XfoqprA0UsYWh-2fSb8T/view?usp=share_link Solutions] ||
[https://youtu.be/2J8qDgwpivU Video 12]
|-
|| 28.01.23 || Relatins, main definitions|| [https://drive.google.com/file/d/1IJAqHsXCQaSFlzZFaH5TpfnNdibKAzen/view?usp=share_link
Problem Set 13] ||[https://drive.google.com/file/d/188uRSv9ALwy4IsPreEbS8J61PDMw9uVw/view?usp=share_link Solutions] ||
[ Video 13]
|}

[https://drive.google.com/file/d/163PgGw33FTt3PUVdVBYCjIHluftfZVol/view?usp=sharing Last year retake]

[https://drive.google.com/file/d/1bljTOb3x0kvYy7cslTOC4B3StYOHi3CX/view Last year test 1]

== Homeworks ==
[https://forms.gle/TAgL2eUkhSyhZKLD9 Homework 1 (Logics)], Deadline 31st October

[https://forms.gle/pVA1a8xbeP54RqAQ7 Homework 2 (Induction)], Deadline 31st November, better to complete before the November Test

Hint🦉 in Problem 5: Do not try to prove P(n) out of P(n-1). Assume that P(1), P(2), ...P(n-1) are all true. For proving P(n) say: lets find the biggest Fibonacci number F_i<n. Then, n = F_i + k. For the k apply your assumption😉😉

[https://drive.google.com/file/d/1k8SKmN9J_DdSs8ibP_9b52n8LxiPf_8U/view?usp=share_link Homework 3]: write down solutions to exam 1 in a perfect manner (like you you are going to print a book of your solutions), Deadline 25th November. You can pass them written or orally on Fridays evenings. Do it if you want to have MAX in the retake(if so happened) and in the exam in the end of the course.

[https://forms.gle/DQUEyuh1vuXgdtr6A Homework 4 (Number theory)], Deadline with bonus 29th December

==Semester 1 ==

[https://docs.google.com/spreadsheets/d/1YHhkk8TCm_qPF0tXyGe7rc-DzubrgSESZUoW6fHMLZA/edit?usp=sharing Current grades and comments]

== References ==

1. [http://discrete.openmathbooks.org/dmoi3.html Discrete Mathematics (An Open Introduction) by Oscar Levin,] p. 197 Logics. Many simple problems with solution to feel the topic.

2. [https://drive.google.com/file/d/1mmNLLQ0--EDihGNRKwSyXLOA1KL7A0lD/view?usp=sharing Lecture notes by Evgeny Dashkov]

PLUS: there is a [https://youtube.com/playlist?list=PLEwK9wdS5g0pk-1YWDc3hezRt_rNpQDf8 folder with records on wikipage ]

3. [http://www.mccme.ru/free-books/shen/shen-induction.pdf Шень А., Математическая индукция. 5-е изд, М.: МЦНМО, 2016.] Many problems to work with three different versions of induction.

== Grading and Results ==

'''Final grade''' = Average(HWs)+ Bonus points

Bonus point number is between 0 to 20. Such points may be given for a variety of auxiliary activities.

Adaptation course in Discrete Math (факультатив)

2023-01-31T17:17:55Z

Nasta.trofimova: /* Course materials */

== General Information ==
The main goal of the Discrete Mathematics Adaptation Course is to help students keep up with the course curriculum by discussing the most important and challenging topics in detail. The second very important goal of the course is to teach students to work competently with mathematical definitions and proofs, correctly logically build solutions to problems and prove statements. The topics of the course are coordinated with the "basic" course of the DSBA and SE program, but its study will also be useful for the direction of AMI. The approximate order of topics is sets and logic, functions and relations, the beginning of number theory, combinatorics, graphs, the foundations of probability theory, generating functions.

== Schedule ==

The classes are organised on Saturdays at 16:20.

== Course materials ==

[https://t.me/+113aheknlsxmYzVi Chat in Telegram]

'''First semester'''

{| class="wikitable"
|-
! Date !! Topic !! Problem Set !! Class note !! Video
|-
|| 21.09.22 || Statements, connectives, quantifiers || [https://drive.google.com/file/d/1kbtRp8c79zE2AspfVb4ZfGZLJRy9Z5j2/view?usp=drivesdk Problem Set 1]|| - ||
|-
|| 28.09.22 || Validity of statements, types of proof|| [https://drive.google.com/file/d/1Q2OlmVzXf4P0ocd3eBet4ktoJ1h1DZyn/view?usp=sharing Problem Set 2] || [https://drive.google.com/file/d/11pdljFmpW57o5OqBH40YwioTW_Ebs_gK/view?usp=sharing Solutions] || -
|-
|| 7.10.22 || Three types of mathematical induction || [https://drive.google.com/file/d/14h2jy4W7KgxBffxE8TKh_13rSG3Wy_Ll/view?usp=sharing Problem Set 3] ||[https://drive.google.com/file/d/1yFnH5QBNxM-1ajoA5y7w9wV_31XeBwWp/view?usp=sharing Solutions] || [https://youtu.be/nljNhVjlnXg Video 3]
|-
|| 14.10.22 || Proofs with induction || [https://drive.google.com/file/d/13vsHkpBV8riwyKOTCh1v1heuAqf0L9nK/view?usp=sharing Problem Set 4] ||[https://drive.google.com/file/d/1PZD-YWikatG9jCbcc1r_Eo5t0y-kdcpj/view?usp=sharing Solutions] || -
|-
|| 21.10.22 || Divisibility. Calculation of remainders. Direct proofs. || [https://drive.google.com/file/d/1rHfC1WRv4IB8kNRMynVWv0C26PXGi137/view?usp=sharing Problem Set 5] ||[https://drive.google.com/file/d/1CvWAD5pDmMB8JFWSFNxOrrT7-Jfp_0Wd/view?usp=sharing Solutions] ||
[https://youtu.be/-OIYkDOkLyk Video 5]
|-
|| 11.11.22 || Great commod divider, the main thorem of arithmetic, direct proofs. || [https://drive.google.com/file/d/1CrF9W2rXFiTMKFoxZO-PJDmhYAx6Ql84/view?usp=share_link Problem Set 6] ||[https://drive.google.com/file/d/1TWSgbLrRtZWRrbneebExE4BPoDzLU4-b/view?usp=share_link Solutions] ||
[https://youtu.be/_2RRlq21gqM Video 6]
|-
|| 19.11.22 || Fermat's Little theorem, inverse elements in groups $\mathbb{Z}_p$, congruences. || [https://drive.google.com/file/d/1IF6rqwLN0Bq8n07mxQ3CAmoMfWplJ3OR/view?usp=share_link Problem Set 7] ||[https://drive.google.com/file/d/1FZevxpUjcPrrtCbxHn-HRh1odDamJqlq/view?usp=share_link Solutions] ||
[https://youtu.be/peuzIDzh1bE Video 7]
|-
|| 25.11.22 || Fermat's Little theorem, inverse elements in groups $\mathbb{Z}_p$, congruences. || [https://drive.google.com/file/d/1CYGJ7B5d426ChuZBozzsLKwMVZeVPgQJ/view?usp=share_link Problem Set 8] ||[https://drive.google.com/file/d/1_PCu2dDhIgN7uE1ijLGLH1USapPskGWH/view?usp=share_link Solutions] ||
[ -]
|-
|| 2.12.22 || Application of Euler's theorem and Euclidean algorithm, cryptography || [https://drive.google.com/file/d/1Oq3grvUbG-yBBbrHqhK_4Ylz4Io-D1Lw/view?usp=share_link Problem Set 9] ||[https://drive.google.com/file/d/1BFDh6-6KVmb65w7qDEQprP6BYUMUW6AQ/view?usp=share_link Solutions] ||
[https://youtu.be/HPpI7VpHrWY Video 9]
|-
|| 9.12.22 || Sets, direct proofs of set identities || [https://drive.google.com/file/d/1C6I_cviJwznCLZ5BKtxUtlUrjpp4Kegw/view?usp=share_link Problem Set 10] ||[https://drive.google.com/file/d/179jjcjhdU0LschqhPEFMPJylunwRiofA/view?usp=share_link Solutions] || [https://youtu.be/7Gk3JxRpeWU Video 10]
|-
|| 16.12.22 || Operations with sets, cardinality and power set || [https://drive.google.com/file/d/1D9A7QTq-7dPN8Xz_jQhsYIknX8cukhZD/view?usp=share_link Problem Set 11] ||[https://drive.google.com/file/d/1B1snvrzqMgUMDEEQqOHVzomfWVwf2t07/view?usp=share_link Solutions] ||
[https://youtu.be/TK4BNYF4vEU Video 11]
|-
|| 21.01.23 || Sets once again, proofs that a statement is wrong|| [https://drive.google.com/file/d/15hSnMr1jVCSJ6boGK5KuEUldlx3-8Pvv/view?usp=share_link Problem Set 12] ||[https://drive.google.com/file/d/1PDsR6DjO_K9-XfoqprA0UsYWh-2fSb8T/view?usp=share_link Solutions] ||
[https://youtu.be/2J8qDgwpivU Video 12]
|-
|| 28.01.23 || Relatins, main definitions|| [https://drive.google.com/file/d/1IJAqHsXCQaSFlzZFaH5TpfnNdibKAzen/view?usp=share_link
Problem Set 13] ||[https://drive.google.com/file/d/188uRSv9ALwy4IsPreEbS8J61PDMw9uVw/view?usp=share_link Solutions] ||
[ Video 13]

|}

[https://drive.google.com/file/d/163PgGw33FTt3PUVdVBYCjIHluftfZVol/view?usp=sharing Last year retake]

[https://drive.google.com/file/d/1bljTOb3x0kvYy7cslTOC4B3StYOHi3CX/view Last year test 1]

== Homeworks ==
[https://forms.gle/TAgL2eUkhSyhZKLD9 Homework 1 (Logics)], Deadline 31st October

[https://forms.gle/pVA1a8xbeP54RqAQ7 Homework 2 (Induction)], Deadline 31st November, better to complete before the November Test

Hint🦉 in Problem 5: Do not try to prove P(n) out of P(n-1). Assume that P(1), P(2), ...P(n-1) are all true. For proving P(n) say: lets find the biggest Fibonacci number F_i<n. Then, n = F_i + k. For the k apply your assumption😉😉

[https://drive.google.com/file/d/1k8SKmN9J_DdSs8ibP_9b52n8LxiPf_8U/view?usp=share_link Homework 3]: write down solutions to exam 1 in a perfect manner (like you you are going to print a book of your solutions), Deadline 25th November. You can pass them written or orally on Fridays evenings. Do it if you want to have MAX in the retake(if so happened) and in the exam in the end of the course.

[https://forms.gle/DQUEyuh1vuXgdtr6A Homework 4 (Number theory)], Deadline with bonus 29th December

==Semester 1 ==

[https://docs.google.com/spreadsheets/d/1YHhkk8TCm_qPF0tXyGe7rc-DzubrgSESZUoW6fHMLZA/edit?usp=sharing Current grades and comments]

== References ==

1. [http://discrete.openmathbooks.org/dmoi3.html Discrete Mathematics (An Open Introduction) by Oscar Levin,] p. 197 Logics. Many simple problems with solution to feel the topic.

2. [https://drive.google.com/file/d/1mmNLLQ0--EDihGNRKwSyXLOA1KL7A0lD/view?usp=sharing Lecture notes by Evgeny Dashkov]

PLUS: there is a [https://youtube.com/playlist?list=PLEwK9wdS5g0pk-1YWDc3hezRt_rNpQDf8 folder with records on wikipage ]

3. [http://www.mccme.ru/free-books/shen/shen-induction.pdf Шень А., Математическая индукция. 5-е изд, М.: МЦНМО, 2016.] Many problems to work with three different versions of induction.

== Grading and Results ==

'''Final grade''' = Average(HWs)+ Bonus points

Bonus point number is between 0 to 20. Such points may be given for a variety of auxiliary activities.

Adaptation course in Discrete Math (факультатив)

2023-01-24T13:51:10Z

Nasta.trofimova:

== General Information ==
The main goal of the Discrete Mathematics Adaptation Course is to help students keep up with the course curriculum by discussing the most important and challenging topics in detail. The second very important goal of the course is to teach students to work competently with mathematical definitions and proofs, correctly logically build solutions to problems and prove statements. The topics of the course are coordinated with the "basic" course of the DSBA and SE program, but its study will also be useful for the direction of AMI. The approximate order of topics is sets and logic, functions and relations, the beginning of number theory, combinatorics, graphs, the foundations of probability theory, generating functions.

== Schedule ==

The classes are organised on Saturdays at 16:20.

== Course materials ==

[https://t.me/+113aheknlsxmYzVi Chat in Telegram]

'''First semester'''

{| class="wikitable"
|-
! Date !! Topic !! Problem Set !! Class note !! Video
|-
|| 21.09.22 || Statements, connectives, quantifiers || [https://drive.google.com/file/d/1kbtRp8c79zE2AspfVb4ZfGZLJRy9Z5j2/view?usp=drivesdk Problem Set 1]|| - ||
|-
|| 28.09.22 || Validity of statements, types of proof|| [https://drive.google.com/file/d/1Q2OlmVzXf4P0ocd3eBet4ktoJ1h1DZyn/view?usp=sharing Problem Set 2] || [https://drive.google.com/file/d/11pdljFmpW57o5OqBH40YwioTW_Ebs_gK/view?usp=sharing Solutions] || -
|-
|| 7.10.22 || Three types of mathematical induction || [https://drive.google.com/file/d/14h2jy4W7KgxBffxE8TKh_13rSG3Wy_Ll/view?usp=sharing Problem Set 3] ||[https://drive.google.com/file/d/1yFnH5QBNxM-1ajoA5y7w9wV_31XeBwWp/view?usp=sharing Solutions] || [https://youtu.be/nljNhVjlnXg Video 3]
|-
|| 14.10.22 || Proofs with induction || [https://drive.google.com/file/d/13vsHkpBV8riwyKOTCh1v1heuAqf0L9nK/view?usp=sharing Problem Set 4] ||[https://drive.google.com/file/d/1PZD-YWikatG9jCbcc1r_Eo5t0y-kdcpj/view?usp=sharing Solutions] || -
|-
|| 21.10.22 || Divisibility. Calculation of remainders. Direct proofs. || [https://drive.google.com/file/d/1rHfC1WRv4IB8kNRMynVWv0C26PXGi137/view?usp=sharing Problem Set 5] ||[https://drive.google.com/file/d/1CvWAD5pDmMB8JFWSFNxOrrT7-Jfp_0Wd/view?usp=sharing Solutions] ||
[https://youtu.be/-OIYkDOkLyk Video 5]
|-
|| 11.11.22 || Great commod divider, the main thorem of arithmetic, direct proofs. || [https://drive.google.com/file/d/1CrF9W2rXFiTMKFoxZO-PJDmhYAx6Ql84/view?usp=share_link Problem Set 6] ||[https://drive.google.com/file/d/1TWSgbLrRtZWRrbneebExE4BPoDzLU4-b/view?usp=share_link Solutions] ||
[https://youtu.be/_2RRlq21gqM Video 6]
|-
|| 19.11.22 || Fermat's Little theorem, inverse elements in groups $\mathbb{Z}_p$, congruences. || [https://drive.google.com/file/d/1IF6rqwLN0Bq8n07mxQ3CAmoMfWplJ3OR/view?usp=share_link Problem Set 7] ||[https://drive.google.com/file/d/1FZevxpUjcPrrtCbxHn-HRh1odDamJqlq/view?usp=share_link Solutions] ||
[https://youtu.be/peuzIDzh1bE Video 7]
|-
|| 25.11.22 || Fermat's Little theorem, inverse elements in groups $\mathbb{Z}_p$, congruences. || [https://drive.google.com/file/d/1CYGJ7B5d426ChuZBozzsLKwMVZeVPgQJ/view?usp=share_link Problem Set 8] ||[https://drive.google.com/file/d/1_PCu2dDhIgN7uE1ijLGLH1USapPskGWH/view?usp=share_link Solutions] ||
[ -]
|-
|| 2.12.22 || Application of Euler's theorem and Euclidean algorithm, cryptography || [https://drive.google.com/file/d/1Oq3grvUbG-yBBbrHqhK_4Ylz4Io-D1Lw/view?usp=share_link Problem Set 9] ||[https://drive.google.com/file/d/1BFDh6-6KVmb65w7qDEQprP6BYUMUW6AQ/view?usp=share_link Solutions] ||
[https://youtu.be/HPpI7VpHrWY Video 9]
|-
|| 9.12.22 || Sets, direct proofs of set identities || [https://drive.google.com/file/d/1C6I_cviJwznCLZ5BKtxUtlUrjpp4Kegw/view?usp=share_link Problem Set 10] ||[https://drive.google.com/file/d/179jjcjhdU0LschqhPEFMPJylunwRiofA/view?usp=share_link Solutions] || [https://youtu.be/7Gk3JxRpeWU Video 10]
|-
|| 16.12.22 || Operations with sets, cardinality and power set || [https://drive.google.com/file/d/1D9A7QTq-7dPN8Xz_jQhsYIknX8cukhZD/view?usp=share_link Problem Set 11] ||[https://drive.google.com/file/d/1B1snvrzqMgUMDEEQqOHVzomfWVwf2t07/view?usp=share_link Solutions] ||
[https://youtu.be/TK4BNYF4vEU Video 11]
|-
|| 21.01.23 || Sets once again, proofs that a statement is wrong|| [https://drive.google.com/file/d/15hSnMr1jVCSJ6boGK5KuEUldlx3-8Pvv/view?usp=share_link Problem Set 12] ||[https://drive.google.com/file/d/1PDsR6DjO_K9-XfoqprA0UsYWh-2fSb8T/view?usp=share_link Solutions] ||
[https://youtu.be/2J8qDgwpivU Video 12]

|}

[https://drive.google.com/file/d/163PgGw33FTt3PUVdVBYCjIHluftfZVol/view?usp=sharing Last year retake]

[https://drive.google.com/file/d/1bljTOb3x0kvYy7cslTOC4B3StYOHi3CX/view Last year test 1]

== Homeworks ==
[https://forms.gle/TAgL2eUkhSyhZKLD9 Homework 1 (Logics)], Deadline 31st October

[https://forms.gle/pVA1a8xbeP54RqAQ7 Homework 2 (Induction)], Deadline 31st November, better to complete before the November Test

Hint🦉 in Problem 5: Do not try to prove P(n) out of P(n-1). Assume that P(1), P(2), ...P(n-1) are all true. For proving P(n) say: lets find the biggest Fibonacci number F_i<n. Then, n = F_i + k. For the k apply your assumption😉😉

[https://drive.google.com/file/d/1k8SKmN9J_DdSs8ibP_9b52n8LxiPf_8U/view?usp=share_link Homework 3]: write down solutions to exam 1 in a perfect manner (like you you are going to print a book of your solutions), Deadline 25th November. You can pass them written or orally on Fridays evenings. Do it if you want to have MAX in the retake(if so happened) and in the exam in the end of the course.

[https://forms.gle/DQUEyuh1vuXgdtr6A Homework 4 (Number theory)], Deadline with bonus 29th December

==Semester 1 ==

[https://docs.google.com/spreadsheets/d/1YHhkk8TCm_qPF0tXyGe7rc-DzubrgSESZUoW6fHMLZA/edit?usp=sharing Current grades and comments]

== References ==

1. [http://discrete.openmathbooks.org/dmoi3.html Discrete Mathematics (An Open Introduction) by Oscar Levin,] p. 197 Logics. Many simple problems with solution to feel the topic.

2. [https://drive.google.com/file/d/1mmNLLQ0--EDihGNRKwSyXLOA1KL7A0lD/view?usp=sharing Lecture notes by Evgeny Dashkov]

PLUS: there is a [https://youtube.com/playlist?list=PLEwK9wdS5g0pk-1YWDc3hezRt_rNpQDf8 folder with records on wikipage ]

3. [http://www.mccme.ru/free-books/shen/shen-induction.pdf Шень А., Математическая индукция. 5-е изд, М.: МЦНМО, 2016.] Many problems to work with three different versions of induction.

== Grading and Results ==

'''Final grade''' = Average(HWs)+ Bonus points

Bonus point number is between 0 to 20. Such points may be given for a variety of auxiliary activities.

Adaptation course in Discrete Math (факультатив)

2023-01-23T10:48:08Z

Nasta.trofimova:

== General Information ==
The main goal of the Discrete Mathematics Adaptation Course is to help students keep up with the course curriculum by discussing the most important and challenging topics in detail. The second very important goal of the course is to teach students to work competently with mathematical definitions and proofs, correctly logically build solutions to problems and prove statements. The topics of the course are coordinated with the "basic" course of the DSBA and SE program, but its study will also be useful for the direction of AMI. The approximate order of topics is sets and logic, functions and relations, the beginning of number theory, combinatorics, graphs, the foundations of probability theory, generating functions.

== Schedule ==

The classes are organised on Saturdays at 16:20.

== Course materials ==

[https://t.me/+113aheknlsxmYzVi Chat in Telegram]

'''First semester'''

{| class="wikitable"
|-
! Date !! Topic !! Problem Set !! Class note !! Video
|-
|| 21.09.22 || Statements, connectives, quantifiers || [https://drive.google.com/file/d/1kbtRp8c79zE2AspfVb4ZfGZLJRy9Z5j2/view?usp=drivesdk Problem Set 1]|| - ||
|-
|| 28.09.22 || Validity of statements, types of proof|| [https://drive.google.com/file/d/1Q2OlmVzXf4P0ocd3eBet4ktoJ1h1DZyn/view?usp=sharing Problem Set 2] || [https://drive.google.com/file/d/11pdljFmpW57o5OqBH40YwioTW_Ebs_gK/view?usp=sharing Solutions] || -
|-
|| 7.10.22 || Three types of mathematical induction || [https://drive.google.com/file/d/14h2jy4W7KgxBffxE8TKh_13rSG3Wy_Ll/view?usp=sharing Problem Set 3] ||[https://drive.google.com/file/d/1yFnH5QBNxM-1ajoA5y7w9wV_31XeBwWp/view?usp=sharing Solutions] || [https://youtu.be/nljNhVjlnXg Video 3]
|-
|| 14.10.22 || Proofs with induction || [https://drive.google.com/file/d/13vsHkpBV8riwyKOTCh1v1heuAqf0L9nK/view?usp=sharing Problem Set 4] ||[https://drive.google.com/file/d/1PZD-YWikatG9jCbcc1r_Eo5t0y-kdcpj/view?usp=sharing Solutions] || -
|-
|| 21.10.22 || Divisibility. Calculation of remainders. Direct proofs. || [https://drive.google.com/file/d/1rHfC1WRv4IB8kNRMynVWv0C26PXGi137/view?usp=sharing Problem Set 5] ||[https://drive.google.com/file/d/1CvWAD5pDmMB8JFWSFNxOrrT7-Jfp_0Wd/view?usp=sharing Solutions] ||
[https://youtu.be/-OIYkDOkLyk Video 5]
|-
|| 11.11.22 || Great commod divider, the main thorem of arithmetic, direct proofs. || [https://drive.google.com/file/d/1CrF9W2rXFiTMKFoxZO-PJDmhYAx6Ql84/view?usp=share_link Problem Set 6] ||[https://drive.google.com/file/d/1TWSgbLrRtZWRrbneebExE4BPoDzLU4-b/view?usp=share_link Solutions] ||
[https://youtu.be/_2RRlq21gqM Video 6]
|-
|| 19.11.22 || Fermat's Little theorem, inverse elements in groups $\mathbb{Z}_p$, congruences. || [https://drive.google.com/file/d/1IF6rqwLN0Bq8n07mxQ3CAmoMfWplJ3OR/view?usp=share_link Problem Set 7] ||[https://drive.google.com/file/d/1FZevxpUjcPrrtCbxHn-HRh1odDamJqlq/view?usp=share_link Solutions] ||
[https://youtu.be/peuzIDzh1bE Video 7]
|-
|| 25.11.22 || Fermat's Little theorem, inverse elements in groups $\mathbb{Z}_p$, congruences. || [https://drive.google.com/file/d/1CYGJ7B5d426ChuZBozzsLKwMVZeVPgQJ/view?usp=share_link Problem Set 8] ||[https://drive.google.com/file/d/1_PCu2dDhIgN7uE1ijLGLH1USapPskGWH/view?usp=share_link Solutions] ||
[ -]
|-
|| 2.12.22 || Application of Euler's theorem and Euclidean algorithm, cryptography || [https://drive.google.com/file/d/1Oq3grvUbG-yBBbrHqhK_4Ylz4Io-D1Lw/view?usp=share_link Problem Set 9] ||[https://drive.google.com/file/d/1BFDh6-6KVmb65w7qDEQprP6BYUMUW6AQ/view?usp=share_link Solutions] ||
[https://youtu.be/HPpI7VpHrWY Video 9]
|-
|| 9.12.22 || Sets, direct proofs of set identities || [https://drive.google.com/file/d/1C6I_cviJwznCLZ5BKtxUtlUrjpp4Kegw/view?usp=share_link Problem Set 10] ||[https://drive.google.com/file/d/179jjcjhdU0LschqhPEFMPJylunwRiofA/view?usp=share_link Solutions] || [https://youtu.be/7Gk3JxRpeWU Video 10]
|-
|| 16.12.22 || Operations with sets, cardinality and power set || [https://drive.google.com/file/d/1D9A7QTq-7dPN8Xz_jQhsYIknX8cukhZD/view?usp=share_link Problem Set 11] ||[https://drive.google.com/file/d/1B1snvrzqMgUMDEEQqOHVzomfWVwf2t07/view?usp=share_link Solutions] ||
[https://youtu.be/TK4BNYF4vEU Video 11]
|-
|| 21.01.23 || Sets once again, proofs that a statement is wrong|| [https://drive.google.com/file/d/15hSnMr1jVCSJ6boGK5KuEUldlx3-8Pvv/view?usp=share_link Problem Set 12] ||[https://drive.google.com/file/d/1PDsR6DjO_K9-XfoqprA0UsYWh-2fSb8T/view?usp=share_link Solutions] ||
[ Video 12]

|}

[https://drive.google.com/file/d/163PgGw33FTt3PUVdVBYCjIHluftfZVol/view?usp=sharing Last year retake]

[https://drive.google.com/file/d/1bljTOb3x0kvYy7cslTOC4B3StYOHi3CX/view Last year test 1]

== Homeworks ==
[https://forms.gle/TAgL2eUkhSyhZKLD9 Homework 1 (Logics)], Deadline 31st October

[https://forms.gle/pVA1a8xbeP54RqAQ7 Homework 2 (Induction)], Deadline 31st November, better to complete before the November Test

Hint🦉 in Problem 5: Do not try to prove P(n) out of P(n-1). Assume that P(1), P(2), ...P(n-1) are all true. For proving P(n) say: lets find the biggest Fibonacci number F_i<n. Then, n = F_i + k. For the k apply your assumption😉😉

[https://drive.google.com/file/d/1k8SKmN9J_DdSs8ibP_9b52n8LxiPf_8U/view?usp=share_link Homework 3]: write down solutions to exam 1 in a perfect manner (like you you are going to print a book of your solutions), Deadline 25th November. You can pass them written or orally on Fridays evenings. Do it if you want to have MAX in the retake(if so happened) and in the exam in the end of the course.

