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LAaG DSBA 2020/2021

2020-09-11T21:18:23Z

Wlad:

== Teachers and Assistants ==
{| class="wikitable" style="text-align:center"
|-
! Group !! 201 (M+P+) !! 202 !! 203 !! 204
|-
|| Lecturer ||colspan="4"| [https://www.hse.ru/org/persons/224875083 Andrey Mazhuga]
|-
|| Teacher || [https://www.hse.ru/org/persons/224875083 Andrey Mazhuga] || colspan="2"| [https://www.hse.ru/org/persons/209813351 Nikita Medved] || [https://www.hse.ru/staff/kaleeva Galina Kaleeva]
|-
|| Schedule || || || || Wednesday, 13.00, G406
[https://docs.google.com/spreadsheets/d/1xblWv0wuX7lkbe-0I8yyBPIhEUAq-U-HhGnuJ0It6xc/edit#gid=0 Zoom]
(for distance learners)
|-
|| Consultations || Wed, ??:?? -- ??:??, room S808 One must notify me beforehand || colspan="2"| TBD || Monday, 14:40-17:00, S913
To join via Zoom [https://t.me/galinakaleeva text me]
|-
|| Assistant || Астанина Ксения kkastanina@edu.hse.ru
|| Васильев Борис bavasilev@edu.hse.ru
|| Княжевский Владимир vvknyazhevskiy@edu.hse.ru
|| Косовская Анна a.dtc@yandex.ru
|-
|| Course Assistant ||colspan="4"| Астанина Ксения kkastanina@edu.hse.ru
|-
|}

== Course Description ==
The course introduces students to the elements of linear algebra and analytic geometry, provides the foundations for understanding some of the main concepts of modern mathematics. There is a strong emphasis in this course on complete proofs of almost all results.

We will approach the subject from both a practical point of view (learning methods and acquiring computational skills
relevant for problem solving) and a theoretical point of view (learning a more abstract and theoretical approach that focuses on achieving a deep understanding of the different abstract concepts).

Topics covered include: matrix algebra, systems of linear equations, permutations, determinants, complex numbers, fields, abstract vector spaces, bilinear and quadratic forms, Euclidean spaces, some elements of analytic geometry, linear operators. It took mathematicians at least two hundred years to comprehend these objects. We plan to accomplish this in one year.

== Grading system ==

During the academic year, the student will be formally graded on the following:
*two in-class oral tests (O1 and O2);
*two in-class written tests (W1 and W2);
*several quizzes (Q1 and Q2, where Qi is the average grade of all the quizzes in the i-th semester);
*several homework assignments (H1 and H2, where Hi is the average grade of all the homework assignments in the i-th semester);
*two written exams (E1 and E2).

All grades (namely, O1, O2, W1, W2, Q1, Q2, H1, H2, E1, and E2) are real numbers from 0 to 10.

'''The cumulative course grade for the first semester''', C1, is obtained '''without rounding''' by the following formula:

'''C1 = 5/16*O1 + 4/16*W1 + 4/16*Q1 + 3/16*H1.'''

'''The intermediate course grade for the first semester''', I1, is obtained by the following formula:

'''I1 = Round1(3/10*E1 + 7/10*C1),'''

where the function Round1(x) is defined as follows: if the decimal part of x is less than 0.2, the grade is rounded downwards; if the decimal part of x is greater than 0.6, the grade is rounded upwards; if the decimal part of x is from the interval [0.2;0.6] and the student's seminar attendance during the first semester is not below 60%, the grade is rounded upwards; otherwise the grade is rounded downwards.

'''The cumulative course grade for the second semester''', C2, is obtained '''without rounding''' by the following formula:

'''C2 = 5/16*O2 + 4/16*W2 + 4/16*Q2 + 3/16*H2.'''

'''The intermediate course grade for the second semester''', I2, is obtained by the following formula:

'''I2 = Round2(3/10*E2 + 7/10*C2),'''

where the function Round2(x) is defined as Round1(x) but with "during the first semester" replaced by "during the second semester".

'''The final grade for the course''', F, is obtained by the following formula:

'''F = Round(1/4*I1 + 3/4*I2),'''

where the function Round(x) is defined as Round1(x) but with "during the first semester" replaced by "during the academic year".

The final grade for the course is included in a diploma supplement.

== Lecture Notes ==

''' Module 1 '''

* [https://www.dropbox.com/s/xbzr7b3upj63rhy/LAaG_Lecture_1.pdf?dl=0 '''Lecture 1'''] (09.09.2020) Matrices, main definitions; special matrices (square matrices, triangular matrices, identity matrices, zero matrices); matrix scalar multiplication; matrix addition; matrix multiplication; main properties of these operations.