[https://forms.gle/DQUEyuh1vuXgdtr6A Homework 4 (Number theory)], Deadline with bonus 29th December

==Semester 1 ==

[https://docs.google.com/spreadsheets/d/1YHhkk8TCm_qPF0tXyGe7rc-DzubrgSESZUoW6fHMLZA/edit?usp=sharing Current grades and comments]

== References ==

1. [http://discrete.openmathbooks.org/dmoi3.html Discrete Mathematics (An Open Introduction) by Oscar Levin,] p. 197 Logics. Many simple problems with solution to feel the topic.

2. [https://drive.google.com/file/d/1mmNLLQ0--EDihGNRKwSyXLOA1KL7A0lD/view?usp=sharing Lecture notes by Evgeny Dashkov]

PLUS: there is a [https://youtube.com/playlist?list=PLEwK9wdS5g0pk-1YWDc3hezRt_rNpQDf8 folder with records on wikipage ]

3. [http://www.mccme.ru/free-books/shen/shen-induction.pdf Шень А., Математическая индукция. 5-е изд, М.: МЦНМО, 2016.] Many problems to work with three different versions of induction.

== Grading and Results ==

'''Final grade''' = Average(HWs)+ Bonus points

Bonus point number is between 0 to 20. Such points may be given for a variety of auxiliary activities.

Adaptation course in Discrete Math (факультатив)

2023-01-23T10:43:55Z

Nasta.trofimova:

== General Information ==
The main goal of the Discrete Mathematics Adaptation Course is to help students keep up with the course curriculum by discussing the most important and challenging topics in detail. The second very important goal of the course is to teach students to work competently with mathematical definitions and proofs, correctly logically build solutions to problems and prove statements. The topics of the course are coordinated with the "basic" course of the DSBA and SE program, but its study will also be useful for the direction of AMI. The approximate order of topics is sets and logic, functions and relations, the beginning of number theory, combinatorics, graphs, the foundations of probability theory, generating functions.

== Schedule ==

The classes are organised on Saturdays at 16:20.

== Course materials ==

[https://t.me/+113aheknlsxmYzVi Chat in Telegram]

'''First semester'''

{| class="wikitable"
|-
! Date !! Topic !! Problem Set !! Class note !! Video
|-
|| 21.09.22 || Statements, connectives, quantifiers || [https://drive.google.com/file/d/1kbtRp8c79zE2AspfVb4ZfGZLJRy9Z5j2/view?usp=drivesdk Problem Set 1]|| - ||
|-
|| 28.09.22 || Validity of statements, types of proof|| [https://drive.google.com/file/d/1Q2OlmVzXf4P0ocd3eBet4ktoJ1h1DZyn/view?usp=sharing Problem Set 2] || [https://drive.google.com/file/d/11pdljFmpW57o5OqBH40YwioTW_Ebs_gK/view?usp=sharing Solutions] || -
|-
|| 7.10.22 || Three types of mathematical induction || [https://drive.google.com/file/d/14h2jy4W7KgxBffxE8TKh_13rSG3Wy_Ll/view?usp=sharing Problem Set 3] ||[https://drive.google.com/file/d/1yFnH5QBNxM-1ajoA5y7w9wV_31XeBwWp/view?usp=sharing Solutions] || [https://youtu.be/nljNhVjlnXg Video 3]
|-
|| 14.10.22 || Proofs with induction || [https://drive.google.com/file/d/13vsHkpBV8riwyKOTCh1v1heuAqf0L9nK/view?usp=sharing Problem Set 4] ||[https://drive.google.com/file/d/1PZD-YWikatG9jCbcc1r_Eo5t0y-kdcpj/view?usp=sharing Solutions] || -
|-
|| 21.10.22 || Divisibility. Calculation of remainders. Direct proofs. || [https://drive.google.com/file/d/1rHfC1WRv4IB8kNRMynVWv0C26PXGi137/view?usp=sharing Problem Set 5] ||[https://drive.google.com/file/d/1CvWAD5pDmMB8JFWSFNxOrrT7-Jfp_0Wd/view?usp=sharing Solutions] ||
[https://youtu.be/-OIYkDOkLyk Video 5]
|-
|| 11.11.22 || Great commod divider, the main thorem of arithmetic, direct proofs. || [https://drive.google.com/file/d/1CrF9W2rXFiTMKFoxZO-PJDmhYAx6Ql84/view?usp=share_link Problem Set 6] ||[https://drive.google.com/file/d/1TWSgbLrRtZWRrbneebExE4BPoDzLU4-b/view?usp=share_link Solutions] ||
[https://youtu.be/_2RRlq21gqM Video 6]
|-
|| 19.11.22 || Fermat's Little theorem, inverse elements in groups $\mathbb{Z}_p$, congruences. || [https://drive.google.com/file/d/1IF6rqwLN0Bq8n07mxQ3CAmoMfWplJ3OR/view?usp=share_link Problem Set 7] ||[https://drive.google.com/file/d/1FZevxpUjcPrrtCbxHn-HRh1odDamJqlq/view?usp=share_link Solutions] ||
[https://youtu.be/peuzIDzh1bE Video 7]
|-
|| 25.11.22 || Fermat's Little theorem, inverse elements in groups $\mathbb{Z}_p$, congruences. || [https://drive.google.com/file/d/1CYGJ7B5d426ChuZBozzsLKwMVZeVPgQJ/view?usp=share_link Problem Set 8] ||[https://drive.google.com/file/d/1_PCu2dDhIgN7uE1ijLGLH1USapPskGWH/view?usp=share_link Solutions] ||
[ -]
|-
|| 2.12.22 || Application of Euler's theorem and Euclidean algorithm, cryptography || [https://drive.google.com/file/d/1Oq3grvUbG-yBBbrHqhK_4Ylz4Io-D1Lw/view?usp=share_link Problem Set 9] ||[https://drive.google.com/file/d/1BFDh6-6KVmb65w7qDEQprP6BYUMUW6AQ/view?usp=share_link Solutions] ||
[https://youtu.be/HPpI7VpHrWY Video 9]
|-
|| 9.12.22 || Sets, direct proofs of set identities || [https://drive.google.com/file/d/1C6I_cviJwznCLZ5BKtxUtlUrjpp4Kegw/view?usp=share_link Problem Set 10] ||[https://drive.google.com/file/d/179jjcjhdU0LschqhPEFMPJylunwRiofA/view?usp=share_link Solutions] || [https://youtu.be/7Gk3JxRpeWU Video 10]
|-
|| 16.12.22 || Operations with sets, cardinality and power set || [https://drive.google.com/file/d/1D9A7QTq-7dPN8Xz_jQhsYIknX8cukhZD/view?usp=share_link Problem Set 11] ||[https://drive.google.com/file/d/1B1snvrzqMgUMDEEQqOHVzomfWVwf2t07/view?usp=share_link Solutions] ||
[https://youtu.be/TK4BNYF4vEU Video 11]
|}

[https://drive.google.com/file/d/163PgGw33FTt3PUVdVBYCjIHluftfZVol/view?usp=sharing Last year retake]

[https://drive.google.com/file/d/1bljTOb3x0kvYy7cslTOC4B3StYOHi3CX/view Last year test 1]

== Homeworks ==
[https://forms.gle/TAgL2eUkhSyhZKLD9 Homework 1 (Logics)], Deadline 31st October

[https://forms.gle/pVA1a8xbeP54RqAQ7 Homework 2 (Induction)], Deadline 31st November, better to complete before the November Test

Hint🦉 in Problem 5: Do not try to prove P(n) out of P(n-1). Assume that P(1), P(2), ...P(n-1) are all true. For proving P(n) say: lets find the biggest Fibonacci number F_i<n. Then, n = F_i + k. For the k apply your assumption😉😉

[https://drive.google.com/file/d/1k8SKmN9J_DdSs8ibP_9b52n8LxiPf_8U/view?usp=share_link Homework 3]: write down solutions to exam 1 in a perfect manner (like you you are going to print a book of your solutions), Deadline 25th November. You can pass them written or orally on Fridays evenings. Do it if you want to have MAX in the retake(if so happened) and in the exam in the end of the course.

[https://forms.gle/DQUEyuh1vuXgdtr6A Homework 4 (Number theory)], Deadline with bonus 29th December

==Semester 1 ==

[https://docs.google.com/spreadsheets/d/1YHhkk8TCm_qPF0tXyGe7rc-DzubrgSESZUoW6fHMLZA/edit?usp=sharing Current grades and comments]

== References ==

1. [http://discrete.openmathbooks.org/dmoi3.html Discrete Mathematics (An Open Introduction) by Oscar Levin,] p. 197 Logics. Many simple problems with solution to feel the topic.

2. [https://drive.google.com/file/d/1mmNLLQ0--EDihGNRKwSyXLOA1KL7A0lD/view?usp=sharing Lecture notes by Evgeny Dashkov]

PLUS: there is a [https://youtube.com/playlist?list=PLEwK9wdS5g0pk-1YWDc3hezRt_rNpQDf8 folder with records on wikipage ]

3. [http://www.mccme.ru/free-books/shen/shen-induction.pdf Шень А., Математическая индукция. 5-е изд, М.: МЦНМО, 2016.] Many problems to work with three different versions of induction.

== Grading and Results ==

'''Final grade''' = Average(HWs)+ Bonus points

Bonus point number is between 0 to 20. Such points may be given for a variety of auxiliary activities.

Discrete Mathematics DSBA 2022/2023

2022-12-19T20:03:27Z

Nasta.trofimova: /* Assignment deadlines */

== Instructors ==

=== The lecturer ===
My name is Evgeny Dashkov. Feel free to contact me via email: edashkov@gmail.com, [https://t.me/edashkov Telegram], or [https://vk.com/evgeny.v.dashkov VK].

=== Seminar instructors ===
{| class="wikitable" style="text-align:center"
|-
! Group !! 221 !! 222 !! 223 !! 224
|-
|| Teachers || Evgeny Dashkov ||colspan="2"| Boris Danilov [https://t.me/brdann Telegram]|| Trofimova Anastasia [https://t.me/AnastasiiaTrofimova Telegram]
|-
|| Teaching Assistants || Arseny Bolotnikov [https://t.me/l0i4b Telegram] ||Daria Ivanova [https://t.me/ivanovskayaaaaa Telegram]|| Artem Ilin [https://t.me/artem_ilinn Telegram] || Marianna Kouis [https://t.me/mariannakouis Telegram]
|-
|| Lecturer’s Assistant || colspan="4"| Alyona Chislova [https://t.me/alenka_chislova Telegram]
|}

== Current performance ==

[https://docs.google.com/spreadsheets/d/1KoXyABY4alQu-Gw3HsYy3Vco9rfvHdYQZuUjE_ERJB8/edit?usp=sharing The Table]

== Homework ==
The homework includes a few problem sets, one in a fortnight or so (the deadlines are announced on giving each set). Every problem set consists of about 10 – 15 problems, some of which are labeled as ‘bonus’ while all the remaining are considered ‘ordinary’. One can get either 0, ½, or 1 point for each problem. For the entire homework, two values are computed:

HW = (the sum of points given for ordinary problems) / #(ordinary problems);

HW* = (the sum of points given for bonus problems) / #(bonus problems).

The value HW1 is similar to HW but restricted to the problem sets given in Module 1.

A student may be required to explain orally his written solution to any problem. His grade for the problem may be decreased if he fails to do so properly.

== Exam 1 ==
A written examination is held past Module 1. Students may not consult any sources during the exam. Some problems of the exam are labeled as ‘bonus’; the others are ‘ordinary’. Each problem solution is graded with either 0, ¼, ½, ¾, or 1 point, and the entire exam with two values:

Exam1 = (the sum of points given for ordinary problems) / #(ordinary problems);

Exam1* = (the sum of points given for bonus problems) / #(bonus problems)

== Colloquium ==
An oral colloquium is held at the beginning of Module 3. Each student is given two questions concerning statements and definitions as well as one question requiring a proof. After no less than 45 minutes of preparation (when using any literature is allowed), the student is required to answer ‘from scratch’, that is, with no recourse to any materials. The examiner may pose additional questions as he sees fit. The student may get from 0 to 7 integer points for his answer; the value

Colloq = (the score given) / 7

is then computed.

== Exam 2 ==
A written examination is held at the end of the Course. Students may not consult any sources during the exam. The examination takes about 120 minutes. Some problems of the exam are labeled as ‘bonus’; the others are ‘ordinary’. Each problem solution is graded with either 0, ¼, ½, ¾, or 1 point; finally, two values are computed:

Exam2 = (the sum of points given for ordinary problems) / #(ordinary problems);

Exam2* = (the sum of points given for bonus problems) / #(bonus problems).

== Bonus activities ==
The students may be graded for a variety of ‘bonus activities’ (like quizzes, etc.) with an overall integer value Bonus from 0 to 25.

== Exam retaking ==
Examinations 1 and 2 are subject to be retaken if Module 1 grade or Final grade (see below), respectively, is unsatisfactory. Retaking the exam is similar to the regular examination. The resulting grade is substituted for that of the latter. The last try Commission retaking is held for those whose final grade is still unsatisfactory after the retaking. A designated Commission carefully examines the student’s performance and gives him a final mark not better than ‘satisfactory’; at that the Commission is not bound by the grading formulas herein.

== Course materials ==

[https://t.me/joinchat/T_YTN4IG1vAJNWT9 Course chat].

=== Lecture notes ===

https://drive.google.com/file/d/1mmNLLQ0--EDihGNRKwSyXLOA1KL7A0lD/view?usp=sharing

=== Classes recordings ===

https://disk.yandex.ru/d/enYKJ6O8NN_3lQ

=== Lecture video archive ===

https://youtube.com/playlist?list=PLEwK9wdS5g0pk-1YWDc3hezRt_rNpQDf8

=== Other resources ===
* [https://tinyurl.com/rwky5vmk The Course's Google Directory]

* [https://www.youtube.com/playlist?list=PL1Uob8iPTHGTidrmrqEHTJ96Pt3-PmML4 Past years' videos]

* We have a [https://meet.edashkov.net.ru dedicated server] to hold an online meeting if we need one.

== Problem sets ==

=== Class problems ===

* [https://drive.google.com/file/d/1EP-diSuOTn9f0ryg18Z2w0xjEp8j0bnl/view?usp=sharing Problem set 1]

* [https://drive.google.com/file/d/12ct99-ORd7A94Gh5g4Nf9riv7UqNMSRc/view?usp=sharing Problem set 2]

* [https://drive.google.com/file/d/1yKKqLsS99V4AhCYqbjafuav2CMCdQTOQ/view?usp=sharing Problem set 3]

* [https://drive.google.com/file/d/1YgH_AdCk4GcKC0KH7xBA4-sUnOYkUvUK/view?usp=share_link Problem set 4]

* [https://drive.google.com/file/d/1M556PSgTJOo5W-AxYEXjFu94VfledpF5/view?usp=share_link Problem set 5]

* [https://drive.google.com/file/d/1-ylVViaBgzxEM-M7Rvrz2iggtK6UiJTY/view?usp=share_link Problem set 6]

=== Homework problems ===

* [https://drive.google.com/file/d/1A8lFPdI3ZvC1vOgz2KEpYcuWOFlsQvb1/view?usp=sharing Homework 1]

* [https://drive.google.com/file/d/1LOPPwGjyVleR_mclxTKUJ_bxFrxt44sW/view?usp=sharing Homework 2a]

* [https://drive.google.com/file/d/1W7k1OTiIMlPOpo-2mwmGegrc4RDHz5_j/view?usp=share_link Homework 2b]

* [https://drive.google.com/file/d/1UvF-3gRwMrnsDAT9H4KDpoUafhrthKPw/view?usp=share_link Homework 3]

=== Assignment deadlines ===

{| class="wikitable"
|-
! Home problem set !! colspan="11" | Deadline
|-
| || 221 || 222 || 223 || 224
|-
| HW 1 №1-3 || || 22.IX || 22.IX || 22.IX
|-
| HW 1 || October 6 || October 6 || October 6 || October 6
|-
| HW 2a №1-3 || || October 20 || October 20 ||
|-
| HW 2a || October 24 || October 27 || October 27 || October 27
|-
| HW 2b №1-7 || November 30 || November 20 || November 20 || November 20
|-
| HW 2b №8-14 || December 14 || December 4 || December 4 || December 4
|-
| HW 3 №1-3 || December 22 || December 22 || December 22 || December 24
|}

'''Each deadline is set by the respective group's instructor.'''

== Grading system ==
For the final grading, we compute the following values:

Module 1 grade = round ((50*HW1 + 50*Exam1)/100);

basic = (21*Exam1 + 21*Colloq + 28*HW + 30*Exam2)/100;

adv = (30*Exam1* + Bonus + 35*HW* + 35*Exam2*)/100;

Final grade = round(min(10, 8 * basic + 2 * adv)).

The final grade is rounded half up to an integer. All the other values are reported with the greatest precision available.

== Recommended reading ==
''Please notice that '''The Book''' for our Course does not exist. The latter is based on many sources.''

# Anderson J. A., Discrete Mathematics With Combinatorics. Prentice Hall, 2003.
# Biggs N. L., Discrete mathematics. 2nd ed., New York; Oxford: Oxford University Press, 2004.
# Gavrilov G. P., Sapozhenko A. A. Problems and Exercises in Discrete Mathematics. Kluwer Texts in the Mathematical Sciences 14. Springer, 1996.
# [http://courses.csail.mit.edu/6.042/spring17/mcs.pdf Lehman E., Thomson Leighton F., Meyer A. R. Mathematics for Computer Science, 2017.]
# [http://www.cs.elte.hu/~lovasz/dmbook.ps Lovasz L., Vesztergombi K. Discrete Mathematics. Lecture Notes; Yale University, 1999.]
# Melnikov O., Sarvanov V., Tyshkevich R., Yemelichev V., Zverovich I. Exercises in Graph Theory. Kluwer Texts in the Mathematical Sciences 19. Springer, 1998.
# Rosen K. H. Discrete Mathematics and Its Applications. McGraw-Hill, 1999.
# Stein C., Drysdale R. L., Bogart K. Discrete mathematics for computer scientists. Addison-Wesley, 2010.
# Vinogradov I. M. Elements of number theory. Dover, 1954.

=== In Russian ===
''If you understand Russian (by any chance), you will probably benefit from reading the following books.''

# Виноградов И. М. Основы теории чисел. 9-е изд., М.: Наука, 1981.
# [http://rubtsov.su/public/DM-HSE-Draft.pdf Вялый М., Подольский В., Рубцов А., Шварц Д., Шень А. Лекции по дискретной математике.]
# Гаврилов Г. П., Сапоженко А. А. Задачи и упражнения по дискретной математике. 3-е изд., М.: ФИЗМАТЛИТ, 2004.
# [https://drive.google.com/file/d/1RM6KX_reBFwUXesWGUEu0sFn2NCaBgvz/view?usp=sharing Дашков Е. В. Введение в математическую логику. Множества и отношения. М.: МФТИ, 2019.]
# Зубков А. М., Севастьянов Б. А., Чистяков В. П. Сборник задач по теории вероятностей. 2-е изд., М.: Наука, 1989.
# Мельников О. И. Теория графов в занимательных задачах. 5-е изд., М.: Книжный дом "ЛИБРОКОМ", 2013.
# [http://www.mccme.ru/free-books/shen/shen-induction.pdf Шень А., Математическая индукция. 5-е изд, М.: МЦНМО, 2016.]

Adaptation course in Discrete Math (факультатив)

2022-12-17T14:25:58Z

Nasta.trofimova:

== General Information ==
The main goal of the Discrete Mathematics Adaptation Course is to help students keep up with the course curriculum by discussing the most important and challenging topics in detail. The second very important goal of the course is to teach students to work competently with mathematical definitions and proofs, correctly logically build solutions to problems and prove statements. The topics of the course are coordinated with the "basic" course of the DSBA and SE program, but its study will also be useful for the direction of AMI. The approximate order of topics is sets and logic, functions and relations, the beginning of number theory, combinatorics, graphs, the foundations of probability theory, generating functions.

== Schedule ==

The classes are organised on Wednesdays at 18:10.

== Course materials ==

[https://t.me/+113aheknlsxmYzVi Chat in Telegram]

'''First semester'''

{| class="wikitable"
|-
! Date !! Topic !! Problem Set !! Class note !! Video
|-
|| 21.09.22 || Statements, connectives, quantifiers || [https://drive.google.com/file/d/1kbtRp8c79zE2AspfVb4ZfGZLJRy9Z5j2/view?usp=drivesdk Problem Set 1]|| - ||
|-
|| 28.09.22 || Validity of statements, types of proof|| [https://drive.google.com/file/d/1Q2OlmVzXf4P0ocd3eBet4ktoJ1h1DZyn/view?usp=sharing Problem Set 2] || [https://drive.google.com/file/d/11pdljFmpW57o5OqBH40YwioTW_Ebs_gK/view?usp=sharing Solutions] || -
|-
|| 7.10.22 || Three types of mathematical induction || [https://drive.google.com/file/d/14h2jy4W7KgxBffxE8TKh_13rSG3Wy_Ll/view?usp=sharing Problem Set 3] ||[https://drive.google.com/file/d/1yFnH5QBNxM-1ajoA5y7w9wV_31XeBwWp/view?usp=sharing Solutions] || [https://youtu.be/nljNhVjlnXg Video 3]
|-
|| 14.10.22 || Proofs with induction || [https://drive.google.com/file/d/13vsHkpBV8riwyKOTCh1v1heuAqf0L9nK/view?usp=sharing Problem Set 4] ||[https://drive.google.com/file/d/1PZD-YWikatG9jCbcc1r_Eo5t0y-kdcpj/view?usp=sharing Solutions] || -
|-
|| 21.10.22 || Divisibility. Calculation of remainders. Direct proofs. || [https://drive.google.com/file/d/1rHfC1WRv4IB8kNRMynVWv0C26PXGi137/view?usp=sharing Problem Set 5] ||[https://drive.google.com/file/d/1CvWAD5pDmMB8JFWSFNxOrrT7-Jfp_0Wd/view?usp=sharing Solutions] ||
[https://youtu.be/-OIYkDOkLyk Video 5]
|-
|| 11.11.22 || Great commod divider, the main thorem of arithmetic, direct proofs. || [https://drive.google.com/file/d/1CrF9W2rXFiTMKFoxZO-PJDmhYAx6Ql84/view?usp=share_link Problem Set 6] ||[https://drive.google.com/file/d/1TWSgbLrRtZWRrbneebExE4BPoDzLU4-b/view?usp=share_link Solutions] ||
[https://youtu.be/_2RRlq21gqM Video 6]
|-
|| 19.11.22 || Fermat's Little theorem, inverse elements in groups $\mathbb{Z}_p$, congruences. || [https://drive.google.com/file/d/1IF6rqwLN0Bq8n07mxQ3CAmoMfWplJ3OR/view?usp=share_link Problem Set 7] ||[https://drive.google.com/file/d/1FZevxpUjcPrrtCbxHn-HRh1odDamJqlq/view?usp=share_link Solutions] ||
[https://youtu.be/peuzIDzh1bE Video 7]
|-
|| 25.11.22 || Fermat's Little theorem, inverse elements in groups $\mathbb{Z}_p$, congruences. || [https://drive.google.com/file/d/1CYGJ7B5d426ChuZBozzsLKwMVZeVPgQJ/view?usp=share_link Problem Set 8] ||[https://drive.google.com/file/d/1_PCu2dDhIgN7uE1ijLGLH1USapPskGWH/view?usp=share_link Solutions] ||
[ -]
|-
|| 2.12.22 || Application of Euler's theorem and Euclidean algorithm, cryptography || [https://drive.google.com/file/d/1Oq3grvUbG-yBBbrHqhK_4Ylz4Io-D1Lw/view?usp=share_link Problem Set 9] ||[https://drive.google.com/file/d/1BFDh6-6KVmb65w7qDEQprP6BYUMUW6AQ/view?usp=share_link Solutions] ||
[https://youtu.be/HPpI7VpHrWY Video 9]
|-
|| 9.12.22 || Sets, direct proofs of set identities || [https://drive.google.com/file/d/1C6I_cviJwznCLZ5BKtxUtlUrjpp4Kegw/view?usp=share_link Problem Set 10] ||[https://drive.google.com/file/d/179jjcjhdU0LschqhPEFMPJylunwRiofA/view?usp=share_link Solutions] || [https://youtu.be/7Gk3JxRpeWU Video 10]
|-
|| 16.12.22 || Operations with sets, cardinality and power set || [https://drive.google.com/file/d/1D9A7QTq-7dPN8Xz_jQhsYIknX8cukhZD/view?usp=share_link Problem Set 11] ||[https://drive.google.com/file/d/1B1snvrzqMgUMDEEQqOHVzomfWVwf2t07/view?usp=share_link Solutions] ||
[https://youtu.be/TK4BNYF4vEU Video 11]
|}

[https://drive.google.com/file/d/163PgGw33FTt3PUVdVBYCjIHluftfZVol/view?usp=sharing Last year retake]

[https://drive.google.com/file/d/1bljTOb3x0kvYy7cslTOC4B3StYOHi3CX/view Last year test 1]

== Homeworks ==
[https://forms.gle/TAgL2eUkhSyhZKLD9 Homework 1 (Logics)], Deadline 31st October

[https://forms.gle/pVA1a8xbeP54RqAQ7 Homework 2 (Induction)], Deadline 31st November, better to complete before the November Test

Hint🦉 in Problem 5: Do not try to prove P(n) out of P(n-1). Assume that P(1), P(2), ...P(n-1) are all true. For proving P(n) say: lets find the biggest Fibonacci number F_i<n. Then, n = F_i + k. For the k apply your assumption😉😉

[https://drive.google.com/file/d/1k8SKmN9J_DdSs8ibP_9b52n8LxiPf_8U/view?usp=share_link Homework 3]: write down solutions to exam 1 in a perfect manner (like you you are going to print a book of your solutions), Deadline 25th November. You can pass them written or orally on Fridays evenings. Do it if you want to have MAX in the retake(if so happened) and in the exam in the end of the course.

[https://forms.gle/DQUEyuh1vuXgdtr6A Homework 4 (Number theory)], Deadline with bonus 29th December

==Semester 1 ==

[https://docs.google.com/spreadsheets/d/1YHhkk8TCm_qPF0tXyGe7rc-DzubrgSESZUoW6fHMLZA/edit?usp=sharing Current grades and comments]

== References ==

1. [http://discrete.openmathbooks.org/dmoi3.html Discrete Mathematics (An Open Introduction) by Oscar Levin,] p. 197 Logics. Many simple problems with solution to feel the topic.

2. [https://drive.google.com/file/d/1mmNLLQ0--EDihGNRKwSyXLOA1KL7A0lD/view?usp=sharing Lecture notes by Evgeny Dashkov]

PLUS: there is a [https://youtube.com/playlist?list=PLEwK9wdS5g0pk-1YWDc3hezRt_rNpQDf8 folder with records on wikipage ]

3. [http://www.mccme.ru/free-books/shen/shen-induction.pdf Шень А., Математическая индукция. 5-е изд, М.: МЦНМО, 2016.] Many problems to work with three different versions of induction.

== Grading and Results ==

'''Final grade''' = Average(HWs)+ Bonus points

Bonus point number is between 0 to 20. Such points may be given for a variety of auxiliary activities.

Adaptation course in Discrete Math (факультатив)

2022-12-17T13:55:12Z

Nasta.trofimova:

== General Information ==
The main goal of the Discrete Mathematics Adaptation Course is to help students keep up with the course curriculum by discussing the most important and challenging topics in detail. The second very important goal of the course is to teach students to work competently with mathematical definitions and proofs, correctly logically build solutions to problems and prove statements. The topics of the course are coordinated with the "basic" course of the DSBA and SE program, but its study will also be useful for the direction of AMI. The approximate order of topics is sets and logic, functions and relations, the beginning of number theory, combinatorics, graphs, the foundations of probability theory, generating functions.

== Schedule ==

The classes are organised on Wednesdays at 18:10.

== Course materials ==

[https://t.me/+113aheknlsxmYzVi Chat in Telegram]

'''First semester'''

{| class="wikitable"
|-
! Date !! Topic !! Problem Set !! Class note !! Video
|-
|| 21.09.22 || Statements, connectives, quantifiers || [https://drive.google.com/file/d/1kbtRp8c79zE2AspfVb4ZfGZLJRy9Z5j2/view?usp=drivesdk Problem Set 1]|| - ||
|-
|| 28.09.22 || Validity of statements, types of proof|| [https://drive.google.com/file/d/1Q2OlmVzXf4P0ocd3eBet4ktoJ1h1DZyn/view?usp=sharing Problem Set 2] || [https://drive.google.com/file/d/11pdljFmpW57o5OqBH40YwioTW_Ebs_gK/view?usp=sharing Solutions] || -
|-
|| 7.10.22 || Three types of mathematical induction || [https://drive.google.com/file/d/14h2jy4W7KgxBffxE8TKh_13rSG3Wy_Ll/view?usp=sharing Problem Set 3] ||[https://drive.google.com/file/d/1yFnH5QBNxM-1ajoA5y7w9wV_31XeBwWp/view?usp=sharing Solutions] || [https://youtu.be/nljNhVjlnXg Video 3]
|-
|| 14.10.22 || Proofs with induction || [https://drive.google.com/file/d/13vsHkpBV8riwyKOTCh1v1heuAqf0L9nK/view?usp=sharing Problem Set 4] ||[https://drive.google.com/file/d/1PZD-YWikatG9jCbcc1r_Eo5t0y-kdcpj/view?usp=sharing Solutions] || -
|-
|| 21.10.22 || Divisibility. Calculation of remainders. Direct proofs. || [https://drive.google.com/file/d/1rHfC1WRv4IB8kNRMynVWv0C26PXGi137/view?usp=sharing Problem Set 5] ||[https://drive.google.com/file/d/1CvWAD5pDmMB8JFWSFNxOrrT7-Jfp_0Wd/view?usp=sharing Solutions] ||
[https://youtu.be/-OIYkDOkLyk Video 5]
|-
|| 11.11.22 || Great commod divider, the main thorem of arithmetic, direct proofs. || [https://drive.google.com/file/d/1CrF9W2rXFiTMKFoxZO-PJDmhYAx6Ql84/view?usp=share_link Problem Set 6] ||[https://drive.google.com/file/d/1TWSgbLrRtZWRrbneebExE4BPoDzLU4-b/view?usp=share_link Solutions] ||
[https://youtu.be/_2RRlq21gqM Video 6]
|-
|| 19.11.22 || Fermat's Little theorem, inverse elements in groups $\mathbb{Z}_p$, congruences. || [https://drive.google.com/file/d/1IF6rqwLN0Bq8n07mxQ3CAmoMfWplJ3OR/view?usp=share_link Problem Set 7] ||[https://drive.google.com/file/d/1FZevxpUjcPrrtCbxHn-HRh1odDamJqlq/view?usp=share_link Solutions] ||
[https://youtu.be/peuzIDzh1bE Video 7]
|-
|| 25.11.22 || Fermat's Little theorem, inverse elements in groups $\mathbb{Z}_p$, congruences. || [https://drive.google.com/file/d/1CYGJ7B5d426ChuZBozzsLKwMVZeVPgQJ/view?usp=share_link Problem Set 8] ||[https://drive.google.com/file/d/1_PCu2dDhIgN7uE1ijLGLH1USapPskGWH/view?usp=share_link Solutions] ||
[ -]
|-
|| 2.12.22 || Application of Euler's theorem and Euclidean algorithm, cryptography || [https://drive.google.com/file/d/1Oq3grvUbG-yBBbrHqhK_4Ylz4Io-D1Lw/view?usp=share_link Problem Set 9] ||[https://drive.google.com/file/d/1BFDh6-6KVmb65w7qDEQprP6BYUMUW6AQ/view?usp=share_link Solutions] ||
[https://youtu.be/HPpI7VpHrWY Video 9]
|-
|| 9.12.22 || Sets, direct proofs of set identities || [https://drive.google.com/file/d/1C6I_cviJwznCLZ5BKtxUtlUrjpp4Kegw/view?usp=share_link Problem Set 10] ||[https://drive.google.com/file/d/179jjcjhdU0LschqhPEFMPJylunwRiofA/view?usp=share_link Solutions] || [https://youtu.be/7Gk3JxRpeWU Video 10]
|-
|| 16.12.22 || Operations with sets, cardinality and power set || [https://drive.google.com/file/d/1D9A7QTq-7dPN8Xz_jQhsYIknX8cukhZD/view?usp=share_link Problem Set 11] ||[https://drive.google.com/file/d/1B1snvrzqMgUMDEEQqOHVzomfWVwf2t07/view?usp=share_link Solutions] ||
[ Video 11]
|}

[https://drive.google.com/file/d/163PgGw33FTt3PUVdVBYCjIHluftfZVol/view?usp=sharing Last year retake]

[https://drive.google.com/file/d/1bljTOb3x0kvYy7cslTOC4B3StYOHi3CX/view Last year test 1]

== Homeworks ==
[https://forms.gle/TAgL2eUkhSyhZKLD9 Homework 1 (Logics)], Deadline 31st October

[https://forms.gle/pVA1a8xbeP54RqAQ7 Homework 2 (Induction)], Deadline 31st November, better to complete before the November Test

Hint🦉 in Problem 5: Do not try to prove P(n) out of P(n-1). Assume that P(1), P(2), ...P(n-1) are all true. For proving P(n) say: lets find the biggest Fibonacci number F_i<n. Then, n = F_i + k. For the k apply your assumption😉😉

[https://drive.google.com/file/d/1k8SKmN9J_DdSs8ibP_9b52n8LxiPf_8U/view?usp=share_link Homework 3]: write down solutions to exam 1 in a perfect manner (like you you are going to print a book of your solutions), Deadline 25th November. You can pass them written or orally on Fridays evenings. Do it if you want to have MAX in the retake(if so happened) and in the exam in the end of the course.

[https://forms.gle/DQUEyuh1vuXgdtr6A Homework 4 (Number theory)], Deadline with bonus 29th December

==Semester 1 ==

[https://docs.google.com/spreadsheets/d/1YHhkk8TCm_qPF0tXyGe7rc-DzubrgSESZUoW6fHMLZA/edit?usp=sharing Current grades and comments]

== References ==

1. [http://discrete.openmathbooks.org/dmoi3.html Discrete Mathematics (An Open Introduction) by Oscar Levin,] p. 197 Logics. Many simple problems with solution to feel the topic.

2. [https://drive.google.com/file/d/1mmNLLQ0--EDihGNRKwSyXLOA1KL7A0lD/view?usp=sharing Lecture notes by Evgeny Dashkov]

PLUS: there is a [https://youtube.com/playlist?list=PLEwK9wdS5g0pk-1YWDc3hezRt_rNpQDf8 folder with records on wikipage ]

3. [http://www.mccme.ru/free-books/shen/shen-induction.pdf Шень А., Математическая индукция. 5-е изд, М.: МЦНМО, 2016.] Many problems to work with three different versions of induction.

== Grading and Results ==

'''Final grade''' = Average(HWs)+ Bonus points

Bonus point number is between 0 to 20. Such points may be given for a variety of auxiliary activities.

Discrete Mathematics DSBA 2022/2023

2022-12-15T21:31:52Z

Nasta.trofimova: /* Assignment deadlines */

== Instructors ==

=== The lecturer ===
My name is Evgeny Dashkov. Feel free to contact me via email: edashkov@gmail.com, [https://t.me/edashkov Telegram], or [https://vk.com/evgeny.v.dashkov VK].

=== Seminar instructors ===
{| class="wikitable" style="text-align:center"
|-
! Group !! 221 !! 222 !! 223 !! 224
|-
|| Teachers || Evgeny Dashkov ||colspan="2"| Boris Danilov [https://t.me/brdann Telegram]|| Trofimova Anastasia [https://t.me/AnastasiiaTrofimova Telegram]
|-
|| Teaching Assistants || Arseny Bolotnikov [https://t.me/l0i4b Telegram] ||Daria Ivanova [https://t.me/ivanovskayaaaaa Telegram]|| Artem Ilin [https://t.me/artem_ilinn Telegram] || Marianna Kouis [https://t.me/mariannakouis Telegram]
|-
|| Lecturer’s Assistant || colspan="4"| Alyona Chislova [https://t.me/alenka_chislova Telegram]
|}

== Current performance ==

[https://docs.google.com/spreadsheets/d/1KoXyABY4alQu-Gw3HsYy3Vco9rfvHdYQZuUjE_ERJB8/edit?usp=sharing The Table]

== Homework ==
The homework includes a few problem sets, one in a fortnight or so (the deadlines are announced on giving each set). Every problem set consists of about 10 – 15 problems, some of which are labeled as ‘bonus’ while all the remaining are considered ‘ordinary’. One can get either 0, ½, or 1 point for each problem. For the entire homework, two values are computed:

HW = (the sum of points given for ordinary problems) / #(ordinary problems);

HW* = (the sum of points given for bonus problems) / #(bonus problems).

The value HW1 is similar to HW but restricted to the problem sets given in Module 1.

A student may be required to explain orally his written solution to any problem. His grade for the problem may be decreased if he fails to do so properly.

== Exam 1 ==
A written examination is held past Module 1. Students may not consult any sources during the exam. Some problems of the exam are labeled as ‘bonus’; the others are ‘ordinary’. Each problem solution is graded with either 0, ¼, ½, ¾, or 1 point, and the entire exam with two values:

Exam1 = (the sum of points given for ordinary problems) / #(ordinary problems);

Exam1* = (the sum of points given for bonus problems) / #(bonus problems)

== Colloquium ==
An oral colloquium is held at the beginning of Module 3. Each student is given two questions concerning statements and definitions as well as one question requiring a proof. After no less than 45 minutes of preparation (when using any literature is allowed), the student is required to answer ‘from scratch’, that is, with no recourse to any materials. The examiner may pose additional questions as he sees fit. The student may get from 0 to 7 integer points for his answer; the value

Colloq = (the score given) / 7

is then computed.

== Exam 2 ==
A written examination is held at the end of the Course. Students may not consult any sources during the exam. The examination takes about 120 minutes. Some problems of the exam are labeled as ‘bonus’; the others are ‘ordinary’. Each problem solution is graded with either 0, ¼, ½, ¾, or 1 point; finally, two values are computed:

Exam2 = (the sum of points given for ordinary problems) / #(ordinary problems);

Exam2* = (the sum of points given for bonus problems) / #(bonus problems).

== Bonus activities ==
The students may be graded for a variety of ‘bonus activities’ (like quizzes, etc.) with an overall integer value Bonus from 0 to 25.

== Exam retaking ==
Examinations 1 and 2 are subject to be retaken if Module 1 grade or Final grade (see below), respectively, is unsatisfactory. Retaking the exam is similar to the regular examination. The resulting grade is substituted for that of the latter. The last try Commission retaking is held for those whose final grade is still unsatisfactory after the retaking. A designated Commission carefully examines the student’s performance and gives him a final mark not better than ‘satisfactory’; at that the Commission is not bound by the grading formulas herein.

== Course materials ==

[https://t.me/joinchat/T_YTN4IG1vAJNWT9 Course chat].

=== Lecture notes ===

https://drive.google.com/file/d/1mmNLLQ0--EDihGNRKwSyXLOA1KL7A0lD/view?usp=sharing

=== Classes recordings ===

https://disk.yandex.ru/d/enYKJ6O8NN_3lQ

=== Lecture video archive ===

https://youtube.com/playlist?list=PLEwK9wdS5g0pk-1YWDc3hezRt_rNpQDf8

=== Other resources ===
* [https://tinyurl.com/rwky5vmk The Course's Google Directory]

* [https://www.youtube.com/playlist?list=PL1Uob8iPTHGTidrmrqEHTJ96Pt3-PmML4 Past years' videos]

* We have a [https://meet.edashkov.net.ru dedicated server] to hold an online meeting if we need one.

== Problem sets ==

=== Class problems ===

* [https://drive.google.com/file/d/1EP-diSuOTn9f0ryg18Z2w0xjEp8j0bnl/view?usp=sharing Problem set 1]

* [https://drive.google.com/file/d/12ct99-ORd7A94Gh5g4Nf9riv7UqNMSRc/view?usp=sharing Problem set 2]

* [https://drive.google.com/file/d/1yKKqLsS99V4AhCYqbjafuav2CMCdQTOQ/view?usp=sharing Problem set 3]

* [https://drive.google.com/file/d/1YgH_AdCk4GcKC0KH7xBA4-sUnOYkUvUK/view?usp=share_link Problem set 4]

* [https://drive.google.com/file/d/1M556PSgTJOo5W-AxYEXjFu94VfledpF5/view?usp=share_link Problem set 5]

* [https://drive.google.com/file/d/1-ylVViaBgzxEM-M7Rvrz2iggtK6UiJTY/view?usp=share_link Problem set 6]

=== Homework problems ===

* [https://drive.google.com/file/d/1A8lFPdI3ZvC1vOgz2KEpYcuWOFlsQvb1/view?usp=sharing Homework 1]

* [https://drive.google.com/file/d/1LOPPwGjyVleR_mclxTKUJ_bxFrxt44sW/view?usp=sharing Homework 2a]

* [https://drive.google.com/file/d/1W7k1OTiIMlPOpo-2mwmGegrc4RDHz5_j/view?usp=share_link Homework 2b]

* [https://drive.google.com/file/d/1UvF-3gRwMrnsDAT9H4KDpoUafhrthKPw/view?usp=share_link Homework 3]

=== Assignment deadlines ===

{| class="wikitable"
|-
! Home problem set !! colspan="11" | Deadline
|-
| || 221 || 222 || 223 || 224
|-
| HW 1 №1-3 || || 22.IX || 22.IX || 22.IX
|-
| HW 1 || October 6 || October 6 || October 6 || October 6
|-
| HW 2a №1-3 || || October 20 || October 20 ||
|-
| HW 2a || October 24 || October 27 || October 27 || October 27
|-
| HW 2b №1-7 || November 30 || November 20 || November 20 || November 20
|-
| HW 2b №8-14 || December 14 || December 4 || December 4 || December 4
|-
| HW 3 №1-3 || || December 22 || December 22 || December 22
|}

'''Each deadline is set by the respective group's instructor.'''

== Grading system ==
For the final grading, we compute the following values:

Module 1 grade = round ((50*HW1 + 50*Exam1)/100);

basic = (21*Exam1 + 21*Colloq + 28*HW + 30*Exam2)/100;

adv = (30*Exam1* + Bonus + 35*HW* + 35*Exam2*)/100;

Final grade = round(min(10, 8 * basic + 2 * adv)).

The final grade is rounded half up to an integer. All the other values are reported with the greatest precision available.

== Recommended reading ==
''Please notice that '''The Book''' for our Course does not exist. The latter is based on many sources.''

# Anderson J. A., Discrete Mathematics With Combinatorics. Prentice Hall, 2003.
# Biggs N. L., Discrete mathematics. 2nd ed., New York; Oxford: Oxford University Press, 2004.
# Gavrilov G. P., Sapozhenko A. A. Problems and Exercises in Discrete Mathematics. Kluwer Texts in the Mathematical Sciences 14. Springer, 1996.
# [http://courses.csail.mit.edu/6.042/spring17/mcs.pdf Lehman E., Thomson Leighton F., Meyer A. R. Mathematics for Computer Science, 2017.]
# [http://www.cs.elte.hu/~lovasz/dmbook.ps Lovasz L., Vesztergombi K. Discrete Mathematics. Lecture Notes; Yale University, 1999.]
# Melnikov O., Sarvanov V., Tyshkevich R., Yemelichev V., Zverovich I. Exercises in Graph Theory. Kluwer Texts in the Mathematical Sciences 19. Springer, 1998.
# Rosen K. H. Discrete Mathematics and Its Applications. McGraw-Hill, 1999.
# Stein C., Drysdale R. L., Bogart K. Discrete mathematics for computer scientists. Addison-Wesley, 2010.
# Vinogradov I. M. Elements of number theory. Dover, 1954.

=== In Russian ===
''If you understand Russian (by any chance), you will probably benefit from reading the following books.''

# Виноградов И. М. Основы теории чисел. 9-е изд., М.: Наука, 1981.
# [http://rubtsov.su/public/DM-HSE-Draft.pdf Вялый М., Подольский В., Рубцов А., Шварц Д., Шень А. Лекции по дискретной математике.]
# Гаврилов Г. П., Сапоженко А. А. Задачи и упражнения по дискретной математике. 3-е изд., М.: ФИЗМАТЛИТ, 2004.
# [https://drive.google.com/file/d/1RM6KX_reBFwUXesWGUEu0sFn2NCaBgvz/view?usp=sharing Дашков Е. В. Введение в математическую логику. Множества и отношения. М.: МФТИ, 2019.]
# Зубков А. М., Севастьянов Б. А., Чистяков В. П. Сборник задач по теории вероятностей. 2-е изд., М.: Наука, 1989.
# Мельников О. И. Теория графов в занимательных задачах. 5-е изд., М.: Книжный дом "ЛИБРОКОМ", 2013.
# [http://www.mccme.ru/free-books/shen/shen-induction.pdf Шень А., Математическая индукция. 5-е изд, М.: МЦНМО, 2016.]

Adaptation course in Discrete Math (факультатив)

2022-12-15T21:29:49Z

Nasta.trofimova:

== General Information ==
The main goal of the Discrete Mathematics Adaptation Course is to help students keep up with the course curriculum by discussing the most important and challenging topics in detail. The second very important goal of the course is to teach students to work competently with mathematical definitions and proofs, correctly logically build solutions to problems and prove statements. The topics of the course are coordinated with the "basic" course of the DSBA and SE program, but its study will also be useful for the direction of AMI. The approximate order of topics is sets and logic, functions and relations, the beginning of number theory, combinatorics, graphs, the foundations of probability theory, generating functions.

== Schedule ==

The classes are organised on Wednesdays at 18:10.

== Course materials ==

[https://t.me/+113aheknlsxmYzVi Chat in Telegram]

'''First semester'''

{| class="wikitable"
|-
! Date !! Topic !! Problem Set !! Class note !! Video
|-
|| 21.09.22 || Statements, connectives, quantifiers || [https://drive.google.com/file/d/1kbtRp8c79zE2AspfVb4ZfGZLJRy9Z5j2/view?usp=drivesdk Problem Set 1]|| - ||
|-
|| 28.09.22 || Validity of statements, types of proof|| [https://drive.google.com/file/d/1Q2OlmVzXf4P0ocd3eBet4ktoJ1h1DZyn/view?usp=sharing Problem Set 2] || [https://drive.google.com/file/d/11pdljFmpW57o5OqBH40YwioTW_Ebs_gK/view?usp=sharing Solutions] || -
|-
|| 7.10.22 || Three types of mathematical induction || [https://drive.google.com/file/d/14h2jy4W7KgxBffxE8TKh_13rSG3Wy_Ll/view?usp=sharing Problem Set 3] ||[https://drive.google.com/file/d/1yFnH5QBNxM-1ajoA5y7w9wV_31XeBwWp/view?usp=sharing Solutions] || [https://youtu.be/nljNhVjlnXg Video 3]
|-
|| 14.10.22 || Proofs with induction || [https://drive.google.com/file/d/13vsHkpBV8riwyKOTCh1v1heuAqf0L9nK/view?usp=sharing Problem Set 4] ||[https://drive.google.com/file/d/1PZD-YWikatG9jCbcc1r_Eo5t0y-kdcpj/view?usp=sharing Solutions] || -
|-
|| 21.10.22 || Divisibility. Calculation of remainders. Direct proofs. || [https://drive.google.com/file/d/1rHfC1WRv4IB8kNRMynVWv0C26PXGi137/view?usp=sharing Problem Set 5] ||[https://drive.google.com/file/d/1CvWAD5pDmMB8JFWSFNxOrrT7-Jfp_0Wd/view?usp=sharing Solutions] ||
[https://youtu.be/-OIYkDOkLyk Video 5]
|-
|| 11.11.22 || Great commod divider, the main thorem of arithmetic, direct proofs. || [https://drive.google.com/file/d/1CrF9W2rXFiTMKFoxZO-PJDmhYAx6Ql84/view?usp=share_link Problem Set 6] ||[https://drive.google.com/file/d/1TWSgbLrRtZWRrbneebExE4BPoDzLU4-b/view?usp=share_link Solutions] ||
[https://youtu.be/_2RRlq21gqM Video 6]
|-
|| 19.11.22 || Fermat's Little theorem, inverse elements in groups $\mathbb{Z}_p$, congruences. || [https://drive.google.com/file/d/1IF6rqwLN0Bq8n07mxQ3CAmoMfWplJ3OR/view?usp=share_link Problem Set 7] ||[https://drive.google.com/file/d/1FZevxpUjcPrrtCbxHn-HRh1odDamJqlq/view?usp=share_link Solutions] ||
[https://youtu.be/peuzIDzh1bE Video 7]
|-
|| 25.11.22 || Fermat's Little theorem, inverse elements in groups $\mathbb{Z}_p$, congruences. || [https://drive.google.com/file/d/1CYGJ7B5d426ChuZBozzsLKwMVZeVPgQJ/view?usp=share_link Problem Set 8] ||[https://drive.google.com/file/d/1_PCu2dDhIgN7uE1ijLGLH1USapPskGWH/view?usp=share_link Solutions] ||
[ -]
|-
|| 2.12.22 || Application of Euler's theorem and Euclidean algorithm, cryptography || [https://drive.google.com/file/d/1Oq3grvUbG-yBBbrHqhK_4Ylz4Io-D1Lw/view?usp=share_link Problem Set 9] ||[https://drive.google.com/file/d/1BFDh6-6KVmb65w7qDEQprP6BYUMUW6AQ/view?usp=share_link Solutions] ||
[https://youtu.be/HPpI7VpHrWY Video 9]
|-
|| 9.12.22 || Sets, direct proofs of set identities || [https://drive.google.com/file/d/1C6I_cviJwznCLZ5BKtxUtlUrjpp4Kegw/view?usp=share_link Problem Set 10] ||[https://drive.google.com/file/d/179jjcjhdU0LschqhPEFMPJylunwRiofA/view?usp=share_link Solutions] || [https://youtu.be/7Gk3JxRpeWU Video 10]
|-
|| 16.12.22 || Operations with sets, cardinality and power set || [https://drive.google.com/file/d/1D9A7QTq-7dPN8Xz_jQhsYIknX8cukhZD/view?usp=share_link Problem Set 11] ||[ Solutions] ||
[ Video 11]
|}

[https://drive.google.com/file/d/163PgGw33FTt3PUVdVBYCjIHluftfZVol/view?usp=sharing Last year retake]

[https://drive.google.com/file/d/1bljTOb3x0kvYy7cslTOC4B3StYOHi3CX/view Last year test 1]

== Homeworks ==
[https://forms.gle/TAgL2eUkhSyhZKLD9 Homework 1 (Logics)], Deadline 31st October

[https://forms.gle/pVA1a8xbeP54RqAQ7 Homework 2 (Induction)], Deadline 31st November, better to complete before the November Test

Hint🦉 in Problem 5: Do not try to prove P(n) out of P(n-1). Assume that P(1), P(2), ...P(n-1) are all true. For proving P(n) say: lets find the biggest Fibonacci number F_i<n. Then, n = F_i + k. For the k apply your assumption😉😉

[https://drive.google.com/file/d/1k8SKmN9J_DdSs8ibP_9b52n8LxiPf_8U/view?usp=share_link Homework 3]: write down solutions to exam 1 in a perfect manner (like you you are going to print a book of your solutions), Deadline 25th November. You can pass them written or orally on Fridays evenings. Do it if you want to have MAX in the retake(if so happened) and in the exam in the end of the course.