== Seminar Notes ==

'''Module 1'''

'''Group 201:'''
*[ '''S 1'''] (09.09.2020)

'''Groups 202 and 203:'''
*[ '''S 1'''] (XX.09.2020)

'''Group 204:'''
*[ '''S 1'''] (ХХ.09.2020)

== Homework ==

'''Module 1'''

'''The obligatory homework for group 201:'''
*[https://www.dropbox.com/s/m9y2wopr1lq0dtv/LAaG_HW_1_C%28201%29.pdf?dl=0 '''HW 1'''] (release: 09.09.2020; deadline: 16.09.2020)

'''The obligatory homework for groups 202 and 203:'''
*An invite to Google Classroom for group 203: 3fyhfue (you can also use [https://classroom.google.com/c/MTU5OTQ0NzgyMTI3?cjc=3fyhfue this link])
*[https://www.dropbox.com/s/2z5gdd4hgyknqpz/LAaG_HW_1.pdf?dl=0 '''HW 1'''] (release: 11.09.2020; deadline: 18.09.2020, 9:00 a.m.)

'''The obligatory homework for group 204:'''
*[https://yadi.sk/i/AX-zxO6kW18GlQ '''HW 1'''] (release: 09.09.2020; deadline: 16.09.2020, 9:00 a. m.; send here: https://clck.ru/Qkq26) Any computational tools are not allowed.

== Results ==

{| class="wikitable" style="text-align:center"
|-
! [https://docs.google.com/spreadsheets/d/1rozrjdjNTabB2ygSTjBsYChSrQrDJCS5ni-hicaFdmU/edit?usp=sharing 201] !! [https://docs.google.com/spreadsheets/d/1rozrjdjNTabB2ygSTjBsYChSrQrDJCS5ni-hicaFdmU/edit#gid=1476291658 202] !! [https://docs.google.com/spreadsheets/d/1rozrjdjNTabB2ygSTjBsYChSrQrDJCS5ni-hicaFdmU/edit#gid=1726530362 203] !!
[https://docs.google.com/spreadsheets/d/1rozrjdjNTabB2ygSTjBsYChSrQrDJCS5ni-hicaFdmU/edit#gid=1726530362 204]
|}

LAaG DSBA 2020/2021

2020-09-11T20:46:30Z

Wlad: Добавил ссылку, куда сдавать дз

== Teachers and Assistants ==
{| class="wikitable" style="text-align:center"
|-
! Group !! 201 (M+P+) !! 202 !! 203 !! 204
|-
|| Lecturer ||colspan="4"| [https://www.hse.ru/org/persons/224875083 Andrey Mazhuga]
|-
|| Teacher || [https://www.hse.ru/org/persons/224875083 Andrey Mazhuga] || colspan="2"| [https://www.hse.ru/org/persons/209813351 Nikita Medved] || [https://www.hse.ru/staff/kaleeva Galina Kaleeva]
|-
|| Schedule || || || || Wednesday, 13.00, G406
[https://docs.google.com/spreadsheets/d/1xblWv0wuX7lkbe-0I8yyBPIhEUAq-U-HhGnuJ0It6xc/edit#gid=0 Zoom]
(for distance learners)
|-
|| Consultations || Wed, ??:?? -- ??:??, room S808 One must notify me beforehand || colspan="2"| TBD || Monday, 14:40-17:00, S913
To join via Zoom [https://t.me/galinakaleeva text me]
|-
|| Assistant || Астанина Ксения kkastanina@edu.hse.ru
|| Васильев Борис bavasilev@edu.hse.ru
|| Княжевский Владимир vvknyazhevskiy@edu.hse.ru
|| Косовская Анна a.dtc@yandex.ru
|-
|| Course Assistant ||colspan="4"| Астанина Ксения kkastanina@edu.hse.ru
|-
|}

== Course Description ==
The course introduces students to the elements of linear algebra and analytic geometry, provides the foundations for understanding some of the main concepts of modern mathematics. There is a strong emphasis in this course on complete proofs of almost all results.

We will approach the subject from both a practical point of view (learning methods and acquiring computational skills
relevant for problem solving) and a theoretical point of view (learning a more abstract and theoretical approach that focuses on achieving a deep understanding of the different abstract concepts).

Topics covered include: matrix algebra, systems of linear equations, permutations, determinants, complex numbers, fields, abstract vector spaces, bilinear and quadratic forms, Euclidean spaces, some elements of analytic geometry, linear operators. It took mathematicians at least two hundred years to comprehend these objects. We plan to accomplish this in one year.