[https://forms.gle/DQUEyuh1vuXgdtr6A Homework 4 (Number theory)], Deadline with bonus 29th December

==Semester 1 ==

[https://docs.google.com/spreadsheets/d/1YHhkk8TCm_qPF0tXyGe7rc-DzubrgSESZUoW6fHMLZA/edit?usp=sharing Current grades and comments]

== References ==

1. [http://discrete.openmathbooks.org/dmoi3.html Discrete Mathematics (An Open Introduction) by Oscar Levin,] p. 197 Logics. Many simple problems with solution to feel the topic.

2. [https://drive.google.com/file/d/1mmNLLQ0--EDihGNRKwSyXLOA1KL7A0lD/view?usp=sharing Lecture notes by Evgeny Dashkov]

PLUS: there is a [https://youtube.com/playlist?list=PLEwK9wdS5g0pk-1YWDc3hezRt_rNpQDf8 folder with records on wikipage ]

3. [http://www.mccme.ru/free-books/shen/shen-induction.pdf Шень А., Математическая индукция. 5-е изд, М.: МЦНМО, 2016.] Many problems to work with three different versions of induction.

== Grading and Results ==

'''Final grade''' = Average(HWs)+ Bonus points

Bonus point number is between 0 to 20. Such points may be given for a variety of auxiliary activities.

Adaptation course in Discrete Math (факультатив)

2022-12-15T21:29:28Z

Nasta.trofimova:

== General Information ==
The main goal of the Discrete Mathematics Adaptation Course is to help students keep up with the course curriculum by discussing the most important and challenging topics in detail. The second very important goal of the course is to teach students to work competently with mathematical definitions and proofs, correctly logically build solutions to problems and prove statements. The topics of the course are coordinated with the "basic" course of the DSBA and SE program, but its study will also be useful for the direction of AMI. The approximate order of topics is sets and logic, functions and relations, the beginning of number theory, combinatorics, graphs, the foundations of probability theory, generating functions.

== Schedule ==

The classes are organised on Wednesdays at 18:10.

== Course materials ==

[https://t.me/+113aheknlsxmYzVi Chat in Telegram]

'''First semester'''

{| class="wikitable"
|-
! Date !! Topic !! Problem Set !! Class note !! Video
|-
|| 21.09.22 || Statements, connectives, quantifiers || [https://drive.google.com/file/d/1kbtRp8c79zE2AspfVb4ZfGZLJRy9Z5j2/view?usp=drivesdk Problem Set 1]|| - ||
|-
|| 28.09.22 || Validity of statements, types of proof|| [https://drive.google.com/file/d/1Q2OlmVzXf4P0ocd3eBet4ktoJ1h1DZyn/view?usp=sharing Problem Set 2] || [https://drive.google.com/file/d/11pdljFmpW57o5OqBH40YwioTW_Ebs_gK/view?usp=sharing Solutions] || -
|-
|| 7.10.22 || Three types of mathematical induction || [https://drive.google.com/file/d/14h2jy4W7KgxBffxE8TKh_13rSG3Wy_Ll/view?usp=sharing Problem Set 3] ||[https://drive.google.com/file/d/1yFnH5QBNxM-1ajoA5y7w9wV_31XeBwWp/view?usp=sharing Solutions] || [https://youtu.be/nljNhVjlnXg Video 3]
|-
|| 14.10.22 || Proofs with induction || [https://drive.google.com/file/d/13vsHkpBV8riwyKOTCh1v1heuAqf0L9nK/view?usp=sharing Problem Set 4] ||[https://drive.google.com/file/d/1PZD-YWikatG9jCbcc1r_Eo5t0y-kdcpj/view?usp=sharing Solutions] || -
|-
|| 21.10.22 || Divisibility. Calculation of remainders. Direct proofs. || [https://drive.google.com/file/d/1rHfC1WRv4IB8kNRMynVWv0C26PXGi137/view?usp=sharing Problem Set 5] ||[https://drive.google.com/file/d/1CvWAD5pDmMB8JFWSFNxOrrT7-Jfp_0Wd/view?usp=sharing Solutions] ||
[https://youtu.be/-OIYkDOkLyk Video 5]
|-
|| 11.11.22 || Great commod divider, the main thorem of arithmetic, direct proofs. || [https://drive.google.com/file/d/1CrF9W2rXFiTMKFoxZO-PJDmhYAx6Ql84/view?usp=share_link Problem Set 6] ||[https://drive.google.com/file/d/1TWSgbLrRtZWRrbneebExE4BPoDzLU4-b/view?usp=share_link Solutions] ||
[https://youtu.be/_2RRlq21gqM Video 6]
|-
|| 19.11.22 || Fermat's Little theorem, inverse elements in groups $\mathbb{Z}_p$, congruences. || [https://drive.google.com/file/d/1IF6rqwLN0Bq8n07mxQ3CAmoMfWplJ3OR/view?usp=share_link Problem Set 7] ||[https://drive.google.com/file/d/1FZevxpUjcPrrtCbxHn-HRh1odDamJqlq/view?usp=share_link Solutions] ||
[https://youtu.be/peuzIDzh1bE Video 7]
|-
|| 25.11.22 || Fermat's Little theorem, inverse elements in groups $\mathbb{Z}_p$, congruences. || [https://drive.google.com/file/d/1CYGJ7B5d426ChuZBozzsLKwMVZeVPgQJ/view?usp=share_link Problem Set 8] ||[https://drive.google.com/file/d/1_PCu2dDhIgN7uE1ijLGLH1USapPskGWH/view?usp=share_link Solutions] ||
[ -]
|-
|| 2.12.22 || Application of Euler's theorem and Euclidean algorithm, cryptography || [https://drive.google.com/file/d/1Oq3grvUbG-yBBbrHqhK_4Ylz4Io-D1Lw/view?usp=share_link Problem Set 9] ||[https://drive.google.com/file/d/1BFDh6-6KVmb65w7qDEQprP6BYUMUW6AQ/view?usp=share_link Solutions] ||
[https://youtu.be/HPpI7VpHrWY Video 9]
|-
|| 9.12.22 || Sets, direct proofs of set identities || [https://drive.google.com/file/d/1C6I_cviJwznCLZ5BKtxUtlUrjpp4Kegw/view?usp=share_link Problem Set 10] ||[https://drive.google.com/file/d/179jjcjhdU0LschqhPEFMPJylunwRiofA/view?usp=share_link Solutions] || [https://youtu.be/7Gk3JxRpeWU Video 10]
|-
|| 16.12.22 || Operations with sets, cardinality and power set || [https://drive.google.com/file/d/1D9A7QTq-7dPN8Xz_jQhsYIknX8cukhZD/view?usp=share_link Problem Set 11] ||[ Solutions] ||
[ Video 11]
|}

[https://drive.google.com/file/d/163PgGw33FTt3PUVdVBYCjIHluftfZVol/view?usp=sharing Last year retake]

[https://drive.google.com/file/d/1bljTOb3x0kvYy7cslTOC4B3StYOHi3CX/view Last year test 1]

== Homeworks ==
[https://forms.gle/TAgL2eUkhSyhZKLD9 Homework 1 (Logics)], Deadline 31st October

[https://forms.gle/pVA1a8xbeP54RqAQ7 Homework 2 (Induction)], Deadline 31st November, better to complete before the November Test
Hint🦉: Do not try to prove P(n) out of P(n-1). Assume that P(1), P(2), ...P(n-1) are all true. For proving P(n) say: lets find the biggest Fibonacci number F_i<n. Then, n = F_i + k. For the k apply your assumption😉😉

[https://drive.google.com/file/d/1k8SKmN9J_DdSs8ibP_9b52n8LxiPf_8U/view?usp=share_link Homework 3]: write down solutions to exam 1 in a perfect manner (like you you are going to print a book of your solutions), Deadline 25th November. You can pass them written or orally on Fridays evenings. Do it if you want to have MAX in the retake(if so happened) and in the exam in the end of the course.

[https://forms.gle/DQUEyuh1vuXgdtr6A Homework 4 (Number theory)], Deadline with bonus 29th December

==Semester 1 ==

[https://docs.google.com/spreadsheets/d/1YHhkk8TCm_qPF0tXyGe7rc-DzubrgSESZUoW6fHMLZA/edit?usp=sharing Current grades and comments]

== References ==

1. [http://discrete.openmathbooks.org/dmoi3.html Discrete Mathematics (An Open Introduction) by Oscar Levin,] p. 197 Logics. Many simple problems with solution to feel the topic.

2. [https://drive.google.com/file/d/1mmNLLQ0--EDihGNRKwSyXLOA1KL7A0lD/view?usp=sharing Lecture notes by Evgeny Dashkov]

PLUS: there is a [https://youtube.com/playlist?list=PLEwK9wdS5g0pk-1YWDc3hezRt_rNpQDf8 folder with records on wikipage ]

3. [http://www.mccme.ru/free-books/shen/shen-induction.pdf Шень А., Математическая индукция. 5-е изд, М.: МЦНМО, 2016.] Many problems to work with three different versions of induction.

== Grading and Results ==

'''Final grade''' = Average(HWs)+ Bonus points

Bonus point number is between 0 to 20. Such points may be given for a variety of auxiliary activities.

Adaptation course in Discrete Math (факультатив)

2022-12-15T21:28:31Z

Nasta.trofimova:

== General Information ==
The main goal of the Discrete Mathematics Adaptation Course is to help students keep up with the course curriculum by discussing the most important and challenging topics in detail. The second very important goal of the course is to teach students to work competently with mathematical definitions and proofs, correctly logically build solutions to problems and prove statements. The topics of the course are coordinated with the "basic" course of the DSBA and SE program, but its study will also be useful for the direction of AMI. The approximate order of topics is sets and logic, functions and relations, the beginning of number theory, combinatorics, graphs, the foundations of probability theory, generating functions.

== Schedule ==

The classes are organised on Wednesdays at 18:10.

== Course materials ==

[https://t.me/+113aheknlsxmYzVi Chat in Telegram]

'''First semester'''

{| class="wikitable"
|-
! Date !! Topic !! Problem Set !! Class note !! Video
|-
|| 21.09.22 || Statements, connectives, quantifiers || [https://drive.google.com/file/d/1kbtRp8c79zE2AspfVb4ZfGZLJRy9Z5j2/view?usp=drivesdk Problem Set 1]|| - ||
|-
|| 28.09.22 || Validity of statements, types of proof|| [https://drive.google.com/file/d/1Q2OlmVzXf4P0ocd3eBet4ktoJ1h1DZyn/view?usp=sharing Problem Set 2] || [https://drive.google.com/file/d/11pdljFmpW57o5OqBH40YwioTW_Ebs_gK/view?usp=sharing Solutions] || -
|-
|| 7.10.22 || Three types of mathematical induction || [https://drive.google.com/file/d/14h2jy4W7KgxBffxE8TKh_13rSG3Wy_Ll/view?usp=sharing Problem Set 3] ||[https://drive.google.com/file/d/1yFnH5QBNxM-1ajoA5y7w9wV_31XeBwWp/view?usp=sharing Solutions] || [https://youtu.be/nljNhVjlnXg Video 3]
|-
|| 14.10.22 || Proofs with induction || [https://drive.google.com/file/d/13vsHkpBV8riwyKOTCh1v1heuAqf0L9nK/view?usp=sharing Problem Set 4] ||[https://drive.google.com/file/d/1PZD-YWikatG9jCbcc1r_Eo5t0y-kdcpj/view?usp=sharing Solutions] || -
|-
|| 21.10.22 || Divisibility. Calculation of remainders. Direct proofs. || [https://drive.google.com/file/d/1rHfC1WRv4IB8kNRMynVWv0C26PXGi137/view?usp=sharing Problem Set 5] ||[https://drive.google.com/file/d/1CvWAD5pDmMB8JFWSFNxOrrT7-Jfp_0Wd/view?usp=sharing Solutions] ||
[https://youtu.be/-OIYkDOkLyk Video 5]
|-
|| 11.11.22 || Great commod divider, the main thorem of arithmetic, direct proofs. || [https://drive.google.com/file/d/1CrF9W2rXFiTMKFoxZO-PJDmhYAx6Ql84/view?usp=share_link Problem Set 6] ||[https://drive.google.com/file/d/1TWSgbLrRtZWRrbneebExE4BPoDzLU4-b/view?usp=share_link Solutions] ||
[https://youtu.be/_2RRlq21gqM Video 6]
|-
|| 19.11.22 || Fermat's Little theorem, inverse elements in groups $\mathbb{Z}_p$, congruences. || [https://drive.google.com/file/d/1IF6rqwLN0Bq8n07mxQ3CAmoMfWplJ3OR/view?usp=share_link Problem Set 7] ||[https://drive.google.com/file/d/1FZevxpUjcPrrtCbxHn-HRh1odDamJqlq/view?usp=share_link Solutions] ||
[https://youtu.be/peuzIDzh1bE Video 7]
|-
|| 25.11.22 || Fermat's Little theorem, inverse elements in groups $\mathbb{Z}_p$, congruences. || [https://drive.google.com/file/d/1CYGJ7B5d426ChuZBozzsLKwMVZeVPgQJ/view?usp=share_link Problem Set 8] ||[https://drive.google.com/file/d/1_PCu2dDhIgN7uE1ijLGLH1USapPskGWH/view?usp=share_link Solutions] ||
[ -]
|-
|| 2.12.22 || Application of Euler's theorem and Euclidean algorithm, cryptography || [https://drive.google.com/file/d/1Oq3grvUbG-yBBbrHqhK_4Ylz4Io-D1Lw/view?usp=share_link Problem Set 9] ||[https://drive.google.com/file/d/1BFDh6-6KVmb65w7qDEQprP6BYUMUW6AQ/view?usp=share_link Solutions] ||
[https://youtu.be/HPpI7VpHrWY Video 9]
|-
|| 9.12.22 || Sets, direct proofs of set identities || [https://drive.google.com/file/d/1C6I_cviJwznCLZ5BKtxUtlUrjpp4Kegw/view?usp=share_link Problem Set 10] ||[https://drive.google.com/file/d/179jjcjhdU0LschqhPEFMPJylunwRiofA/view?usp=share_link Solutions] || [https://youtu.be/7Gk3JxRpeWU Video 10]
|-
|| 16.12.22 || Operations with sets, cardinality and power set || [https://drive.google.com/file/d/1D9A7QTq-7dPN8Xz_jQhsYIknX8cukhZD/view?usp=share_link Problem Set 11] ||[ Solutions] ||
[ Video 11]
|}

[https://drive.google.com/file/d/163PgGw33FTt3PUVdVBYCjIHluftfZVol/view?usp=sharing Last year retake]

[https://drive.google.com/file/d/1bljTOb3x0kvYy7cslTOC4B3StYOHi3CX/view Last year test 1]

== Homeworks ==
[https://forms.gle/TAgL2eUkhSyhZKLD9 Homework 1 (Logics)], Deadline 31st October

[https://forms.gle/pVA1a8xbeP54RqAQ7 Homework 2 (Induction)], Deadline 31st November, better to complete before the November Test

[https://drive.google.com/file/d/1k8SKmN9J_DdSs8ibP_9b52n8LxiPf_8U/view?usp=share_link Homework 3]: write down solutions to exam 1 in a perfect manner (like you you are going to print a book of your solutions), Deadline 25th November. You can pass them written or orally on Fridays evenings. Do it if you want to have MAX in the retake(if so happened) and in the exam in the end of the course.

[https://forms.gle/DQUEyuh1vuXgdtr6A Homework 4 (Number theory)], Deadline with bonus 29th December

==Semester 1 ==

[https://docs.google.com/spreadsheets/d/1YHhkk8TCm_qPF0tXyGe7rc-DzubrgSESZUoW6fHMLZA/edit?usp=sharing Current grades and comments]

== References ==

1. [http://discrete.openmathbooks.org/dmoi3.html Discrete Mathematics (An Open Introduction) by Oscar Levin,] p. 197 Logics. Many simple problems with solution to feel the topic.

2. [https://drive.google.com/file/d/1mmNLLQ0--EDihGNRKwSyXLOA1KL7A0lD/view?usp=sharing Lecture notes by Evgeny Dashkov]

PLUS: there is a [https://youtube.com/playlist?list=PLEwK9wdS5g0pk-1YWDc3hezRt_rNpQDf8 folder with records on wikipage ]

3. [http://www.mccme.ru/free-books/shen/shen-induction.pdf Шень А., Математическая индукция. 5-е изд, М.: МЦНМО, 2016.] Many problems to work with three different versions of induction.

== Grading and Results ==

'''Final grade''' = Average(HWs)+ Bonus points

Bonus point number is between 0 to 20. Such points may be given for a variety of auxiliary activities.

Adaptation course in Discrete Math (факультатив)

2022-12-15T18:16:47Z

Nasta.trofimova:

== General Information ==
The main goal of the Discrete Mathematics Adaptation Course is to help students keep up with the course curriculum by discussing the most important and challenging topics in detail. The second very important goal of the course is to teach students to work competently with mathematical definitions and proofs, correctly logically build solutions to problems and prove statements. The topics of the course are coordinated with the "basic" course of the DSBA and SE program, but its study will also be useful for the direction of AMI. The approximate order of topics is sets and logic, functions and relations, the beginning of number theory, combinatorics, graphs, the foundations of probability theory, generating functions.

== Schedule ==

The classes are organised on Wednesdays at 18:10.

== Course materials ==

[https://t.me/+113aheknlsxmYzVi Chat in Telegram]

'''First semester'''

{| class="wikitable"
|-
! Date !! Topic !! Problem Set !! Class note !! Video
|-
|| 21.09.22 || Statements, connectives, quantifiers || [https://drive.google.com/file/d/1kbtRp8c79zE2AspfVb4ZfGZLJRy9Z5j2/view?usp=drivesdk Problem Set 1]|| - ||
|-
|| 28.09.22 || Validity of statements, types of proof|| [https://drive.google.com/file/d/1Q2OlmVzXf4P0ocd3eBet4ktoJ1h1DZyn/view?usp=sharing Problem Set 2] || [https://drive.google.com/file/d/11pdljFmpW57o5OqBH40YwioTW_Ebs_gK/view?usp=sharing Solutions] || -
|-
|| 7.10.22 || Three types of mathematical induction || [https://drive.google.com/file/d/14h2jy4W7KgxBffxE8TKh_13rSG3Wy_Ll/view?usp=sharing Problem Set 3] ||[https://drive.google.com/file/d/1yFnH5QBNxM-1ajoA5y7w9wV_31XeBwWp/view?usp=sharing Solutions] || [https://youtu.be/nljNhVjlnXg Video 3]
|-
|| 14.10.22 || Proofs with induction || [https://drive.google.com/file/d/13vsHkpBV8riwyKOTCh1v1heuAqf0L9nK/view?usp=sharing Problem Set 4] ||[https://drive.google.com/file/d/1PZD-YWikatG9jCbcc1r_Eo5t0y-kdcpj/view?usp=sharing Solutions] || -
|-
|| 21.10.22 || Divisibility. Calculation of remainders. Direct proofs. || [https://drive.google.com/file/d/1rHfC1WRv4IB8kNRMynVWv0C26PXGi137/view?usp=sharing Problem Set 5] ||[https://drive.google.com/file/d/1CvWAD5pDmMB8JFWSFNxOrrT7-Jfp_0Wd/view?usp=sharing Solutions] ||
[https://youtu.be/-OIYkDOkLyk Video 5]
|-
|| 11.11.22 || Great commod divider, the main thorem of arithmetic, direct proofs. || [https://drive.google.com/file/d/1CrF9W2rXFiTMKFoxZO-PJDmhYAx6Ql84/view?usp=share_link Problem Set 6] ||[https://drive.google.com/file/d/1TWSgbLrRtZWRrbneebExE4BPoDzLU4-b/view?usp=share_link Solutions] ||
[https://youtu.be/_2RRlq21gqM Video 6]
|-
|| 19.11.22 || Fermat's Little theorem, inverse elements in groups $\mathbb{Z}_p$, congruences. || [https://drive.google.com/file/d/1IF6rqwLN0Bq8n07mxQ3CAmoMfWplJ3OR/view?usp=share_link Problem Set 7] ||[https://drive.google.com/file/d/1FZevxpUjcPrrtCbxHn-HRh1odDamJqlq/view?usp=share_link Solutions] ||
[https://youtu.be/peuzIDzh1bE Video 7]
|-
|| 25.11.22 || Fermat's Little theorem, inverse elements in groups $\mathbb{Z}_p$, congruences. || [https://drive.google.com/file/d/1CYGJ7B5d426ChuZBozzsLKwMVZeVPgQJ/view?usp=share_link Problem Set 8] ||[https://drive.google.com/file/d/1_PCu2dDhIgN7uE1ijLGLH1USapPskGWH/view?usp=share_link Solutions] ||
[ -]
|-
|| 2.12.22 || Application of Euler's theorem and Euclidean algorithm, cryptography || [https://drive.google.com/file/d/1Oq3grvUbG-yBBbrHqhK_4Ylz4Io-D1Lw/view?usp=share_link Problem Set 9] ||[https://drive.google.com/file/d/1BFDh6-6KVmb65w7qDEQprP6BYUMUW6AQ/view?usp=share_link Solutions] ||
[https://youtu.be/HPpI7VpHrWY Video 9]
|-
|| 9.12.22 || Sets, direct proofs of set identities || [https://drive.google.com/file/d/1C6I_cviJwznCLZ5BKtxUtlUrjpp4Kegw/view?usp=share_link Problem Set 10] ||[https://drive.google.com/file/d/179jjcjhdU0LschqhPEFMPJylunwRiofA/view?usp=share_link Solutions] || [https://youtu.be/7Gk3JxRpeWU Video 10]
|-
|| 16.12.22 || Sets. || [ Problem Set 11] ||[ Solutions] ||
[ Video 11]
|}

[https://drive.google.com/file/d/163PgGw33FTt3PUVdVBYCjIHluftfZVol/view?usp=sharing Last year retake]

[https://drive.google.com/file/d/1bljTOb3x0kvYy7cslTOC4B3StYOHi3CX/view Last year test 1]

== Homeworks ==
[https://forms.gle/TAgL2eUkhSyhZKLD9 Homework 1 (Logics)], Deadline 31st October

[https://forms.gle/pVA1a8xbeP54RqAQ7 Homework 2 (Induction)], Deadline 31st November, better to complete before the November Test

[https://drive.google.com/file/d/1k8SKmN9J_DdSs8ibP_9b52n8LxiPf_8U/view?usp=share_link Homework 3]: write down solutions to exam 1 in a perfect manner (like you you are going to print a book of your solutions), Deadline 25th November. You can pass them written or orally on Fridays evenings. Do it if you want to have MAX in the retake(if so happened) and in the exam in the end of the course.

[https://forms.gle/DQUEyuh1vuXgdtr6A Homework 4 (Number theory)], Deadline with bonus 29th December

==Semester 1 ==

[https://docs.google.com/spreadsheets/d/1YHhkk8TCm_qPF0tXyGe7rc-DzubrgSESZUoW6fHMLZA/edit?usp=sharing Current grades and comments]

== References ==

1. [http://discrete.openmathbooks.org/dmoi3.html Discrete Mathematics (An Open Introduction) by Oscar Levin,] p. 197 Logics. Many simple problems with solution to feel the topic.

2. [https://drive.google.com/file/d/1mmNLLQ0--EDihGNRKwSyXLOA1KL7A0lD/view?usp=sharing Lecture notes by Evgeny Dashkov]

PLUS: there is a [https://youtube.com/playlist?list=PLEwK9wdS5g0pk-1YWDc3hezRt_rNpQDf8 folder with records on wikipage ]

3. [http://www.mccme.ru/free-books/shen/shen-induction.pdf Шень А., Математическая индукция. 5-е изд, М.: МЦНМО, 2016.] Many problems to work with three different versions of induction.

== Grading and Results ==

'''Final grade''' = Average(HWs)+ Bonus points

Bonus point number is between 0 to 20. Such points may be given for a variety of auxiliary activities.

Discrete Mathematics DSBA 2022/2023

2022-12-12T13:59:01Z

Nasta.trofimova:

== Instructors ==

=== The lecturer ===
My name is Evgeny Dashkov. Feel free to contact me via email: edashkov@gmail.com, [https://t.me/edashkov Telegram], or [https://vk.com/evgeny.v.dashkov VK].

=== Seminar instructors ===
{| class="wikitable" style="text-align:center"
|-
! Group !! 221 !! 222 !! 223 !! 224
|-
|| Teachers || Evgeny Dashkov ||colspan="2"| Boris Danilov [https://t.me/brdann Telegram]|| Trofimova Anastasia [https://t.me/AnastasiiaTrofimova Telegram]
|-
|| Teaching Assistants || Arseny Bolotnikov [https://t.me/l0i4b Telegram] ||Daria Ivanova [https://t.me/ivanovskayaaaaa Telegram]|| Artem Ilin [https://t.me/artem_ilinn Telegram] || Marianna Kouis [https://t.me/mariannakouis Telegram]
|-
|| Lecturer’s Assistant || colspan="4"| Alyona Chislova [https://t.me/alenka_chislova Telegram]
|}

== Current performance ==

[https://docs.google.com/spreadsheets/d/1KoXyABY4alQu-Gw3HsYy3Vco9rfvHdYQZuUjE_ERJB8/edit?usp=sharing The Table]

== Homework ==
The homework includes a few problem sets, one in a fortnight or so (the deadlines are announced on giving each set). Every problem set consists of about 10 – 15 problems, some of which are labeled as ‘bonus’ while all the remaining are considered ‘ordinary’. One can get either 0, ½, or 1 point for each problem. For the entire homework, two values are computed:

HW = (the sum of points given for ordinary problems) / #(ordinary problems);

HW* = (the sum of points given for bonus problems) / #(bonus problems).

The value HW1 is similar to HW but restricted to the problem sets given in Module 1.

A student may be required to explain orally his written solution to any problem. His grade for the problem may be decreased if he fails to do so properly.

== Exam 1 ==
A written examination is held past Module 1. Students may not consult any sources during the exam. Some problems of the exam are labeled as ‘bonus’; the others are ‘ordinary’. Each problem solution is graded with either 0, ¼, ½, ¾, or 1 point, and the entire exam with two values:

Exam1 = (the sum of points given for ordinary problems) / #(ordinary problems);

Exam1* = (the sum of points given for bonus problems) / #(bonus problems)

== Colloquium ==
An oral colloquium is held at the beginning of Module 3. Each student is given two questions concerning statements and definitions as well as one question requiring a proof. After no less than 45 minutes of preparation (when using any literature is allowed), the student is required to answer ‘from scratch’, that is, with no recourse to any materials. The examiner may pose additional questions as he sees fit. The student may get from 0 to 7 integer points for his answer; the value

Colloq = (the score given) / 7

is then computed.

== Exam 2 ==
A written examination is held at the end of the Course. Students may not consult any sources during the exam. The examination takes about 120 minutes. Some problems of the exam are labeled as ‘bonus’; the others are ‘ordinary’. Each problem solution is graded with either 0, ¼, ½, ¾, or 1 point; finally, two values are computed:

Exam2 = (the sum of points given for ordinary problems) / #(ordinary problems);

Exam2* = (the sum of points given for bonus problems) / #(bonus problems).

== Bonus activities ==
The students may be graded for a variety of ‘bonus activities’ (like quizzes, etc.) with an overall integer value Bonus from 0 to 25.

== Exam retaking ==
Examinations 1 and 2 are subject to be retaken if Module 1 grade or Final grade (see below), respectively, is unsatisfactory. Retaking the exam is similar to the regular examination. The resulting grade is substituted for that of the latter. The last try Commission retaking is held for those whose final grade is still unsatisfactory after the retaking. A designated Commission carefully examines the student’s performance and gives him a final mark not better than ‘satisfactory’; at that the Commission is not bound by the grading formulas herein.

== Course materials ==

[https://t.me/joinchat/T_YTN4IG1vAJNWT9 Course chat].

=== Lecture notes ===

https://drive.google.com/file/d/1mmNLLQ0--EDihGNRKwSyXLOA1KL7A0lD/view?usp=sharing

=== Classes recordings ===

https://disk.yandex.ru/d/enYKJ6O8NN_3lQ

=== Lecture video archive ===

https://youtube.com/playlist?list=PLEwK9wdS5g0pk-1YWDc3hezRt_rNpQDf8

=== Other resources ===
* [https://tinyurl.com/rwky5vmk The Course's Google Directory]

* [https://www.youtube.com/playlist?list=PL1Uob8iPTHGTidrmrqEHTJ96Pt3-PmML4 Past years' videos]

* We have a [https://meet.edashkov.net.ru dedicated server] to hold an online meeting if we need one.

== Problem sets ==

=== Class problems ===

* [https://drive.google.com/file/d/1EP-diSuOTn9f0ryg18Z2w0xjEp8j0bnl/view?usp=sharing Problem set 1]

* [https://drive.google.com/file/d/12ct99-ORd7A94Gh5g4Nf9riv7UqNMSRc/view?usp=sharing Problem set 2]

* [https://drive.google.com/file/d/1yKKqLsS99V4AhCYqbjafuav2CMCdQTOQ/view?usp=sharing Problem set 3]

* [https://drive.google.com/file/d/1YgH_AdCk4GcKC0KH7xBA4-sUnOYkUvUK/view?usp=share_link Problem set 4]

* [https://drive.google.com/file/d/1M556PSgTJOo5W-AxYEXjFu94VfledpF5/view?usp=share_link Problem set 5]

* [https://drive.google.com/file/d/1-ylVViaBgzxEM-M7Rvrz2iggtK6UiJTY/view?usp=share_link Problem set 6]

=== Homework problems ===

* [https://drive.google.com/file/d/1A8lFPdI3ZvC1vOgz2KEpYcuWOFlsQvb1/view?usp=sharing Homework 1]

* [https://drive.google.com/file/d/1LOPPwGjyVleR_mclxTKUJ_bxFrxt44sW/view?usp=sharing Homework 2a]

* [https://drive.google.com/file/d/1W7k1OTiIMlPOpo-2mwmGegrc4RDHz5_j/view?usp=share_link Homework 2b]

* [https://drive.google.com/file/d/1dIsP4Jp3MBHv0wANv-pDdkxPbrcMrDod/view?usp=share_link Homework 3]

=== Assignment deadlines ===

{| class="wikitable"
|-
! Home problem set !! colspan="11" | Deadline
|-
| || 221 || 222 || 223 || 224
|-
| HW 1 №1-3 || || 22.IX || 22.IX || 22.IX
|-
| HW 1 || October 6 || October 6 || October 6 || October 6
|-
| HW 2a №1-3 || || October 20 || October 20 ||
|-
| HW 2a || October 24 || October 27 || October 27 || October 27
|-
| HW 2b №1-7 || November 30 || November 20 || November 20 || November 20
|-
| HW 2b №8-14 || December 14 || December 4 || December 4 || December 4
|-
| HW 3 №1-5 || || || || December 22

|}

'''Each deadline is set by the respective group's instructor.'''

== Grading system ==
For the final grading, we compute the following values:

Module 1 grade = round ((50*HW1 + 50*Exam1)/100);

basic = (21*Exam1 + 21*Colloq + 28*HW + 30*Exam2)/100;

adv = (30*Exam1* + Bonus + 35*HW* + 35*Exam2*)/100;

Final grade = round(min(10, 8 * basic + 2 * adv)).

The final grade is rounded half up to an integer. All the other values are reported with the greatest precision available.

== Recommended reading ==
''Please notice that '''The Book''' for our Course does not exist. The latter is based on many sources.''

# Anderson J. A., Discrete Mathematics With Combinatorics. Prentice Hall, 2003.
# Biggs N. L., Discrete mathematics. 2nd ed., New York; Oxford: Oxford University Press, 2004.
# Gavrilov G. P., Sapozhenko A. A. Problems and Exercises in Discrete Mathematics. Kluwer Texts in the Mathematical Sciences 14. Springer, 1996.
# [http://courses.csail.mit.edu/6.042/spring17/mcs.pdf Lehman E., Thomson Leighton F., Meyer A. R. Mathematics for Computer Science, 2017.]
# [http://www.cs.elte.hu/~lovasz/dmbook.ps Lovasz L., Vesztergombi K. Discrete Mathematics. Lecture Notes; Yale University, 1999.]
# Melnikov O., Sarvanov V., Tyshkevich R., Yemelichev V., Zverovich I. Exercises in Graph Theory. Kluwer Texts in the Mathematical Sciences 19. Springer, 1998.
# Rosen K. H. Discrete Mathematics and Its Applications. McGraw-Hill, 1999.
# Stein C., Drysdale R. L., Bogart K. Discrete mathematics for computer scientists. Addison-Wesley, 2010.
# Vinogradov I. M. Elements of number theory. Dover, 1954.

=== In Russian ===
''If you understand Russian (by any chance), you will probably benefit from reading the following books.''

# Виноградов И. М. Основы теории чисел. 9-е изд., М.: Наука, 1981.
# [http://rubtsov.su/public/DM-HSE-Draft.pdf Вялый М., Подольский В., Рубцов А., Шварц Д., Шень А. Лекции по дискретной математике.]
# Гаврилов Г. П., Сапоженко А. А. Задачи и упражнения по дискретной математике. 3-е изд., М.: ФИЗМАТЛИТ, 2004.
# [https://drive.google.com/file/d/1RM6KX_reBFwUXesWGUEu0sFn2NCaBgvz/view?usp=sharing Дашков Е. В. Введение в математическую логику. Множества и отношения. М.: МФТИ, 2019.]
# Зубков А. М., Севастьянов Б. А., Чистяков В. П. Сборник задач по теории вероятностей. 2-е изд., М.: Наука, 1989.
# Мельников О. И. Теория графов в занимательных задачах. 5-е изд., М.: Книжный дом "ЛИБРОКОМ", 2013.
# [http://www.mccme.ru/free-books/shen/shen-induction.pdf Шень А., Математическая индукция. 5-е изд, М.: МЦНМО, 2016.]

Adaptation course in Discrete Math (факультатив)

2022-12-08T20:22:07Z

Nasta.trofimova:

== General Information ==
The main goal of the Discrete Mathematics Adaptation Course is to help students keep up with the course curriculum by discussing the most important and challenging topics in detail. The second very important goal of the course is to teach students to work competently with mathematical definitions and proofs, correctly logically build solutions to problems and prove statements. The topics of the course are coordinated with the "basic" course of the DSBA and SE program, but its study will also be useful for the direction of AMI. The approximate order of topics is sets and logic, functions and relations, the beginning of number theory, combinatorics, graphs, the foundations of probability theory, generating functions.

== Schedule ==

The classes are organised on Wednesdays at 18:10.

== Course materials ==

[https://t.me/+113aheknlsxmYzVi Chat in Telegram]

'''First semester'''

{| class="wikitable"
|-
! Date !! Topic !! Problem Set !! Class note !! Video
|-
|| 21.09.22 || Statements, connectives, quantifiers || [https://drive.google.com/file/d/1kbtRp8c79zE2AspfVb4ZfGZLJRy9Z5j2/view?usp=drivesdk Problem Set 1]|| - ||
|-
|| 28.09.22 || Validity of statements, types of proof|| [https://drive.google.com/file/d/1Q2OlmVzXf4P0ocd3eBet4ktoJ1h1DZyn/view?usp=sharing Problem Set 2] || [https://drive.google.com/file/d/11pdljFmpW57o5OqBH40YwioTW_Ebs_gK/view?usp=sharing Solutions] || -
|-
|| 7.10.22 || Three types of mathematical induction || [https://drive.google.com/file/d/14h2jy4W7KgxBffxE8TKh_13rSG3Wy_Ll/view?usp=sharing Problem Set 3] ||[https://drive.google.com/file/d/1yFnH5QBNxM-1ajoA5y7w9wV_31XeBwWp/view?usp=sharing Solutions] || [https://youtu.be/nljNhVjlnXg Video 3]
|-
|| 14.10.22 || Proofs with induction || [https://drive.google.com/file/d/13vsHkpBV8riwyKOTCh1v1heuAqf0L9nK/view?usp=sharing Problem Set 4] ||[https://drive.google.com/file/d/1PZD-YWikatG9jCbcc1r_Eo5t0y-kdcpj/view?usp=sharing Solutions] || -
|-
|| 21.10.22 || Divisibility. Calculation of remainders. Direct proofs. || [https://drive.google.com/file/d/1rHfC1WRv4IB8kNRMynVWv0C26PXGi137/view?usp=sharing Problem Set 5] ||[https://drive.google.com/file/d/1CvWAD5pDmMB8JFWSFNxOrrT7-Jfp_0Wd/view?usp=sharing Solutions] ||
[https://youtu.be/-OIYkDOkLyk Video 5]
|-
|| 11.11.22 || Great commod divider, the main thorem of arithmetic, direct proofs. || [https://drive.google.com/file/d/1CrF9W2rXFiTMKFoxZO-PJDmhYAx6Ql84/view?usp=share_link Problem Set 6] ||[https://drive.google.com/file/d/1TWSgbLrRtZWRrbneebExE4BPoDzLU4-b/view?usp=share_link Solutions] ||
[https://youtu.be/_2RRlq21gqM Video 6]
|-
|| 19.11.22 || Fermat's Little theorem, inverse elements in groups $\mathbb{Z}_p$, congruences. || [https://drive.google.com/file/d/1IF6rqwLN0Bq8n07mxQ3CAmoMfWplJ3OR/view?usp=share_link Problem Set 7] ||[https://drive.google.com/file/d/1FZevxpUjcPrrtCbxHn-HRh1odDamJqlq/view?usp=share_link Solutions] ||
[https://youtu.be/peuzIDzh1bE Video 7]
|-
|| 25.11.22 || Fermat's Little theorem, inverse elements in groups $\mathbb{Z}_p$, congruences. || [https://drive.google.com/file/d/1CYGJ7B5d426ChuZBozzsLKwMVZeVPgQJ/view?usp=share_link Problem Set 8] ||[https://drive.google.com/file/d/1_PCu2dDhIgN7uE1ijLGLH1USapPskGWH/view?usp=share_link Solutions] ||
[ -]
|-
|| 2.12.22 || Application of Euler's theorem and Euclidean algorithm, cryptography || [https://drive.google.com/file/d/1Oq3grvUbG-yBBbrHqhK_4Ylz4Io-D1Lw/view?usp=share_link Problem Set 9] ||[https://drive.google.com/file/d/1BFDh6-6KVmb65w7qDEQprP6BYUMUW6AQ/view?usp=share_link Solutions] ||
[https://youtu.be/HPpI7VpHrWY Video 9]
|-
|| 9.12.22 || Sets, direct proofs of set identities || [https://drive.google.com/file/d/1C6I_cviJwznCLZ5BKtxUtlUrjpp4Kegw/view?usp=share_link Problem Set 10] ||[ Solutions] || [ Video 10]
|-
|| 16.12.22 || Sets. || [ Problem Set 11] ||[ Solutions] ||
[ Video 11]
|}

[https://drive.google.com/file/d/163PgGw33FTt3PUVdVBYCjIHluftfZVol/view?usp=sharing Last year retake]

[https://drive.google.com/file/d/1bljTOb3x0kvYy7cslTOC4B3StYOHi3CX/view Last year test 1]

== Homeworks ==
[https://forms.gle/TAgL2eUkhSyhZKLD9 Homework 1 (Logics)], Deadline 31st October

[https://forms.gle/pVA1a8xbeP54RqAQ7 Homework 2 (Induction)], Deadline 31st November, better to complete before the November Test

[https://drive.google.com/file/d/1k8SKmN9J_DdSs8ibP_9b52n8LxiPf_8U/view?usp=share_link Homework 3]: write down solutions to exam 1 in a perfect manner (like you you are going to print a book of your solutions), Deadline 25th November. You can pass them written or orally on Fridays evenings. Do it if you want to have MAX in the retake(if so happened) and in the exam in the end of the course.

[https://forms.gle/DQUEyuh1vuXgdtr6A Homework 4 (Number theory)], Deadline with bonus 29th December

==Semester 1 ==

[https://docs.google.com/spreadsheets/d/1YHhkk8TCm_qPF0tXyGe7rc-DzubrgSESZUoW6fHMLZA/edit?usp=sharing Current grades and comments]

== References ==

1. [http://discrete.openmathbooks.org/dmoi3.html Discrete Mathematics (An Open Introduction) by Oscar Levin,] p. 197 Logics. Many simple problems with solution to feel the topic.

2. [https://drive.google.com/file/d/1mmNLLQ0--EDihGNRKwSyXLOA1KL7A0lD/view?usp=sharing Lecture notes by Evgeny Dashkov]

PLUS: there is a [https://youtube.com/playlist?list=PLEwK9wdS5g0pk-1YWDc3hezRt_rNpQDf8 folder with records on wikipage ]

3. [http://www.mccme.ru/free-books/shen/shen-induction.pdf Шень А., Математическая индукция. 5-е изд, М.: МЦНМО, 2016.] Many problems to work with three different versions of induction.

== Grading and Results ==

'''Final grade''' = Average(HWs)+ Bonus points

Bonus point number is between 0 to 20. Such points may be given for a variety of auxiliary activities.

Adaptation course in Discrete Math (факультатив)

2022-12-08T20:21:55Z

Nasta.trofimova:

== General Information ==
The main goal of the Discrete Mathematics Adaptation Course is to help students keep up with the course curriculum by discussing the most important and challenging topics in detail. The second very important goal of the course is to teach students to work competently with mathematical definitions and proofs, correctly logically build solutions to problems and prove statements. The topics of the course are coordinated with the "basic" course of the DSBA and SE program, but its study will also be useful for the direction of AMI. The approximate order of topics is sets and logic, functions and relations, the beginning of number theory, combinatorics, graphs, the foundations of probability theory, generating functions.

== Schedule ==

The classes are organised on Wednesdays at 18:10.

== Course materials ==

[https://t.me/+113aheknlsxmYzVi Chat in Telegram]

'''First semester'''

{| class="wikitable"
|-
! Date !! Topic !! Problem Set !! Class note !! Video
|-
|| 21.09.22 || Statements, connectives, quantifiers || [https://drive.google.com/file/d/1kbtRp8c79zE2AspfVb4ZfGZLJRy9Z5j2/view?usp=drivesdk Problem Set 1]|| - ||
|-
|| 28.09.22 || Validity of statements, types of proof|| [https://drive.google.com/file/d/1Q2OlmVzXf4P0ocd3eBet4ktoJ1h1DZyn/view?usp=sharing Problem Set 2] || [https://drive.google.com/file/d/11pdljFmpW57o5OqBH40YwioTW_Ebs_gK/view?usp=sharing Solutions] || -
|-
|| 7.10.22 || Three types of mathematical induction || [https://drive.google.com/file/d/14h2jy4W7KgxBffxE8TKh_13rSG3Wy_Ll/view?usp=sharing Problem Set 3] ||[https://drive.google.com/file/d/1yFnH5QBNxM-1ajoA5y7w9wV_31XeBwWp/view?usp=sharing Solutions] || [https://youtu.be/nljNhVjlnXg Video 3]
|-
|| 14.10.22 || Proofs with induction || [https://drive.google.com/file/d/13vsHkpBV8riwyKOTCh1v1heuAqf0L9nK/view?usp=sharing Problem Set 4] ||[https://drive.google.com/file/d/1PZD-YWikatG9jCbcc1r_Eo5t0y-kdcpj/view?usp=sharing Solutions] || -
|-
|| 21.10.22 || Divisibility. Calculation of remainders. Direct proofs. || [https://drive.google.com/file/d/1rHfC1WRv4IB8kNRMynVWv0C26PXGi137/view?usp=sharing Problem Set 5] ||[https://drive.google.com/file/d/1CvWAD5pDmMB8JFWSFNxOrrT7-Jfp_0Wd/view?usp=sharing Solutions] ||
[https://youtu.be/-OIYkDOkLyk Video 5]
|-
|| 11.11.22 || Great commod divider, the main thorem of arithmetic, direct proofs. || [https://drive.google.com/file/d/1CrF9W2rXFiTMKFoxZO-PJDmhYAx6Ql84/view?usp=share_link Problem Set 6] ||[https://drive.google.com/file/d/1TWSgbLrRtZWRrbneebExE4BPoDzLU4-b/view?usp=share_link Solutions] ||
[https://youtu.be/_2RRlq21gqM Video 6]
|-
|| 19.11.22 || Fermat's Little theorem, inverse elements in groups $\mathbb{Z}_p$, congruences. || [https://drive.google.com/file/d/1IF6rqwLN0Bq8n07mxQ3CAmoMfWplJ3OR/view?usp=share_link Problem Set 7] ||[https://drive.google.com/file/d/1FZevxpUjcPrrtCbxHn-HRh1odDamJqlq/view?usp=share_link Solutions] ||
[https://youtu.be/peuzIDzh1bE Video 7]
|-
|| 25.11.22 || Fermat's Little theorem, inverse elements in groups $\mathbb{Z}_p$, congruences. || [https://drive.google.com/file/d/1CYGJ7B5d426ChuZBozzsLKwMVZeVPgQJ/view?usp=share_link Problem Set 8] ||[https://drive.google.com/file/d/1_PCu2dDhIgN7uE1ijLGLH1USapPskGWH/view?usp=share_link Solutions] ||
[ -]
|-
|| 2.12.22 || Application of Euler's theorem and Euclidean algorithm, cryptography || [https://drive.google.com/file/d/1Oq3grvUbG-yBBbrHqhK_4Ylz4Io-D1Lw/view?usp=share_link Problem Set 9] ||[https://drive.google.com/file/d/1BFDh6-6KVmb65w7qDEQprP6BYUMUW6AQ/view?usp=share_link Solutions] ||
[https://youtu.be/HPpI7VpHrWY Video 9]
|-
|| 9.12.22 || Sets, direct proofs of set identities || [https://drive.google.com/file/d/1C6I_cviJwznCLZ5BKtxUtlUrjpp4Kegw/view?usp=share_link Problem Set 10] ||[ Solutions] || [ Video 10]
|-
|| 16.12.22 || Sets. || [ Problem Set 11] ||[ Solutions] ||
[ Video 11]
|}

[https://drive.google.com/file/d/163PgGw33FTt3PUVdVBYCjIHluftfZVol/view?usp=sharing Last year retake]

[https://drive.google.com/file/d/1bljTOb3x0kvYy7cslTOC4B3StYOHi3CX/view Last year test 1]

== Homeworks ==
[https://forms.gle/TAgL2eUkhSyhZKLD9 Homework 1 (Logics)], Deadline 31st October

[https://forms.gle/pVA1a8xbeP54RqAQ7 Homework 2 (Induction)], Deadline 31st November, better to complete before the November Test

[https://drive.google.com/file/d/1k8SKmN9J_DdSs8ibP_9b52n8LxiPf_8U/view?usp=share_link Homework 3]: write down solutions to exam 1 in a perfect manner (like you you are going to print a book of your solutions), Deadline 25th November. You can pass them written or orally on Fridays evenings. Do it if you want to have MAX in the retake(if so happened) and in the exam in the end of the course.

[https://forms.gle/DQUEyuh1vuXgdtr6A Homework 4 (Number theory)], Deadline with bonus 29 December

==Semester 1 ==

[https://docs.google.com/spreadsheets/d/1YHhkk8TCm_qPF0tXyGe7rc-DzubrgSESZUoW6fHMLZA/edit?usp=sharing Current grades and comments]

== References ==

1. [http://discrete.openmathbooks.org/dmoi3.html Discrete Mathematics (An Open Introduction) by Oscar Levin,] p. 197 Logics. Many simple problems with solution to feel the topic.

2. [https://drive.google.com/file/d/1mmNLLQ0--EDihGNRKwSyXLOA1KL7A0lD/view?usp=sharing Lecture notes by Evgeny Dashkov]

PLUS: there is a [https://youtube.com/playlist?list=PLEwK9wdS5g0pk-1YWDc3hezRt_rNpQDf8 folder with records on wikipage ]

3. [http://www.mccme.ru/free-books/shen/shen-induction.pdf Шень А., Математическая индукция. 5-е изд, М.: МЦНМО, 2016.] Many problems to work with three different versions of induction.

== Grading and Results ==

'''Final grade''' = Average(HWs)+ Bonus points

Bonus point number is between 0 to 20. Such points may be given for a variety of auxiliary activities.

Adaptation course in Discrete Math (факультатив)

2022-12-08T20:21:18Z

Nasta.trofimova:

== General Information ==
The main goal of the Discrete Mathematics Adaptation Course is to help students keep up with the course curriculum by discussing the most important and challenging topics in detail. The second very important goal of the course is to teach students to work competently with mathematical definitions and proofs, correctly logically build solutions to problems and prove statements. The topics of the course are coordinated with the "basic" course of the DSBA and SE program, but its study will also be useful for the direction of AMI. The approximate order of topics is sets and logic, functions and relations, the beginning of number theory, combinatorics, graphs, the foundations of probability theory, generating functions.

== Schedule ==

The classes are organised on Wednesdays at 18:10.