== Grading system ==

During the academic year, the student will be formally graded on the following:
*two in-class oral tests (O1 and O2);
*two in-class written tests (W1 and W2);
*several quizzes (Q1 and Q2, where Qi is the average grade of all the quizzes in the i-th semester);
*several homework assignments (H1 and H2, where Hi is the average grade of all the homework assignments in the i-th semester);
*two written exams (E1 and E2).

All grades (namely, O1, O2, W1, W2, Q1, Q2, H1, H2, E1, and E2) are real numbers from 0 to 10.

'''The cumulative course grade for the first semester''', C1, is obtained '''without rounding''' by the following formula:

'''C1 = 5/16*O1 + 4/16*W1 + 4/16*Q1 + 3/16*H1.'''

'''The intermediate course grade for the first semester''', I1, is obtained by the following formula:

'''I1 = Round1(3/10*E1 + 7/10*C1),'''

where the function Round1(x) is defined as follows: if the decimal part of x is less than 0.2, the grade is rounded downwards; if the decimal part of x is greater than 0.6, the grade is rounded upwards; if the decimal part of x is from the interval [0.2;0.6] and the student's seminar attendance during the first semester is not below 60%, the grade is rounded upwards; otherwise the grade is rounded downwards.

'''The cumulative course grade for the second semester''', C2, is obtained '''without rounding''' by the following formula:

'''C2 = 5/16*O2 + 4/16*W2 + 4/16*Q2 + 3/16*H2.'''

'''The intermediate course grade for the second semester''', I2, is obtained by the following formula:

'''I2 = Round2(3/10*E2 + 7/10*C2),'''

where the function Round2(x) is defined as Round1(x) but with "during the first semester" replaced by "during the second semester".

'''The final grade for the course''', F, is obtained by the following formula:

'''F = Round(1/4*I1 + 3/4*I2),'''

where the function Round(x) is defined as Round1(x) but with "during the first semester" replaced by "during the academic year".

The final grade for the course is included in a diploma supplement.

== Lecture Notes ==

''' Module 1 '''

* [https://www.dropbox.com/s/xbzr7b3upj63rhy/LAaG_Lecture_1.pdf?dl=0 '''Lecture 1'''] (09.09.2020) Matrices, main definitions; special matrices (square matrices, triangular matrices, identity matrices, zero matrices); matrix scalar multiplication; matrix addition; matrix multiplication; main properties of these operations.

== Seminar Notes ==

'''Module 1'''

'''Group 201:'''
*[ '''S 1'''] (09.09.2020)

'''Groups 202 and 203:'''
*[ '''S 1'''] (XX.09.2020)

'''Group 204:'''
*[ '''S 1'''] (ХХ.09.2020)

== Homework ==

'''Module 1'''

'''The obligatory homework for group 201:'''
*[https://www.dropbox.com/s/m9y2wopr1lq0dtv/LAaG_HW_1_C%28201%29.pdf?dl=0 '''HW 1'''] (release: 09.09.2020; deadline: 16.09.2020)

'''The obligatory homework for groups 202 and 203:'''
*An invite to Google Classroom for group 203: 3fyhfue
*[https://www.dropbox.com/s/2z5gdd4hgyknqpz/LAaG_HW_1.pdf?dl=0 '''HW 1'''] (release: 11.09.2020; deadline: 18.09.2020, 9:00 a.m.)

'''The obligatory homework for group 204:'''
*[https://yadi.sk/i/AX-zxO6kW18GlQ '''HW 1'''] (release: 09.09.2020; deadline: 16.09.2020, 9:00 a. m.; send here: https://clck.ru/Qkq26) Any computational tools are not allowed.

== Results ==

{| class="wikitable" style="text-align:center"
|-
! [https://docs.google.com/spreadsheets/d/1rozrjdjNTabB2ygSTjBsYChSrQrDJCS5ni-hicaFdmU/edit?usp=sharing 201] !! [https://docs.google.com/spreadsheets/d/1rozrjdjNTabB2ygSTjBsYChSrQrDJCS5ni-hicaFdmU/edit#gid=1476291658 202] !! [https://docs.google.com/spreadsheets/d/1rozrjdjNTabB2ygSTjBsYChSrQrDJCS5ni-hicaFdmU/edit#gid=1726530362 203] !!
[https://docs.google.com/spreadsheets/d/1rozrjdjNTabB2ygSTjBsYChSrQrDJCS5ni-hicaFdmU/edit#gid=1726530362 204]
|}

Линейная алгебра и геометрия на ПМИ 2020/2021 (основной поток)