== Course materials ==

[https://t.me/+113aheknlsxmYzVi Chat in Telegram]

'''First semester'''

{| class="wikitable"
|-
! Date !! Topic !! Problem Set !! Class note !! Video
|-
|| 21.09.22 || Statements, connectives, quantifiers || [https://drive.google.com/file/d/1kbtRp8c79zE2AspfVb4ZfGZLJRy9Z5j2/view?usp=drivesdk Problem Set 1]|| - ||
|-
|| 28.09.22 || Validity of statements, types of proof|| [https://drive.google.com/file/d/1Q2OlmVzXf4P0ocd3eBet4ktoJ1h1DZyn/view?usp=sharing Problem Set 2] || [https://drive.google.com/file/d/11pdljFmpW57o5OqBH40YwioTW_Ebs_gK/view?usp=sharing Solutions] || -
|-
|| 7.10.22 || Three types of mathematical induction || [https://drive.google.com/file/d/14h2jy4W7KgxBffxE8TKh_13rSG3Wy_Ll/view?usp=sharing Problem Set 3] ||[https://drive.google.com/file/d/1yFnH5QBNxM-1ajoA5y7w9wV_31XeBwWp/view?usp=sharing Solutions] || [https://youtu.be/nljNhVjlnXg Video 3]
|-
|| 14.10.22 || Proofs with induction || [https://drive.google.com/file/d/13vsHkpBV8riwyKOTCh1v1heuAqf0L9nK/view?usp=sharing Problem Set 4] ||[https://drive.google.com/file/d/1PZD-YWikatG9jCbcc1r_Eo5t0y-kdcpj/view?usp=sharing Solutions] || -
|-
|| 21.10.22 || Divisibility. Calculation of remainders. Direct proofs. || [https://drive.google.com/file/d/1rHfC1WRv4IB8kNRMynVWv0C26PXGi137/view?usp=sharing Problem Set 5] ||[https://drive.google.com/file/d/1CvWAD5pDmMB8JFWSFNxOrrT7-Jfp_0Wd/view?usp=sharing Solutions] ||
[https://youtu.be/-OIYkDOkLyk Video 5]
|-
|| 11.11.22 || Great commod divider, the main thorem of arithmetic, direct proofs. || [https://drive.google.com/file/d/1CrF9W2rXFiTMKFoxZO-PJDmhYAx6Ql84/view?usp=share_link Problem Set 6] ||[https://drive.google.com/file/d/1TWSgbLrRtZWRrbneebExE4BPoDzLU4-b/view?usp=share_link Solutions] ||
[https://youtu.be/_2RRlq21gqM Video 6]
|-
|| 19.11.22 || Fermat's Little theorem, inverse elements in groups $\mathbb{Z}_p$, congruences. || [https://drive.google.com/file/d/1IF6rqwLN0Bq8n07mxQ3CAmoMfWplJ3OR/view?usp=share_link Problem Set 7] ||[https://drive.google.com/file/d/1FZevxpUjcPrrtCbxHn-HRh1odDamJqlq/view?usp=share_link Solutions] ||
[https://youtu.be/peuzIDzh1bE Video 7]
|-
|| 25.11.22 || Fermat's Little theorem, inverse elements in groups $\mathbb{Z}_p$, congruences. || [https://drive.google.com/file/d/1CYGJ7B5d426ChuZBozzsLKwMVZeVPgQJ/view?usp=share_link Problem Set 8] ||[https://drive.google.com/file/d/1_PCu2dDhIgN7uE1ijLGLH1USapPskGWH/view?usp=share_link Solutions] ||
[ -]
|-
|| 2.12.22 || Application of Euler's theorem and Euclidean algorithm, cryptography || [https://drive.google.com/file/d/1Oq3grvUbG-yBBbrHqhK_4Ylz4Io-D1Lw/view?usp=share_link Problem Set 9] ||[https://drive.google.com/file/d/1BFDh6-6KVmb65w7qDEQprP6BYUMUW6AQ/view?usp=share_link Solutions] ||
[https://youtu.be/HPpI7VpHrWY Video 9]
|-
|| 9.12.22 || Sets, direct proofs of set identities || [https://drive.google.com/file/d/1C6I_cviJwznCLZ5BKtxUtlUrjpp4Kegw/view?usp=share_link Problem Set 10] ||[ Solutions] || [ Video 10]
|-
|| 16.12.22 || Sets. || [ Problem Set 11] ||[ Solutions] ||
[ Video 11]
|}

[https://drive.google.com/file/d/163PgGw33FTt3PUVdVBYCjIHluftfZVol/view?usp=sharing Last year retake]

[https://drive.google.com/file/d/1bljTOb3x0kvYy7cslTOC4B3StYOHi3CX/view Last year test 1]

== Homeworks ==
[https://forms.gle/TAgL2eUkhSyhZKLD9 Homework 1 (Logics)], Deadline 31st October

[https://forms.gle/pVA1a8xbeP54RqAQ7 Homework 2 (Induction)], Deadline 31st November, better to complete before the November Test

[https://drive.google.com/file/d/1k8SKmN9J_DdSs8ibP_9b52n8LxiPf_8U/view?usp=share_link Homework 3]: write down solutions to exam 1 in a perfect manner (like you you are going to print a book of your solutions), Deadline 25th November. You can pass them written or orally on Fridays evenings. Do it if you want to have MAX in the retake(if so happened) and in the exam in the end of the course.

[https://forms.gle/DQUEyuh1vuXgdtr6A Homework 4 (Number theory), Deadline 29 December ]

==Semester 1 ==

[https://docs.google.com/spreadsheets/d/1YHhkk8TCm_qPF0tXyGe7rc-DzubrgSESZUoW6fHMLZA/edit?usp=sharing Current grades and comments]

== References ==

1. [http://discrete.openmathbooks.org/dmoi3.html Discrete Mathematics (An Open Introduction) by Oscar Levin,] p. 197 Logics. Many simple problems with solution to feel the topic.

2. [https://drive.google.com/file/d/1mmNLLQ0--EDihGNRKwSyXLOA1KL7A0lD/view?usp=sharing Lecture notes by Evgeny Dashkov]

PLUS: there is a [https://youtube.com/playlist?list=PLEwK9wdS5g0pk-1YWDc3hezRt_rNpQDf8 folder with records on wikipage ]

3. [http://www.mccme.ru/free-books/shen/shen-induction.pdf Шень А., Математическая индукция. 5-е изд, М.: МЦНМО, 2016.] Many problems to work with three different versions of induction.

== Grading and Results ==

'''Final grade''' = Average(HWs)+ Bonus points

Bonus point number is between 0 to 20. Such points may be given for a variety of auxiliary activities.

Adaptation course in Discrete Math (факультатив)

2022-12-08T20:02:51Z

Nasta.trofimova: /* Course materials */

== General Information ==
The main goal of the Discrete Mathematics Adaptation Course is to help students keep up with the course curriculum by discussing the most important and challenging topics in detail. The second very important goal of the course is to teach students to work competently with mathematical definitions and proofs, correctly logically build solutions to problems and prove statements. The topics of the course are coordinated with the "basic" course of the DSBA and SE program, but its study will also be useful for the direction of AMI. The approximate order of topics is sets and logic, functions and relations, the beginning of number theory, combinatorics, graphs, the foundations of probability theory, generating functions.

== Schedule ==

The classes are organised on Wednesdays at 18:10.

== Course materials ==

[https://t.me/+113aheknlsxmYzVi Chat in Telegram]

'''First semester'''

{| class="wikitable"
|-
! Date !! Topic !! Problem Set !! Class note !! Video
|-
|| 21.09.22 || Statements, connectives, quantifiers || [https://drive.google.com/file/d/1kbtRp8c79zE2AspfVb4ZfGZLJRy9Z5j2/view?usp=drivesdk Problem Set 1]|| - ||
|-
|| 28.09.22 || Validity of statements, types of proof|| [https://drive.google.com/file/d/1Q2OlmVzXf4P0ocd3eBet4ktoJ1h1DZyn/view?usp=sharing Problem Set 2] || [https://drive.google.com/file/d/11pdljFmpW57o5OqBH40YwioTW_Ebs_gK/view?usp=sharing Solutions] || -
|-
|| 7.10.22 || Three types of mathematical induction || [https://drive.google.com/file/d/14h2jy4W7KgxBffxE8TKh_13rSG3Wy_Ll/view?usp=sharing Problem Set 3] ||[https://drive.google.com/file/d/1yFnH5QBNxM-1ajoA5y7w9wV_31XeBwWp/view?usp=sharing Solutions] || [https://youtu.be/nljNhVjlnXg Video 3]
|-
|| 14.10.22 || Proofs with induction || [https://drive.google.com/file/d/13vsHkpBV8riwyKOTCh1v1heuAqf0L9nK/view?usp=sharing Problem Set 4] ||[https://drive.google.com/file/d/1PZD-YWikatG9jCbcc1r_Eo5t0y-kdcpj/view?usp=sharing Solutions] || -
|-
|| 21.10.22 || Divisibility. Calculation of remainders. Direct proofs. || [https://drive.google.com/file/d/1rHfC1WRv4IB8kNRMynVWv0C26PXGi137/view?usp=sharing Problem Set 5] ||[https://drive.google.com/file/d/1CvWAD5pDmMB8JFWSFNxOrrT7-Jfp_0Wd/view?usp=sharing Solutions] ||
[https://youtu.be/-OIYkDOkLyk Video 5]
|-
|| 11.11.22 || Great commod divider, the main thorem of arithmetic, direct proofs. || [https://drive.google.com/file/d/1CrF9W2rXFiTMKFoxZO-PJDmhYAx6Ql84/view?usp=share_link Problem Set 6] ||[https://drive.google.com/file/d/1TWSgbLrRtZWRrbneebExE4BPoDzLU4-b/view?usp=share_link Solutions] ||
[https://youtu.be/_2RRlq21gqM Video 6]
|-
|| 19.11.22 || Fermat's Little theorem, inverse elements in groups $\mathbb{Z}_p$, congruences. || [https://drive.google.com/file/d/1IF6rqwLN0Bq8n07mxQ3CAmoMfWplJ3OR/view?usp=share_link Problem Set 7] ||[https://drive.google.com/file/d/1FZevxpUjcPrrtCbxHn-HRh1odDamJqlq/view?usp=share_link Solutions] ||
[https://youtu.be/peuzIDzh1bE Video 7]
|-
|| 25.11.22 || Fermat's Little theorem, inverse elements in groups $\mathbb{Z}_p$, congruences. || [https://drive.google.com/file/d/1CYGJ7B5d426ChuZBozzsLKwMVZeVPgQJ/view?usp=share_link Problem Set 8] ||[https://drive.google.com/file/d/1_PCu2dDhIgN7uE1ijLGLH1USapPskGWH/view?usp=share_link Solutions] ||
[ -]
|-
|| 2.12.22 || Application of Euler's theorem and Euclidean algorithm, cryptography || [https://drive.google.com/file/d/1Oq3grvUbG-yBBbrHqhK_4Ylz4Io-D1Lw/view?usp=share_link Problem Set 9] ||[https://drive.google.com/file/d/1BFDh6-6KVmb65w7qDEQprP6BYUMUW6AQ/view?usp=share_link Solutions] ||
[https://youtu.be/HPpI7VpHrWY Video 9]
|-
|| 9.12.22 || Sets, direct proofs of set identities || [https://drive.google.com/file/d/1C6I_cviJwznCLZ5BKtxUtlUrjpp4Kegw/view?usp=share_link Problem Set 10] ||[ Solutions] || [ Video 10]
|-
|| 16.12.22 || Sets. || [ Problem Set 11] ||[ Solutions] ||
[ Video 11]
|}

[https://drive.google.com/file/d/163PgGw33FTt3PUVdVBYCjIHluftfZVol/view?usp=sharing Last year retake]

[https://drive.google.com/file/d/1bljTOb3x0kvYy7cslTOC4B3StYOHi3CX/view Last year test 1]

== Homeworks ==
[https://forms.gle/TAgL2eUkhSyhZKLD9 Homework 1 (Logics)], Deadline 31st October

[https://forms.gle/pVA1a8xbeP54RqAQ7 Homework 2 (Induction)], Deadline 31st November, better to complete before the November Test

[https://drive.google.com/file/d/1k8SKmN9J_DdSs8ibP_9b52n8LxiPf_8U/view?usp=share_link Homework 3]: write down solutions to exam 1 in a perfect manner (like you you are going to print a book of your solutions), Deadline 25th November. You can pass them written or orally on Fridays evenings. Do it if you want to have MAX in the retake(if so happened) and in the exam in the end of the course.

==Semester 1 ==

[https://docs.google.com/spreadsheets/d/1YHhkk8TCm_qPF0tXyGe7rc-DzubrgSESZUoW6fHMLZA/edit?usp=sharing Current grades and comments]

== References ==

1. [http://discrete.openmathbooks.org/dmoi3.html Discrete Mathematics (An Open Introduction) by Oscar Levin,] p. 197 Logics. Many simple problems with solution to feel the topic.

2. [https://drive.google.com/file/d/1mmNLLQ0--EDihGNRKwSyXLOA1KL7A0lD/view?usp=sharing Lecture notes by Evgeny Dashkov]

PLUS: there is a [https://youtube.com/playlist?list=PLEwK9wdS5g0pk-1YWDc3hezRt_rNpQDf8 folder with records on wikipage ]

3. [http://www.mccme.ru/free-books/shen/shen-induction.pdf Шень А., Математическая индукция. 5-е изд, М.: МЦНМО, 2016.] Many problems to work with three different versions of induction.

== Grading and Results ==

'''Final grade''' = Average(HWs)+ Bonus points

Bonus point number is between 0 to 20. Such points may be given for a variety of auxiliary activities.

Adaptation course in Discrete Math (факультатив)

2022-12-08T19:43:08Z

Nasta.trofimova: /* Course materials */

== General Information ==
The main goal of the Discrete Mathematics Adaptation Course is to help students keep up with the course curriculum by discussing the most important and challenging topics in detail. The second very important goal of the course is to teach students to work competently with mathematical definitions and proofs, correctly logically build solutions to problems and prove statements. The topics of the course are coordinated with the "basic" course of the DSBA and SE program, but its study will also be useful for the direction of AMI. The approximate order of topics is sets and logic, functions and relations, the beginning of number theory, combinatorics, graphs, the foundations of probability theory, generating functions.

== Schedule ==

The classes are organised on Wednesdays at 18:10.

== Course materials ==

[https://t.me/+113aheknlsxmYzVi Chat in Telegram]

'''First semester'''

{| class="wikitable"
|-
! Date !! Topic !! Problem Set !! Class note !! Video
|-
|| 21.09.22 || Statements, connectives, quantifiers || [https://drive.google.com/file/d/1kbtRp8c79zE2AspfVb4ZfGZLJRy9Z5j2/view?usp=drivesdk Problem Set 1]|| - ||
|-
|| 28.09.22 || Validity of statements, types of proof|| [https://drive.google.com/file/d/1Q2OlmVzXf4P0ocd3eBet4ktoJ1h1DZyn/view?usp=sharing Problem Set 2] || [https://drive.google.com/file/d/11pdljFmpW57o5OqBH40YwioTW_Ebs_gK/view?usp=sharing Solutions] || -
|-
|| 7.10.22 || Three types of mathematical induction || [https://drive.google.com/file/d/14h2jy4W7KgxBffxE8TKh_13rSG3Wy_Ll/view?usp=sharing Problem Set 3] ||[https://drive.google.com/file/d/1yFnH5QBNxM-1ajoA5y7w9wV_31XeBwWp/view?usp=sharing Solutions] || [https://youtu.be/nljNhVjlnXg Video 3]
|-
|| 14.10.22 || Proofs with induction || [https://drive.google.com/file/d/13vsHkpBV8riwyKOTCh1v1heuAqf0L9nK/view?usp=sharing Problem Set 4] ||[https://drive.google.com/file/d/1PZD-YWikatG9jCbcc1r_Eo5t0y-kdcpj/view?usp=sharing Solutions] || -
|-
|| 21.10.22 || Divisibility. Calculation of remainders. Direct proofs. || [https://drive.google.com/file/d/1rHfC1WRv4IB8kNRMynVWv0C26PXGi137/view?usp=sharing Problem Set 5] ||[https://drive.google.com/file/d/1CvWAD5pDmMB8JFWSFNxOrrT7-Jfp_0Wd/view?usp=sharing Solutions] ||
[https://youtu.be/-OIYkDOkLyk Video 5]
|-
|| 11.11.22 || Great commod divider, the main thorem of arithmetic, direct proofs. || [https://drive.google.com/file/d/1CrF9W2rXFiTMKFoxZO-PJDmhYAx6Ql84/view?usp=share_link Problem Set 6] ||[https://drive.google.com/file/d/1TWSgbLrRtZWRrbneebExE4BPoDzLU4-b/view?usp=share_link Solutions] ||
[https://youtu.be/_2RRlq21gqM Video 6]
|-
|| 19.11.22 || Fermat's Little theorem, inverse elements in groups $\mathbb{Z}_p$, congruences. || [https://drive.google.com/file/d/1IF6rqwLN0Bq8n07mxQ3CAmoMfWplJ3OR/view?usp=share_link Problem Set 7] ||[https://drive.google.com/file/d/1FZevxpUjcPrrtCbxHn-HRh1odDamJqlq/view?usp=share_link Solutions] ||
[https://youtu.be/peuzIDzh1bE Video 7]
|-
|| 25.11.22 || Fermat's Little theorem, inverse elements in groups $\mathbb{Z}_p$, congruences. || [https://drive.google.com/file/d/1CYGJ7B5d426ChuZBozzsLKwMVZeVPgQJ/view?usp=share_link Problem Set 8] ||[https://drive.google.com/file/d/1_PCu2dDhIgN7uE1ijLGLH1USapPskGWH/view?usp=share_link Solutions] ||
[ -]
|-
|| 2.12.22 || Application of Euler's theorem and Euclidean algorithm, cryptography || [https://drive.google.com/file/d/1Oq3grvUbG-yBBbrHqhK_4Ylz4Io-D1Lw/view?usp=share_link Problem Set 9] ||[https://drive.google.com/file/d/1BFDh6-6KVmb65w7qDEQprP6BYUMUW6AQ/view?usp=share_link Solutions] ||
[https://youtu.be/HPpI7VpHrWY Video 9]
|-
|| 9.12.22 || Sets. || [ Problem Set 10] ||[ Solutions] ||
[ Video 10]
|-
|| 16.12.22 || Sets. || [ Problem Set 11] ||[ Solutions] ||
[ Video 11]
|}

[https://drive.google.com/file/d/163PgGw33FTt3PUVdVBYCjIHluftfZVol/view?usp=sharing Last year retake]

[https://drive.google.com/file/d/1bljTOb3x0kvYy7cslTOC4B3StYOHi3CX/view Last year test 1]

== Homeworks ==
[https://forms.gle/TAgL2eUkhSyhZKLD9 Homework 1 (Logics)], Deadline 31st October

[https://forms.gle/pVA1a8xbeP54RqAQ7 Homework 2 (Induction)], Deadline 31st November, better to complete before the November Test

[https://drive.google.com/file/d/1k8SKmN9J_DdSs8ibP_9b52n8LxiPf_8U/view?usp=share_link Homework 3]: write down solutions to exam 1 in a perfect manner (like you you are going to print a book of your solutions), Deadline 25th November. You can pass them written or orally on Fridays evenings. Do it if you want to have MAX in the retake(if so happened) and in the exam in the end of the course.

==Semester 1 ==

[https://docs.google.com/spreadsheets/d/1YHhkk8TCm_qPF0tXyGe7rc-DzubrgSESZUoW6fHMLZA/edit?usp=sharing Current grades and comments]

== References ==

1. [http://discrete.openmathbooks.org/dmoi3.html Discrete Mathematics (An Open Introduction) by Oscar Levin,] p. 197 Logics. Many simple problems with solution to feel the topic.

2. [https://drive.google.com/file/d/1mmNLLQ0--EDihGNRKwSyXLOA1KL7A0lD/view?usp=sharing Lecture notes by Evgeny Dashkov]

PLUS: there is a [https://youtube.com/playlist?list=PLEwK9wdS5g0pk-1YWDc3hezRt_rNpQDf8 folder with records on wikipage ]

3. [http://www.mccme.ru/free-books/shen/shen-induction.pdf Шень А., Математическая индукция. 5-е изд, М.: МЦНМО, 2016.] Many problems to work with three different versions of induction.

== Grading and Results ==

'''Final grade''' = Average(HWs)+ Bonus points

Bonus point number is between 0 to 20. Such points may be given for a variety of auxiliary activities.

Discrete Mathematics DSBA 2022/2023

2022-12-08T19:32:48Z

Nasta.trofimova: /* Assignment deadlines */

== Instructors ==

=== The lecturer ===
My name is Evgeny Dashkov. Feel free to contact me via email: edashkov@gmail.com, [https://t.me/edashkov Telegram], or [https://vk.com/evgeny.v.dashkov VK].

=== Seminar instructors ===
{| class="wikitable" style="text-align:center"
|-
! Group !! 221 !! 222 !! 223 !! 224
|-
|| Teachers || Evgeny Dashkov ||colspan="2"| Boris Danilov [https://t.me/brdann Telegram]|| Trofimova Anastasia [https://t.me/AnastasiiaTrofimova Telegram]
|-
|| Teaching Assistants || Arseny Bolotnikov [https://t.me/l0i4b Telegram] ||Daria Ivanova [https://t.me/ivanovskayaaaaa Telegram]|| Artem Ilin [https://t.me/artem_ilinn Telegram] || Marianna Kouis [https://t.me/mariannakouis Telegram]
|-
|| Lecturer’s Assistant || colspan="4"| Alyona Chislova [https://t.me/alenka_chislova Telegram]
|}

== Current performance ==

[https://docs.google.com/spreadsheets/d/1KoXyABY4alQu-Gw3HsYy3Vco9rfvHdYQZuUjE_ERJB8/edit?usp=sharing The Table]

== Homework ==
The homework includes a few problem sets, one in a fortnight or so (the deadlines are announced on giving each set). Every problem set consists of about 10 – 15 problems, some of which are labeled as ‘bonus’ while all the remaining are considered ‘ordinary’. One can get either 0, ½, or 1 point for each problem. For the entire homework, two values are computed:

HW = (the sum of points given for ordinary problems) / #(ordinary problems);

HW* = (the sum of points given for bonus problems) / #(bonus problems).

The value HW1 is similar to HW but restricted to the problem sets given in Module 1.

A student may be required to explain orally his written solution to any problem. His grade for the problem may be decreased if he fails to do so properly.

== Exam 1 ==
A written examination is held past Module 1. Students may not consult any sources during the exam. Some problems of the exam are labeled as ‘bonus’; the others are ‘ordinary’. Each problem solution is graded with either 0, ¼, ½, ¾, or 1 point, and the entire exam with two values:

Exam1 = (the sum of points given for ordinary problems) / #(ordinary problems);

Exam1* = (the sum of points given for bonus problems) / #(bonus problems)

== Colloquium ==
An oral colloquium is held at the beginning of Module 3. Each student is given two questions concerning statements and definitions as well as one question requiring a proof. After no less than 45 minutes of preparation (when using any literature is allowed), the student is required to answer ‘from scratch’, that is, with no recourse to any materials. The examiner may pose additional questions as he sees fit. The student may get from 0 to 7 integer points for his answer; the value

Colloq = (the score given) / 7

is then computed.

== Exam 2 ==
A written examination is held at the end of the Course. Students may not consult any sources during the exam. The examination takes about 120 minutes. Some problems of the exam are labeled as ‘bonus’; the others are ‘ordinary’. Each problem solution is graded with either 0, ¼, ½, ¾, or 1 point; finally, two values are computed:

Exam2 = (the sum of points given for ordinary problems) / #(ordinary problems);

Exam2* = (the sum of points given for bonus problems) / #(bonus problems).

== Bonus activities ==
The students may be graded for a variety of ‘bonus activities’ (like quizzes, etc.) with an overall integer value Bonus from 0 to 25.

== Exam retaking ==
Examinations 1 and 2 are subject to be retaken if Module 1 grade or Final grade (see below), respectively, is unsatisfactory. Retaking the exam is similar to the regular examination. The resulting grade is substituted for that of the latter. The last try Commission retaking is held for those whose final grade is still unsatisfactory after the retaking. A designated Commission carefully examines the student’s performance and gives him a final mark not better than ‘satisfactory’; at that the Commission is not bound by the grading formulas herein.

== Course materials ==

[https://t.me/joinchat/T_YTN4IG1vAJNWT9 Course chat].

=== Lecture notes ===

https://drive.google.com/file/d/1mmNLLQ0--EDihGNRKwSyXLOA1KL7A0lD/view?usp=sharing

=== Classes recordings ===

https://disk.yandex.ru/d/enYKJ6O8NN_3lQ

=== Lecture video archive ===

https://youtube.com/playlist?list=PLEwK9wdS5g0pk-1YWDc3hezRt_rNpQDf8

=== Other resources ===
* [https://tinyurl.com/rwky5vmk The Course's Google Directory]

* [https://www.youtube.com/playlist?list=PL1Uob8iPTHGTidrmrqEHTJ96Pt3-PmML4 Past years' videos]

* We have a [https://meet.edashkov.net.ru dedicated server] to hold an online meeting if we need one.

== Problem sets ==

=== Class problems ===

* [https://drive.google.com/file/d/1EP-diSuOTn9f0ryg18Z2w0xjEp8j0bnl/view?usp=sharing Problem set 1]

* [https://drive.google.com/file/d/12ct99-ORd7A94Gh5g4Nf9riv7UqNMSRc/view?usp=sharing Problem set 2]

* [https://drive.google.com/file/d/1yKKqLsS99V4AhCYqbjafuav2CMCdQTOQ/view?usp=sharing Problem set 3]

* [https://drive.google.com/file/d/1YgH_AdCk4GcKC0KH7xBA4-sUnOYkUvUK/view?usp=share_link Problem set 4]

* [https://drive.google.com/file/d/1M556PSgTJOo5W-AxYEXjFu94VfledpF5/view?usp=share_link Problem set 5]

* [https://drive.google.com/file/d/1-ylVViaBgzxEM-M7Rvrz2iggtK6UiJTY/view?usp=share_link Problem set 6]

=== Homework problems ===

* [https://drive.google.com/file/d/1A8lFPdI3ZvC1vOgz2KEpYcuWOFlsQvb1/view?usp=sharing Homework 1]

* [https://drive.google.com/file/d/1LOPPwGjyVleR_mclxTKUJ_bxFrxt44sW/view?usp=sharing Homework 2a]

* [https://drive.google.com/file/d/1W7k1OTiIMlPOpo-2mwmGegrc4RDHz5_j/view?usp=share_link Homework 2b]

=== Assignment deadlines ===

{| class="wikitable"
|-
! Home problem set !! colspan="11" | Deadline
|-
| || 221 || 222 || 223 || 224
|-
| HW 1 №1-3 || || 22.IX || 22.IX || 22.IX
|-
| HW 1 || October 6 || October 6 || October 6 || October 6
|-
| HW 2a №1-3 || || October 20 || October 20 ||
|-
| HW 2a || October 24 || October 27 || October 27 || October 27
|-
| HW 2b №1-7 || November 30 || November 20 || November 20 || November 20
|-
| HW 2b №8-14 || December 14 || December 4 || December 4 || December 4
|-
| HW 3 №1-5 || || || || December 22

|}

'''Each deadline is set by the respective group's instructor.'''

== Grading system ==
For the final grading, we compute the following values:

Module 1 grade = round ((50*HW1 + 50*Exam1)/100);

basic = (21*Exam1 + 21*Colloq + 28*HW + 30*Exam2)/100;

adv = (30*Exam1* + Bonus + 35*HW* + 35*Exam2*)/100;

Final grade = round(min(10, 8 * basic + 2 * adv)).

The final grade is rounded half up to an integer. All the other values are reported with the greatest precision available.

== Recommended reading ==
''Please notice that '''The Book''' for our Course does not exist. The latter is based on many sources.''

# Anderson J. A., Discrete Mathematics With Combinatorics. Prentice Hall, 2003.
# Biggs N. L., Discrete mathematics. 2nd ed., New York; Oxford: Oxford University Press, 2004.
# Gavrilov G. P., Sapozhenko A. A. Problems and Exercises in Discrete Mathematics. Kluwer Texts in the Mathematical Sciences 14. Springer, 1996.
# [http://courses.csail.mit.edu/6.042/spring17/mcs.pdf Lehman E., Thomson Leighton F., Meyer A. R. Mathematics for Computer Science, 2017.]
# [http://www.cs.elte.hu/~lovasz/dmbook.ps Lovasz L., Vesztergombi K. Discrete Mathematics. Lecture Notes; Yale University, 1999.]
# Melnikov O., Sarvanov V., Tyshkevich R., Yemelichev V., Zverovich I. Exercises in Graph Theory. Kluwer Texts in the Mathematical Sciences 19. Springer, 1998.
# Rosen K. H. Discrete Mathematics and Its Applications. McGraw-Hill, 1999.
# Stein C., Drysdale R. L., Bogart K. Discrete mathematics for computer scientists. Addison-Wesley, 2010.
# Vinogradov I. M. Elements of number theory. Dover, 1954.

=== In Russian ===
''If you understand Russian (by any chance), you will probably benefit from reading the following books.''

# Виноградов И. М. Основы теории чисел. 9-е изд., М.: Наука, 1981.
# [http://rubtsov.su/public/DM-HSE-Draft.pdf Вялый М., Подольский В., Рубцов А., Шварц Д., Шень А. Лекции по дискретной математике.]
# Гаврилов Г. П., Сапоженко А. А. Задачи и упражнения по дискретной математике. 3-е изд., М.: ФИЗМАТЛИТ, 2004.
# [https://drive.google.com/file/d/1RM6KX_reBFwUXesWGUEu0sFn2NCaBgvz/view?usp=sharing Дашков Е. В. Введение в математическую логику. Множества и отношения. М.: МФТИ, 2019.]
# Зубков А. М., Севастьянов Б. А., Чистяков В. П. Сборник задач по теории вероятностей. 2-е изд., М.: Наука, 1989.
# Мельников О. И. Теория графов в занимательных задачах. 5-е изд., М.: Книжный дом "ЛИБРОКОМ", 2013.
# [http://www.mccme.ru/free-books/shen/shen-induction.pdf Шень А., Математическая индукция. 5-е изд, М.: МЦНМО, 2016.]

Adaptation course in Discrete Math (факультатив)

2022-12-03T13:03:49Z

Nasta.trofimova:

== General Information ==
The main goal of the Discrete Mathematics Adaptation Course is to help students keep up with the course curriculum by discussing the most important and challenging topics in detail. The second very important goal of the course is to teach students to work competently with mathematical definitions and proofs, correctly logically build solutions to problems and prove statements. The topics of the course are coordinated with the "basic" course of the DSBA and SE program, but its study will also be useful for the direction of AMI. The approximate order of topics is sets and logic, functions and relations, the beginning of number theory, combinatorics, graphs, the foundations of probability theory, generating functions.

== Schedule ==

The classes are organised on Wednesdays at 18:10.

== Course materials ==

[https://t.me/+113aheknlsxmYzVi Chat in Telegram]

'''First semester'''

{| class="wikitable"
|-
! Date !! Topic !! Problem Set !! Class note !! Video
|-
|| 21.09.22 || Statements, connectives, quantifiers || [https://drive.google.com/file/d/1kbtRp8c79zE2AspfVb4ZfGZLJRy9Z5j2/view?usp=drivesdk Problem Set 1]|| - ||
|-
|| 28.09.22 || Validity of statements, types of proof|| [https://drive.google.com/file/d/1Q2OlmVzXf4P0ocd3eBet4ktoJ1h1DZyn/view?usp=sharing Problem Set 2] || [https://drive.google.com/file/d/11pdljFmpW57o5OqBH40YwioTW_Ebs_gK/view?usp=sharing Solutions] || -
|-
|| 7.10.22 || Three types of mathematical induction || [https://drive.google.com/file/d/14h2jy4W7KgxBffxE8TKh_13rSG3Wy_Ll/view?usp=sharing Problem Set 3] ||[https://drive.google.com/file/d/1yFnH5QBNxM-1ajoA5y7w9wV_31XeBwWp/view?usp=sharing Solutions] || [https://youtu.be/nljNhVjlnXg Video 3]
|-
|| 14.10.22 || Proofs with induction || [https://drive.google.com/file/d/13vsHkpBV8riwyKOTCh1v1heuAqf0L9nK/view?usp=sharing Problem Set 4] ||[https://drive.google.com/file/d/1PZD-YWikatG9jCbcc1r_Eo5t0y-kdcpj/view?usp=sharing Solutions] || -
|-
|| 21.10.22 || Divisibility. Calculation of remainders. Direct proofs. || [https://drive.google.com/file/d/1rHfC1WRv4IB8kNRMynVWv0C26PXGi137/view?usp=sharing Problem Set 5] ||[https://drive.google.com/file/d/1CvWAD5pDmMB8JFWSFNxOrrT7-Jfp_0Wd/view?usp=sharing Solutions] ||
[https://youtu.be/-OIYkDOkLyk Video 5]
|-
|| 11.11.22 || Great commod divider, the main thorem of arithmetic, direct proofs. || [https://drive.google.com/file/d/1CrF9W2rXFiTMKFoxZO-PJDmhYAx6Ql84/view?usp=share_link Problem Set 6] ||[https://drive.google.com/file/d/1TWSgbLrRtZWRrbneebExE4BPoDzLU4-b/view?usp=share_link Solutions] ||
[https://youtu.be/_2RRlq21gqM Video 6]
|-
|| 19.11.22 || Fermat's Little theorem, inverse elements in groups $\mathbb{Z}_p$, congruences. || [https://drive.google.com/file/d/1IF6rqwLN0Bq8n07mxQ3CAmoMfWplJ3OR/view?usp=share_link Problem Set 7] ||[https://drive.google.com/file/d/1FZevxpUjcPrrtCbxHn-HRh1odDamJqlq/view?usp=share_link Solutions] ||
[https://youtu.be/peuzIDzh1bE Video 7]
|-
|| 25.11.22 || Fermat's Little theorem, inverse elements in groups $\mathbb{Z}_p$, congruences. || [https://drive.google.com/file/d/1CYGJ7B5d426ChuZBozzsLKwMVZeVPgQJ/view?usp=share_link Problem Set 8] ||[https://drive.google.com/file/d/1_PCu2dDhIgN7uE1ijLGLH1USapPskGWH/view?usp=share_link Solutions] ||
[ -]
|-
|| 2.12.22 || Application of Euler's theorem and Euclidean algorithm, cryptography || [https://drive.google.com/file/d/1Oq3grvUbG-yBBbrHqhK_4Ylz4Io-D1Lw/view?usp=share_link Problem Set 9] ||[https://drive.google.com/file/d/1BFDh6-6KVmb65w7qDEQprP6BYUMUW6AQ/view?usp=share_link Solutions] ||
[Soon Video 9]
|}

[https://drive.google.com/file/d/163PgGw33FTt3PUVdVBYCjIHluftfZVol/view?usp=sharing Last year retake]

[https://drive.google.com/file/d/1bljTOb3x0kvYy7cslTOC4B3StYOHi3CX/view Last year test 1]

== Homeworks ==
[https://forms.gle/TAgL2eUkhSyhZKLD9 Homework 1 (Logics)], Deadline 31st October

[https://forms.gle/pVA1a8xbeP54RqAQ7 Homework 2 (Induction)], Deadline 31st November, better to complete before the November Test

[https://drive.google.com/file/d/1k8SKmN9J_DdSs8ibP_9b52n8LxiPf_8U/view?usp=share_link Homework 3]: write down solutions to exam 1 in a perfect manner (like you you are going to print a book of your solutions), Deadline 25th November. You can pass them written or orally on Fridays evenings. Do it if you want to have MAX in the retake(if so happened) and in the exam in the end of the course.

==Semester 1 ==

[https://docs.google.com/spreadsheets/d/1YHhkk8TCm_qPF0tXyGe7rc-DzubrgSESZUoW6fHMLZA/edit?usp=sharing Current grades and comments]

== References ==

1. [http://discrete.openmathbooks.org/dmoi3.html Discrete Mathematics (An Open Introduction) by Oscar Levin,] p. 197 Logics. Many simple problems with solution to feel the topic.

2. [https://drive.google.com/file/d/1mmNLLQ0--EDihGNRKwSyXLOA1KL7A0lD/view?usp=sharing Lecture notes by Evgeny Dashkov]

PLUS: there is a [https://youtube.com/playlist?list=PLEwK9wdS5g0pk-1YWDc3hezRt_rNpQDf8 folder with records on wikipage ]

3. [http://www.mccme.ru/free-books/shen/shen-induction.pdf Шень А., Математическая индукция. 5-е изд, М.: МЦНМО, 2016.] Many problems to work with three different versions of induction.

== Grading and Results ==

'''Final grade''' = Average(HWs)+ Bonus points

Bonus point number is between 0 to 20. Such points may be given for a variety of auxiliary activities.

Adaptation course in Discrete Math (факультатив)

2022-12-01T20:53:42Z

Nasta.trofimova:

== General Information ==
The main goal of the Discrete Mathematics Adaptation Course is to help students keep up with the course curriculum by discussing the most important and challenging topics in detail. The second very important goal of the course is to teach students to work competently with mathematical definitions and proofs, correctly logically build solutions to problems and prove statements. The topics of the course are coordinated with the "basic" course of the DSBA and SE program, but its study will also be useful for the direction of AMI. The approximate order of topics is sets and logic, functions and relations, the beginning of number theory, combinatorics, graphs, the foundations of probability theory, generating functions.

== Schedule ==

The classes are organised on Wednesdays at 18:10.

== Course materials ==

[https://t.me/+113aheknlsxmYzVi Chat in Telegram]

'''First semester'''

{| class="wikitable"
|-
! Date !! Topic !! Problem Set !! Class note !! Video
|-
|| 21.09.22 || Statements, connectives, quantifiers || [https://drive.google.com/file/d/1kbtRp8c79zE2AspfVb4ZfGZLJRy9Z5j2/view?usp=drivesdk Problem Set 1]|| - ||
|-
|| 28.09.22 || Validity of statements, types of proof|| [https://drive.google.com/file/d/1Q2OlmVzXf4P0ocd3eBet4ktoJ1h1DZyn/view?usp=sharing Problem Set 2] || [https://drive.google.com/file/d/11pdljFmpW57o5OqBH40YwioTW_Ebs_gK/view?usp=sharing Solutions] || -
|-
|| 7.10.22 || Three types of mathematical induction || [https://drive.google.com/file/d/14h2jy4W7KgxBffxE8TKh_13rSG3Wy_Ll/view?usp=sharing Problem Set 3] ||[https://drive.google.com/file/d/1yFnH5QBNxM-1ajoA5y7w9wV_31XeBwWp/view?usp=sharing Solutions] || [https://youtu.be/nljNhVjlnXg Video 3]
|-
|| 14.10.22 || Proofs with induction || [https://drive.google.com/file/d/13vsHkpBV8riwyKOTCh1v1heuAqf0L9nK/view?usp=sharing Problem Set 4] ||[https://drive.google.com/file/d/1PZD-YWikatG9jCbcc1r_Eo5t0y-kdcpj/view?usp=sharing Solutions] || -
|-
|| 21.10.22 || Divisibility. Calculation of remainders. Direct proofs. || [https://drive.google.com/file/d/1rHfC1WRv4IB8kNRMynVWv0C26PXGi137/view?usp=sharing Problem Set 5] ||[https://drive.google.com/file/d/1CvWAD5pDmMB8JFWSFNxOrrT7-Jfp_0Wd/view?usp=sharing Solutions] ||
[https://youtu.be/-OIYkDOkLyk Video 5]
|-
|| 11.11.22 || Great commod divider, the main thorem of arithmetic, direct proofs. || [https://drive.google.com/file/d/1CrF9W2rXFiTMKFoxZO-PJDmhYAx6Ql84/view?usp=share_link Problem Set 6] ||[https://drive.google.com/file/d/1TWSgbLrRtZWRrbneebExE4BPoDzLU4-b/view?usp=share_link Solutions] ||
[https://youtu.be/_2RRlq21gqM Video 6]
|-
|| 19.11.22 || Fermat's Little theorem, inverse elements in groups $\mathbb{Z}_p$, congruences. || [https://drive.google.com/file/d/1IF6rqwLN0Bq8n07mxQ3CAmoMfWplJ3OR/view?usp=share_link Problem Set 7] ||[https://drive.google.com/file/d/1FZevxpUjcPrrtCbxHn-HRh1odDamJqlq/view?usp=share_link Solutions] ||
[https://youtu.be/peuzIDzh1bE Video 7]
|-
|| 25.11.22 || Fermat's Little theorem, inverse elements in groups $\mathbb{Z}_p$, congruences. || [https://drive.google.com/file/d/1CYGJ7B5d426ChuZBozzsLKwMVZeVPgQJ/view?usp=share_link Problem Set 8] ||[https://drive.google.com/file/d/1_PCu2dDhIgN7uE1ijLGLH1USapPskGWH/view?usp=share_link Solutions] ||
[ -]
|-
|| 2.12.22 || Application of Euler's theorem and Euclidean algorithm, cryptography || [https://drive.google.com/file/d/1Oq3grvUbG-yBBbrHqhK_4Ylz4Io-D1Lw/view?usp=share_link Problem Set 9] ||[ Solutions] ||
[ Video 9]
|}

[https://drive.google.com/file/d/163PgGw33FTt3PUVdVBYCjIHluftfZVol/view?usp=sharing Last year retake]

[https://drive.google.com/file/d/1bljTOb3x0kvYy7cslTOC4B3StYOHi3CX/view Last year test 1]

== Homeworks ==
[https://forms.gle/TAgL2eUkhSyhZKLD9 Homework 1 (Logics)], Deadline 31st October

[https://forms.gle/pVA1a8xbeP54RqAQ7 Homework 2 (Induction)], Deadline 31st November, better to complete before the November Test

[https://drive.google.com/file/d/1k8SKmN9J_DdSs8ibP_9b52n8LxiPf_8U/view?usp=share_link Homework 3]: write down solutions to exam 1 in a perfect manner (like you you are going to print a book of your solutions), Deadline 25th November. You can pass them written or orally on Fridays evenings. Do it if you want to have MAX in the retake(if so happened) and in the exam in the end of the course.

==Semester 1 ==

[https://docs.google.com/spreadsheets/d/1YHhkk8TCm_qPF0tXyGe7rc-DzubrgSESZUoW6fHMLZA/edit?usp=sharing Current grades and comments]

== References ==

1. [http://discrete.openmathbooks.org/dmoi3.html Discrete Mathematics (An Open Introduction) by Oscar Levin,] p. 197 Logics. Many simple problems with solution to feel the topic.

2. [https://drive.google.com/file/d/1mmNLLQ0--EDihGNRKwSyXLOA1KL7A0lD/view?usp=sharing Lecture notes by Evgeny Dashkov]

PLUS: there is a [https://youtube.com/playlist?list=PLEwK9wdS5g0pk-1YWDc3hezRt_rNpQDf8 folder with records on wikipage ]

3. [http://www.mccme.ru/free-books/shen/shen-induction.pdf Шень А., Математическая индукция. 5-е изд, М.: МЦНМО, 2016.] Many problems to work with three different versions of induction.

== Grading and Results ==

'''Final grade''' = Average(HWs)+ Bonus points

Bonus point number is between 0 to 20. Such points may be given for a variety of auxiliary activities.

Adaptation course in Discrete Math (факультатив)

2022-12-01T20:53:25Z

Nasta.trofimova: /* Course materials */

== General Information ==
The main goal of the Discrete Mathematics Adaptation Course is to help students keep up with the course curriculum by discussing the most important and challenging topics in detail. The second very important goal of the course is to teach students to work competently with mathematical definitions and proofs, correctly logically build solutions to problems and prove statements. The topics of the course are coordinated with the "basic" course of the DSBA and SE program, but its study will also be useful for the direction of AMI. The approximate order of topics is sets and logic, functions and relations, the beginning of number theory, combinatorics, graphs, the foundations of probability theory, generating functions.

== Schedule ==

The classes are organised on Wednesdays at 18:10.

== Course materials ==

[https://t.me/+113aheknlsxmYzVi Chat in Telegram]

'''First semester'''

{| class="wikitable"
|-
! Date !! Topic !! Problem Set !! Class note !! Video
|-
|| 21.09.22 || Statements, connectives, quantifiers || [https://drive.google.com/file/d/1kbtRp8c79zE2AspfVb4ZfGZLJRy9Z5j2/view?usp=drivesdk Problem Set 1]|| - ||
|-
|| 28.09.22 || Validity of statements, types of proof|| [https://drive.google.com/file/d/1Q2OlmVzXf4P0ocd3eBet4ktoJ1h1DZyn/view?usp=sharing Problem Set 2] || [https://drive.google.com/file/d/11pdljFmpW57o5OqBH40YwioTW_Ebs_gK/view?usp=sharing Solutions] || -
|-
|| 7.10.22 || Three types of mathematical induction || [https://drive.google.com/file/d/14h2jy4W7KgxBffxE8TKh_13rSG3Wy_Ll/view?usp=sharing Problem Set 3] ||[https://drive.google.com/file/d/1yFnH5QBNxM-1ajoA5y7w9wV_31XeBwWp/view?usp=sharing Solutions] || [https://youtu.be/nljNhVjlnXg Video 3]
|-
|| 14.10.22 || Proofs with induction || [https://drive.google.com/file/d/13vsHkpBV8riwyKOTCh1v1heuAqf0L9nK/view?usp=sharing Problem Set 4] ||[https://drive.google.com/file/d/1PZD-YWikatG9jCbcc1r_Eo5t0y-kdcpj/view?usp=sharing Solutions] || -
|-
|| 21.10.22 || Divisibility. Calculation of remainders. Direct proofs. || [https://drive.google.com/file/d/1rHfC1WRv4IB8kNRMynVWv0C26PXGi137/view?usp=sharing Problem Set 5] ||[https://drive.google.com/file/d/1CvWAD5pDmMB8JFWSFNxOrrT7-Jfp_0Wd/view?usp=sharing Solutions] ||
[https://youtu.be/-OIYkDOkLyk Video 5]
|-
|| 11.11.22 || Great commod divider, the main thorem of arithmetic, direct proofs. || [https://drive.google.com/file/d/1CrF9W2rXFiTMKFoxZO-PJDmhYAx6Ql84/view?usp=share_link Problem Set 6] ||[https://drive.google.com/file/d/1TWSgbLrRtZWRrbneebExE4BPoDzLU4-b/view?usp=share_link Solutions] ||
[https://youtu.be/_2RRlq21gqM Video 6]
|-
|| 19.11.22 || Fermat's Little theorem, inverse elements in groups $\mathbb{Z}_p$, congruences. || [https://drive.google.com/file/d/1IF6rqwLN0Bq8n07mxQ3CAmoMfWplJ3OR/view?usp=share_link Problem Set 7] ||[https://drive.google.com/file/d/1FZevxpUjcPrrtCbxHn-HRh1odDamJqlq/view?usp=share_link Solutions] ||
[https://youtu.be/peuzIDzh1bE Video 7]
|-
|| 25.11.22 || Fermat's Little theorem, inverse elements in groups $\mathbb{Z}_p$, congruences. || [https://drive.google.com/file/d/1CYGJ7B5d426ChuZBozzsLKwMVZeVPgQJ/view?usp=share_link Problem Set 8] ||[https://drive.google.com/file/d/1_PCu2dDhIgN7uE1ijLGLH1USapPskGWH/view?usp=share_link Solutions] ||
[ Video 8]
|-
|| 2.12.22 || Application of Euler's theorem and Euclidean algorithm, cryptography || [https://drive.google.com/file/d/1Oq3grvUbG-yBBbrHqhK_4Ylz4Io-D1Lw/view?usp=share_link Problem Set 9] ||[ Solutions] ||
[ Video 9]
|}

[https://drive.google.com/file/d/163PgGw33FTt3PUVdVBYCjIHluftfZVol/view?usp=sharing Last year retake]

[https://drive.google.com/file/d/1bljTOb3x0kvYy7cslTOC4B3StYOHi3CX/view Last year test 1]

== Homeworks ==
[https://forms.gle/TAgL2eUkhSyhZKLD9 Homework 1 (Logics)], Deadline 31st October

[https://forms.gle/pVA1a8xbeP54RqAQ7 Homework 2 (Induction)], Deadline 31st November, better to complete before the November Test

[https://drive.google.com/file/d/1k8SKmN9J_DdSs8ibP_9b52n8LxiPf_8U/view?usp=share_link Homework 3]: write down solutions to exam 1 in a perfect manner (like you you are going to print a book of your solutions), Deadline 25th November. You can pass them written or orally on Fridays evenings. Do it if you want to have MAX in the retake(if so happened) and in the exam in the end of the course.

==Semester 1 ==

[https://docs.google.com/spreadsheets/d/1YHhkk8TCm_qPF0tXyGe7rc-DzubrgSESZUoW6fHMLZA/edit?usp=sharing Current grades and comments]

== References ==

1. [http://discrete.openmathbooks.org/dmoi3.html Discrete Mathematics (An Open Introduction) by Oscar Levin,] p. 197 Logics. Many simple problems with solution to feel the topic.

2. [https://drive.google.com/file/d/1mmNLLQ0--EDihGNRKwSyXLOA1KL7A0lD/view?usp=sharing Lecture notes by Evgeny Dashkov]

PLUS: there is a [https://youtube.com/playlist?list=PLEwK9wdS5g0pk-1YWDc3hezRt_rNpQDf8 folder with records on wikipage ]

3. [http://www.mccme.ru/free-books/shen/shen-induction.pdf Шень А., Математическая индукция. 5-е изд, М.: МЦНМО, 2016.] Many problems to work with three different versions of induction.

== Grading and Results ==

'''Final grade''' = Average(HWs)+ Bonus points

Bonus point number is between 0 to 20. Such points may be given for a variety of auxiliary activities.

Discrete Mathematics DSBA 2022/2023

2022-12-01T06:52:23Z

Nasta.trofimova: /* Assignment deadlines */

== Instructors ==

=== The lecturer ===
My name is Evgeny Dashkov. Feel free to contact me via email: edashkov@gmail.com, [https://t.me/edashkov Telegram], or [https://vk.com/evgeny.v.dashkov VK].

=== Seminar instructors ===
{| class="wikitable" style="text-align:center"
|-
! Group !! 221 !! 222 !! 223 !! 224
|-
|| Teachers || Evgeny Dashkov ||colspan="2"| Boris Danilov [https://t.me/brdann Telegram]|| Trofimova Anastasia [https://t.me/AnastasiiaTrofimova Telegram]
|-
|| Teaching Assistants || Arseny Bolotnikov [https://t.me/l0i4b Telegram] ||Daria Ivanova [https://t.me/ivanovskayaaaaa Telegram]|| Artem Ilin [https://t.me/artem_ilinn Telegram] || Marianna Kouis [https://t.me/mariannakouis Telegram]
|-
|| Lecturer’s Assistant || colspan="4"| Alyona Chislova [https://t.me/alenka_chislova Telegram]
|}

== Current performance ==

[https://docs.google.com/spreadsheets/d/1KoXyABY4alQu-Gw3HsYy3Vco9rfvHdYQZuUjE_ERJB8/edit?usp=sharing The Table]

== Homework ==
The homework includes a few problem sets, one in a fortnight or so (the deadlines are announced on giving each set). Every problem set consists of about 10 – 15 problems, some of which are labeled as ‘bonus’ while all the remaining are considered ‘ordinary’. One can get either 0, ½, or 1 point for each problem. For the entire homework, two values are computed:

HW = (the sum of points given for ordinary problems) / #(ordinary problems);

HW* = (the sum of points given for bonus problems) / #(bonus problems).

The value HW1 is similar to HW but restricted to the problem sets given in Module 1.

A student may be required to explain orally his written solution to any problem. His grade for the problem may be decreased if he fails to do so properly.

== Exam 1 ==
A written examination is held past Module 1. Students may not consult any sources during the exam. Some problems of the exam are labeled as ‘bonus’; the others are ‘ordinary’. Each problem solution is graded with either 0, ¼, ½, ¾, or 1 point, and the entire exam with two values:

Exam1 = (the sum of points given for ordinary problems) / #(ordinary problems);

Exam1* = (the sum of points given for bonus problems) / #(bonus problems)

== Colloquium ==
An oral colloquium is held at the beginning of Module 3. Each student is given two questions concerning statements and definitions as well as one question requiring a proof. After no less than 45 minutes of preparation (when using any literature is allowed), the student is required to answer ‘from scratch’, that is, with no recourse to any materials. The examiner may pose additional questions as he sees fit. The student may get from 0 to 7 integer points for his answer; the value

Colloq = (the score given) / 7

is then computed.