2020-09-09T11:14:28Z

Wlad: Добавил ссылку на свой телеграмм

Telegram-канал: [https://t.me/joinchat/AAAAAFR2V7QEK9js1zjIiQ https://t.me/joinchat/AAAAAFR2V7QEK9js1zjIiQ]

= Преподаватели и учебные ассистенты =

{| class="wikitable" style="text-align:center"
|-
! Группа !! БПМИ203 !! БПМИ205 !! БПМИ206 !! БПМИ207 !! БПМИ208 !! БПМИ209 !! БПМИ2010 !! БПМИ2011 !! БПМИ2012
|-
|| Лектор ||colspan="9"| [http://www.hse.ru/org/persons/112929840 Роман Авдеев]
|-
|| Семинарист || [https://www.hse.ru/org/persons/209508745 Дима Трушин] || [http://www.hse.ru/org/persons/112929840 Роман Авдеев] || [https://t.me/aibrain Айбек Аланов] || colspan="2"|[mailto:ssmirnov@higeom.math.msu.su Сергей Смирнов] || [https://www.hse.ru/org/persons/161646591 Станислав Федотов] || [https://www.hse.ru/org/persons/224876117 Антон Шафаревич] || colspan="2"| [https://www.hse.ru/org/persons/304055991 Юлия Зайцева]
|-
|| Ассистент || [https://t.me/beast_sl Сергей Лоптев] || [https://t.me/grenlayk Ольга Козлова] || Анна Фёдорова || Александр Тренин || Мария Солодуха || [https://t.me/AntonMedvede Антон Медведев] || [https://t.me/nastygorodi Анастасия Городилова] || Алиса Вернигор || [https://t.me/grammar_anarchist Владимир Княжевский]
|}

= Расписание консультаций =

= Формы контроля знаний студентов =

*Коллоквиум
*Контрольная работа
*Большие домашние задания (делящиеся на индивидуальные домашние задания и лабораторные работы)
*Активность и работа на семинарах
*Экзамен

Бонус:
*Устная сдача задач из листков

= Порядок формирования итоговой оценки =

== 2-й модуль ==
Итоговая оценка за 1-2 модули вычисляется по формуле

Oитоговая = min(10; 0,4*Oэкз + 0,22*Oколл + 0,16*Oк/р + 0,16*Oд/з + 0,08*Oсем + 0,08*Oл),

где Oэкз — оценка за экзамен, Oколл — оценка за коллоквиум, Oк/р — оценка за контрольную работу, Oд/з — оценка за большие домашние задания, Oсем — оценка за работу на семинарах и Oл — оценка за сдачу задач из листков.

Все вычисления по указанной формуле используют неокруглённые значения промежуточных оценок. Способ округления итоговой оценки — арифметический.

= Краткое содержание лекций =

'''Лекция 1''' (7.09.2019) [[https://www.dropbox.com/s/ttoti50j3etdyi7/Lec01_2020-09-07.pdf?dl=0 '''слайды''']]. Матрицы. Равенство матриц. Операции сложения и умножения на скаляр для матриц, свойства этих операций. Пространство R^n, его отождествление с матрицами-столбцами высоты n. Транспонирование матриц, его простейшие свойства. Умножение матриц, примеры.

= Листки с задачами =

Задачи из листков можно сдавать любому семинаристу по данному предмету (в том числе с пилотного потока) в часы его консультаций или по договорённости.

Правила сдачи и оценивания задач из листков:

* каждый пункт в листке считается отдельной задачей
* сдача задачи возможна только при наличии её решения в письменном виде
* результатом сдачи одной задачи может быть 0 или 1

= Индивидуальные домашние задания =

= Лабораторные работы =

= Контрольные работы =

= Коллоквиумы =

= Экзамены =

Формат проведения: письменная работа

= Ведомости текущего контроля =

= Литература =

== Учебники ==

* А.И. Кострикин. Введение в алгебру. Часть I. Основы алгебры. М.: Физматлит, 1994
* А.И. Кострикин. Введение в алгебру. Часть II. Линейная алгебра. М.: Физматлит, 2000
* Э.Б. Винберг. Курс алгебры. М.: Факториал, 1999 (или любое последующее издание)
* А.А. Михалёв, А.В. Михалёв. Начала алгебры. Часть I. М.: Интернет-университет информационных технологий, 2005

== Сборники задач ==

* И.В. Проскуряков. Сборник задач по линейной алгебре (любое издание, например М.: БИНОМ, 2005)
* Сборник задач по алгебре под редакцией А.Н. Кострикина. Новое издание. М.: МЦНМО, 2009
* Г.Д. Ким, Л.В. Крицков. Алгебра и аналитическая геометрия. Теоремы и задачи. Том I. М.: "Планета знаний", 2007