== Exam 2 ==
A written examination is held at the end of the Course. Students may not consult any sources during the exam. The examination takes about 120 minutes. Some problems of the exam are labeled as ‘bonus’; the others are ‘ordinary’. Each problem solution is graded with either 0, ¼, ½, ¾, or 1 point; finally, two values are computed:

Exam2 = (the sum of points given for ordinary problems) / #(ordinary problems);

Exam2* = (the sum of points given for bonus problems) / #(bonus problems).

== Bonus activities ==
The students may be graded for a variety of ‘bonus activities’ (like quizzes, etc.) with an overall integer value Bonus from 0 to 25.

== Exam retaking ==
Examinations 1 and 2 are subject to be retaken if Module 1 grade or Final grade (see below), respectively, is unsatisfactory. Retaking the exam is similar to the regular examination. The resulting grade is substituted for that of the latter. The last try Commission retaking is held for those whose final grade is still unsatisfactory after the retaking. A designated Commission carefully examines the student’s performance and gives him a final mark not better than ‘satisfactory’; at that the Commission is not bound by the grading formulas herein.

== Course materials ==

[https://t.me/joinchat/T_YTN4IG1vAJNWT9 Course chat].

=== Lecture notes ===

https://drive.google.com/file/d/1mmNLLQ0--EDihGNRKwSyXLOA1KL7A0lD/view?usp=sharing

=== Classes recordings ===

https://disk.yandex.ru/d/enYKJ6O8NN_3lQ

=== Lecture video archive ===

https://youtube.com/playlist?list=PLEwK9wdS5g0pk-1YWDc3hezRt_rNpQDf8

=== Other resources ===
* [https://tinyurl.com/rwky5vmk The Course's Google Directory]

* [https://www.youtube.com/playlist?list=PL1Uob8iPTHGTidrmrqEHTJ96Pt3-PmML4 Past years' videos]

* We have a [https://meet.edashkov.net.ru dedicated server] to hold an online meeting if we need one.

== Problem sets ==

=== Class problems ===

* [https://drive.google.com/file/d/1EP-diSuOTn9f0ryg18Z2w0xjEp8j0bnl/view?usp=sharing Problem set 1]

* [https://drive.google.com/file/d/12ct99-ORd7A94Gh5g4Nf9riv7UqNMSRc/view?usp=sharing Problem set 2]

* [https://drive.google.com/file/d/1yKKqLsS99V4AhCYqbjafuav2CMCdQTOQ/view?usp=sharing Problem set 3]

* [https://drive.google.com/file/d/1YgH_AdCk4GcKC0KH7xBA4-sUnOYkUvUK/view?usp=share_link Problem set 4]

=== Homework problems ===

* [https://drive.google.com/file/d/1A8lFPdI3ZvC1vOgz2KEpYcuWOFlsQvb1/view?usp=sharing Homework 1]

* [https://drive.google.com/file/d/1LOPPwGjyVleR_mclxTKUJ_bxFrxt44sW/view?usp=sharing Homework 2a]

* [https://drive.google.com/file/d/1W7k1OTiIMlPOpo-2mwmGegrc4RDHz5_j/view?usp=share_link Homework 2b]

=== Assignment deadlines ===

{| class="wikitable"
|-
! Home problem set !! colspan="11" | Deadline
|-
| || 221 || 222 || 223 || 224
|-
| HW 1 №1-3 || || 22.IX || 22.IX || 22.IX
|-
| HW 1 || October 6 || October 6 || October 6 || October 6
|-
| HW 2a №1-3 || || October 20 || October 20 ||
|-
| HW 2a || October 24 || October 27 || October 27 || October 27
|-
| HW 2b №1-7 || November 30 || November 20 || November 20 || November 20
|-
| HW 2b №8-14 || || December 4 || December 4 || December 4
|}

'''Each deadline is set by the respective group's instructor.'''

== Grading system ==
For the final grading, we compute the following values:

Module 1 grade = round ((50*HW1 + 50*Exam1)/100);

basic = (21*Exam1 + 21*Colloq + 28*HW + 30*Exam2)/100;

adv = (30*Exam1* + Bonus + 35*HW* + 35*Exam2*)/100;

Final grade = round(min(10, 8 * basic + 2 * adv)).

The final grade is rounded half up to an integer. All the other values are reported with the greatest precision available.

== Recommended reading ==
''Please notice that '''The Book''' for our Course does not exist. The latter is based on many sources.''

# Anderson J. A., Discrete Mathematics With Combinatorics. Prentice Hall, 2003.
# Biggs N. L., Discrete mathematics. 2nd ed., New York; Oxford: Oxford University Press, 2004.
# Gavrilov G. P., Sapozhenko A. A. Problems and Exercises in Discrete Mathematics. Kluwer Texts in the Mathematical Sciences 14. Springer, 1996.
# [http://courses.csail.mit.edu/6.042/spring17/mcs.pdf Lehman E., Thomson Leighton F., Meyer A. R. Mathematics for Computer Science, 2017.]
# [http://www.cs.elte.hu/~lovasz/dmbook.ps Lovasz L., Vesztergombi K. Discrete Mathematics. Lecture Notes; Yale University, 1999.]
# Melnikov O., Sarvanov V., Tyshkevich R., Yemelichev V., Zverovich I. Exercises in Graph Theory. Kluwer Texts in the Mathematical Sciences 19. Springer, 1998.
# Rosen K. H. Discrete Mathematics and Its Applications. McGraw-Hill, 1999.
# Stein C., Drysdale R. L., Bogart K. Discrete mathematics for computer scientists. Addison-Wesley, 2010.
# Vinogradov I. M. Elements of number theory. Dover, 1954.

=== In Russian ===
''If you understand Russian (by any chance), you will probably benefit from reading the following books.''

# Виноградов И. М. Основы теории чисел. 9-е изд., М.: Наука, 1981.
# [http://rubtsov.su/public/DM-HSE-Draft.pdf Вялый М., Подольский В., Рубцов А., Шварц Д., Шень А. Лекции по дискретной математике.]
# Гаврилов Г. П., Сапоженко А. А. Задачи и упражнения по дискретной математике. 3-е изд., М.: ФИЗМАТЛИТ, 2004.
# [https://drive.google.com/file/d/1RM6KX_reBFwUXesWGUEu0sFn2NCaBgvz/view?usp=sharing Дашков Е. В. Введение в математическую логику. Множества и отношения. М.: МФТИ, 2019.]
# Зубков А. М., Севастьянов Б. А., Чистяков В. П. Сборник задач по теории вероятностей. 2-е изд., М.: Наука, 1989.
# Мельников О. И. Теория графов в занимательных задачах. 5-е изд., М.: Книжный дом "ЛИБРОКОМ", 2013.
# [http://www.mccme.ru/free-books/shen/shen-induction.pdf Шень А., Математическая индукция. 5-е изд, М.: МЦНМО, 2016.]

Discrete Mathematics DSBA 2022/2023

2022-11-21T19:14:29Z

Nasta.trofimova:

== Instructors ==

=== The lecturer ===
My name is Evgeny Dashkov. Feel free to contact me via email: edashkov@gmail.com, [https://t.me/edashkov Telegram], or [https://vk.com/evgeny.v.dashkov VK].

=== Seminar instructors ===
{| class="wikitable" style="text-align:center"
|-
! Group !! 221 !! 222 !! 223 !! 224
|-
|| Teachers || Evgeny Dashkov ||colspan="2"| Boris Danilov [https://t.me/brdann Telegram]|| Trofimova Anastasia [https://t.me/AnastasiiaTrofimova Telegram]
|-
|| Teaching Assistants || Arseny Bolotnikov [https://t.me/l0i4b Telegram] ||Daria Ivanova [https://t.me/ivanovskayaaaaa Telegram]|| Artem Ilin [https://t.me/artem_ilinn Telegram] || Marianna Kouis [https://t.me/mariannakouis Telegram]
|}

== Current performance ==

[https://docs.google.com/spreadsheets/d/1KoXyABY4alQu-Gw3HsYy3Vco9rfvHdYQZuUjE_ERJB8/edit?usp=sharing The Table]

== Homework ==
The homework includes a few problem sets, one in a fortnight or so (the deadlines are announced on giving each set). Every problem set consists of about 10 – 15 problems, some of which are labeled as ‘bonus’ while all the remaining are considered ‘ordinary’. One can get either 0, ½, or 1 point for each problem. For the entire homework, two values are computed:

HW = (the sum of points given for ordinary problems) / #(ordinary problems);

HW* = (the sum of points given for bonus problems) / #(bonus problems).

The value HW1 is similar to HW but restricted to the problem sets given in Module 1.

A student may be required to explain orally his written solution to any problem. His grade for the problem may be decreased if he fails to do so properly.

== Exam 1 ==
A written examination is held past Module 1. Students may not consult any sources during the exam. Some problems of the exam are labeled as ‘bonus’; the others are ‘ordinary’. Each problem solution is graded with either 0, ¼, ½, ¾, or 1 point, and the entire exam with two values:

Exam1 = (the sum of points given for ordinary problems) / #(ordinary problems);

Exam1* = (the sum of points given for bonus problems) / #(bonus problems)

== Colloquium ==
An oral colloquium is held at the beginning of Module 3. Each student is given two questions concerning statements and definitions as well as one question requiring a proof. After no less than 45 minutes of preparation (when using any literature is allowed), the student is required to answer ‘from scratch’, that is, with no recourse to any materials. The examiner may pose additional questions as he sees fit. The student may get from 0 to 7 integer points for his answer; the value

Colloq = (the score given) / 7

is then computed.

== Exam 2 ==
A written examination is held at the end of the Course. Students may not consult any sources during the exam. The examination takes about 120 minutes. Some problems of the exam are labeled as ‘bonus’; the others are ‘ordinary’. Each problem solution is graded with either 0, ¼, ½, ¾, or 1 point; finally, two values are computed:

Exam2 = (the sum of points given for ordinary problems) / #(ordinary problems);

Exam2* = (the sum of points given for bonus problems) / #(bonus problems).

== Bonus activities ==
The students may be graded for a variety of ‘bonus activities’ (like quizzes, etc.) with an overall integer value Bonus from 0 to 25.

== Exam retaking ==
Examinations 1 and 2 are subject to be retaken if Module 1 grade or Final grade (see below), respectively, is unsatisfactory. Retaking the exam is similar to the regular examination. The resulting grade is substituted for that of the latter. The last try Commission retaking is held for those whose final grade is still unsatisfactory after the retaking. A designated Commission carefully examines the student’s performance and gives him a final mark not better than ‘satisfactory’; at that the Commission is not bound by the grading formulas herein.

== Course materials ==

[https://t.me/joinchat/T_YTN4IG1vAJNWT9 Course chat].

=== Lecture notes ===

https://drive.google.com/file/d/1mmNLLQ0--EDihGNRKwSyXLOA1KL7A0lD/view?usp=sharing

=== Lecture video archive ===

https://youtube.com/playlist?list=PLEwK9wdS5g0pk-1YWDc3hezRt_rNpQDf8

=== Other resources ===
* [https://tinyurl.com/rwky5vmk The Course's Google Directory]

* [https://www.youtube.com/playlist?list=PL1Uob8iPTHGTidrmrqEHTJ96Pt3-PmML4 Past years' videos]

* We have a [https://meet.edashkov.net.ru dedicated server] to hold an online meeting if we need one.

== Problem sets ==

=== Class problems ===

* [https://drive.google.com/file/d/1EP-diSuOTn9f0ryg18Z2w0xjEp8j0bnl/view?usp=sharing Problem set 1]

* [https://drive.google.com/file/d/12ct99-ORd7A94Gh5g4Nf9riv7UqNMSRc/view?usp=sharing Problem set 2]

* [https://drive.google.com/file/d/1yKKqLsS99V4AhCYqbjafuav2CMCdQTOQ/view?usp=sharing Problem set 3]

* [https://drive.google.com/file/d/1YgH_AdCk4GcKC0KH7xBA4-sUnOYkUvUK/view?usp=share_link Problem set 4]

=== Homework problems ===

* [https://drive.google.com/file/d/1A8lFPdI3ZvC1vOgz2KEpYcuWOFlsQvb1/view?usp=sharing Homework 1]

* [https://drive.google.com/file/d/1LOPPwGjyVleR_mclxTKUJ_bxFrxt44sW/view?usp=sharing Homework 2a]

* [https://drive.google.com/file/d/1W7k1OTiIMlPOpo-2mwmGegrc4RDHz5_j/view?usp=share_link Homework 2b]

=== Assignment deadlines ===

{| class="wikitable"
|-
! Home problem set !! colspan="11" | Deadline
|-
| || 221 || 222 || 223 || 224
|-
| HW 1 №1-3 || || 22.IX || 22.IX || 22.IX
|-
| HW 1 || October 6 || October 6 || October 6 || October 6
|-
| HW 2a №1-3 || || October 20 || October 20 ||
|-
| HW 2a || October 24 || October 27 || October 27 || October 27
|-
| HW 2b №1-7 || || November 20 || November 20 || November 20
|}

'''Each deadline is set by the respective group's instructor.'''

== Grading system ==
For the final grading, we compute the following values:

Module 1 grade = round ((50*HW1 + 50*Exam1)/100);

basic = (21*Exam1 + 21*Colloq + 28*HW + 30*Exam2)/100;

adv = (30*Exam1* + Bonus + 35*HW* + 35*Exam2*)/100;

Final grade = round(min(10, 8 * basic + 2 * adv)).

The final grade is rounded half up to an integer. All the other values are reported with the greatest precision available.

== Recommended reading ==
''Please notice that '''The Book''' for our Course does not exist. The latter is based on many sources.''

# Anderson J. A., Discrete Mathematics With Combinatorics. Prentice Hall, 2003.
# Biggs N. L., Discrete mathematics. 2nd ed., New York; Oxford: Oxford University Press, 2004.
# Gavrilov G. P., Sapozhenko A. A. Problems and Exercises in Discrete Mathematics. Kluwer Texts in the Mathematical Sciences 14. Springer, 1996.
# [http://courses.csail.mit.edu/6.042/spring17/mcs.pdf Lehman E., Thomson Leighton F., Meyer A. R. Mathematics for Computer Science, 2017.]
# [http://www.cs.elte.hu/~lovasz/dmbook.ps Lovasz L., Vesztergombi K. Discrete Mathematics. Lecture Notes; Yale University, 1999.]
# Melnikov O., Sarvanov V., Tyshkevich R., Yemelichev V., Zverovich I. Exercises in Graph Theory. Kluwer Texts in the Mathematical Sciences 19. Springer, 1998.
# Rosen K. H. Discrete Mathematics and Its Applications. McGraw-Hill, 1999.
# Stein C., Drysdale R. L., Bogart K. Discrete mathematics for computer scientists. Addison-Wesley, 2010.
# Vinogradov I. M. Elements of number theory. Dover, 1954.

=== In Russian ===
''If you understand Russian (by any chance), you will probably benefit from reading the following books.''

# Виноградов И. М. Основы теории чисел. 9-е изд., М.: Наука, 1981.
# [http://rubtsov.su/public/DM-HSE-Draft.pdf Вялый М., Подольский В., Рубцов А., Шварц Д., Шень А. Лекции по дискретной математике.]
# Гаврилов Г. П., Сапоженко А. А. Задачи и упражнения по дискретной математике. 3-е изд., М.: ФИЗМАТЛИТ, 2004.
# [https://drive.google.com/file/d/1RM6KX_reBFwUXesWGUEu0sFn2NCaBgvz/view?usp=sharing Дашков Е. В. Введение в математическую логику. Множества и отношения. М.: МФТИ, 2019.]
# Зубков А. М., Севастьянов Б. А., Чистяков В. П. Сборник задач по теории вероятностей. 2-е изд., М.: Наука, 1989.
# Мельников О. И. Теория графов в занимательных задачах. 5-е изд., М.: Книжный дом "ЛИБРОКОМ", 2013.
# [http://www.mccme.ru/free-books/shen/shen-induction.pdf Шень А., Математическая индукция. 5-е изд, М.: МЦНМО, 2016.]

Adaptation course in Discrete Math (факультатив)

2022-11-19T15:09:53Z

Nasta.trofimova:

Adaptation course in Discrete Math (факультатив)

2022-11-18T23:01:48Z

Nasta.trofimova: /* Course materials */

Discrete Mathematics DSBA 2022/2023

2022-11-10T18:34:18Z

Nasta.trofimova: /* Assignment deadlines */

== Instructors ==

=== The lecturer ===
My name is Evgeny Dashkov. Feel free to contact me via email: edashkov@gmail.com, [https://t.me/edashkov Telegram], or [https://vk.com/evgeny.v.dashkov VK].

=== Seminar instructors ===
{| class="wikitable" style="text-align:center"
|-
! Group !! 221 !! 222 !! 223 !! 224
|-
|| Teachers || Evgeny Dashkov ||colspan="2"| Boris Danilov [https://t.me/brdann Telegram]|| Trofimova Anastasia [https://t.me/AnastasiiaTrofimova Telegram]
|-
|| Teaching Assistants || Arseny Bolotnikov [https://t.me/l0i4b Telegram] ||Daria Ivanova [https://t.me/ivanovskayaaaaa Telegram]|| Artem Ilin [https://t.me/artem_ilinn Telegram] || Marianna Kouis [https://t.me/mariannakouis Telegram]
|}

== Current performance ==

[https://docs.google.com/spreadsheets/d/1KoXyABY4alQu-Gw3HsYy3Vco9rfvHdYQZuUjE_ERJB8/edit?usp=sharing The Table]

== Homework ==
The homework includes a few problem sets, one in a fortnight or so (the deadlines are announced on giving each set). Every problem set consists of about 10 – 15 problems, some of which are labeled as ‘bonus’ while all the remaining are considered ‘ordinary’. One can get either 0, ½, or 1 point for each problem. For the entire homework, two values are computed:

HW = (the sum of points given for ordinary problems) / #(ordinary problems);

HW* = (the sum of points given for bonus problems) / #(bonus problems).

The value HW1 is similar to HW but restricted to the problem sets given in Module 1.

A student may be required to explain orally his written solution to any problem. His grade for the problem may be decreased if he fails to do so properly.

== Exam 1 ==
A written examination is held past Module 1. Students may not consult any sources during the exam. Some problems of the exam are labeled as ‘bonus’; the others are ‘ordinary’. Each problem solution is graded with either 0, ¼, ½, ¾, or 1 point, and the entire exam with two values:

Exam1 = (the sum of points given for ordinary problems) / #(ordinary problems);

Exam1* = (the sum of points given for bonus problems) / #(bonus problems)

== Colloquium ==
An oral colloquium is held at the beginning of Module 3. Each student is given two questions concerning statements and definitions as well as one question requiring a proof. After no less than 45 minutes of preparation (when using any literature is allowed), the student is required to answer ‘from scratch’, that is, with no recourse to any materials. The examiner may pose additional questions as he sees fit. The student may get from 0 to 7 integer points for his answer; the value

Colloq = (the score given) / 7

is then computed.

== Exam 2 ==
A written examination is held at the end of the Course. Students may not consult any sources during the exam. The examination takes about 120 minutes. Some problems of the exam are labeled as ‘bonus’; the others are ‘ordinary’. Each problem solution is graded with either 0, ¼, ½, ¾, or 1 point; finally, two values are computed:

Exam2 = (the sum of points given for ordinary problems) / #(ordinary problems);

Exam2* = (the sum of points given for bonus problems) / #(bonus problems).

== Bonus activities ==
The students may be graded for a variety of ‘bonus activities’ (like quizzes, etc.) with an overall integer value Bonus from 0 to 25.

== Exam retaking ==
Examinations 1 and 2 are subject to be retaken if Module 1 grade or Final grade (see below), respectively, is unsatisfactory. Retaking the exam is similar to the regular examination. The resulting grade is substituted for that of the latter. The last try Commission retaking is held for those whose final grade is still unsatisfactory after the retaking. A designated Commission carefully examines the student’s performance and gives him a final mark not better than ‘satisfactory’; at that the Commission is not bound by the grading formulas herein.

== Course materials ==

[https://t.me/joinchat/T_YTN4IG1vAJNWT9 Course chat].

=== Lecture notes ===

https://drive.google.com/file/d/1mmNLLQ0--EDihGNRKwSyXLOA1KL7A0lD/view?usp=sharing

=== Lecture video archive ===

https://youtube.com/playlist?list=PLEwK9wdS5g0pk-1YWDc3hezRt_rNpQDf8

=== Other resources ===
* [https://tinyurl.com/rwky5vmk The Course's Google Directory]

* [https://www.youtube.com/playlist?list=PL1Uob8iPTHGTidrmrqEHTJ96Pt3-PmML4 Past years' videos]

* We have a [https://meet.edashkov.net.ru dedicated server] to hold an online meeting if we need one.

== Problem sets ==

=== Class problems ===

* [https://drive.google.com/file/d/1EP-diSuOTn9f0ryg18Z2w0xjEp8j0bnl/view?usp=sharing Problem set 1]

* [https://drive.google.com/file/d/12ct99-ORd7A94Gh5g4Nf9riv7UqNMSRc/view?usp=sharing Problem set 2]

* [https://drive.google.com/file/d/1yKKqLsS99V4AhCYqbjafuav2CMCdQTOQ/view?usp=sharing Problem set 3]

* [https://drive.google.com/file/d/1YgH_AdCk4GcKC0KH7xBA4-sUnOYkUvUK/view?usp=share_link Problem set 4]

=== Homework problems ===

* [https://drive.google.com/file/d/1A8lFPdI3ZvC1vOgz2KEpYcuWOFlsQvb1/view?usp=sharing Homework 1]

* [https://drive.google.com/file/d/1LOPPwGjyVleR_mclxTKUJ_bxFrxt44sW/view?usp=sharing Homework 2a]

* [https://drive.google.com/file/d/1W7k1OTiIMlPOpo-2mwmGegrc4RDHz5_j/view?usp=share_link Homework 2b]

=== Assignment deadlines ===

{| class="wikitable"
|-
! Home problem set !! colspan="11" | Deadline
|-
| || 221 || 222 || 223 || 224
|-
| HW 1 №1-3 || || 22.IX || 22.IX || 22.IX
|-
| HW 1 || October 6 || October 6 || October 6 || October 6
|-
| HW 2a №1-3 || || October 20 || October 20 ||
|-
| HW 2a || October 24 || October 27 || October 27 || October 27
|-
| HW 2b №1-7 || || November 17 || November 17 || November 18
|}

'''Each deadline is set by the respective group's instructor.'''

== Grading system ==
For the final grading, we compute the following values:

Module 1 grade = round ((50*HW1 + 50*Exam1)/100);

basic = (21*Exam1 + 21*Colloq + 28*HW + 30*Exam2)/100;

adv = (30*Exam1* + Bonus + 35*HW* + 35*Exam2*)/100;

Final grade = round(min(10, 8 * basic + 2 * adv)).

The final grade is rounded half up to an integer. All the other values are reported with the greatest precision available.

== Recommended reading ==
''Please notice that '''The Book''' for our Course does not exist. The latter is based on many sources.''

# Anderson J. A., Discrete Mathematics With Combinatorics. Prentice Hall, 2003.
# Biggs N. L., Discrete mathematics. 2nd ed., New York; Oxford: Oxford University Press, 2004.
# Gavrilov G. P., Sapozhenko A. A. Problems and Exercises in Discrete Mathematics. Kluwer Texts in the Mathematical Sciences 14. Springer, 1996.
# [http://courses.csail.mit.edu/6.042/spring17/mcs.pdf Lehman E., Thomson Leighton F., Meyer A. R. Mathematics for Computer Science, 2017.]
# [http://www.cs.elte.hu/~lovasz/dmbook.ps Lovasz L., Vesztergombi K. Discrete Mathematics. Lecture Notes; Yale University, 1999.]
# Melnikov O., Sarvanov V., Tyshkevich R., Yemelichev V., Zverovich I. Exercises in Graph Theory. Kluwer Texts in the Mathematical Sciences 19. Springer, 1998.
# Rosen K. H. Discrete Mathematics and Its Applications. McGraw-Hill, 1999.
# Stein C., Drysdale R. L., Bogart K. Discrete mathematics for computer scientists. Addison-Wesley, 2010.
# Vinogradov I. M. Elements of number theory. Dover, 1954.

=== In Russian ===
''If you understand Russian (by any chance), you will probably benefit from reading the following books.''

# Виноградов И. М. Основы теории чисел. 9-е изд., М.: Наука, 1981.
# [http://rubtsov.su/public/DM-HSE-Draft.pdf Вялый М., Подольский В., Рубцов А., Шварц Д., Шень А. Лекции по дискретной математике.]
# Гаврилов Г. П., Сапоженко А. А. Задачи и упражнения по дискретной математике. 3-е изд., М.: ФИЗМАТЛИТ, 2004.
# [https://drive.google.com/file/d/1RM6KX_reBFwUXesWGUEu0sFn2NCaBgvz/view?usp=sharing Дашков Е. В. Введение в математическую логику. Множества и отношения. М.: МФТИ, 2019.]
# Зубков А. М., Севастьянов Б. А., Чистяков В. П. Сборник задач по теории вероятностей. 2-е изд., М.: Наука, 1989.
# Мельников О. И. Теория графов в занимательных задачах. 5-е изд., М.: Книжный дом "ЛИБРОКОМ", 2013.
# [http://www.mccme.ru/free-books/shen/shen-induction.pdf Шень А., Математическая индукция. 5-е изд, М.: МЦНМО, 2016.]

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