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	<title>Wiki - Факультет компьютерных наук - Вклад [ru]</title>
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	<updated>2026-09-21T11:36:39Z</updated>
	<subtitle>Вклад</subtitle>
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	<entry>
		<id>https://wiki.cs.hse.ru/index.php?title=Stochastic_analysis_2020_2021&amp;diff=47000</id>
		<title>Stochastic analysis 2020 2021</title>
		<link rel="alternate" type="text/html" href="https://wiki.cs.hse.ru/index.php?title=Stochastic_analysis_2020_2021&amp;diff=47000"/>
		<updated>2020-11-07T00:41:55Z</updated>

		<summary type="html">&lt;p&gt;Smomitya: &lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;== Lecturers and Seminarists ==&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot; style=&amp;quot;text-align:center&amp;quot;&lt;br /&gt;
|-&lt;br /&gt;
|| Lecturer || [https://www.hse.ru/staff/anaumov Naumov Alexey ] || [anaumov@hse.ru] || T924&lt;br /&gt;
|-&lt;br /&gt;
|| Lecturer || [https://www.hse.ru/org/persons/93130881 Belomestny Denis ] || [dbelomestny@hse.ru] || T926&lt;br /&gt;
|- &lt;br /&gt;
|| Seminarist || [https://www.hse.ru/org/persons/219484540 Samsonov Sergey] || [svsamsonov@hse.ru] || T926&lt;br /&gt;
|-&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
== About the course ==&lt;br /&gt;
This page contains materials for Stochastic Analysis course in 2020/2021 year, mandatory one for 1st year Master students of the Statistical Learning Theory program (HSE and Skoltech).&lt;br /&gt;
&lt;br /&gt;
== Grading == &lt;br /&gt;
The final grade consists of 3 components (each is non-negative real number from 0 to 10, without any intermediate rounding) :&lt;br /&gt;
* O&amp;lt;sub&amp;gt;HW&amp;lt;/sub&amp;gt; for the hometasks&lt;br /&gt;
* O&amp;lt;sub&amp;gt;Mid-term&amp;lt;/sub&amp;gt; for the midterm exam&lt;br /&gt;
* O&amp;lt;sub&amp;gt;Exam&amp;lt;/sub&amp;gt; for the final exam  &lt;br /&gt;
The formula for the final grade is &lt;br /&gt;
* O&amp;lt;sub&amp;gt;Final&amp;lt;/sub&amp;gt; = 0.3*O&amp;lt;sub&amp;gt;HW&amp;lt;/sub&amp;gt; + 0.3*O&amp;lt;sub&amp;gt;Mid-term&amp;lt;/sub&amp;gt; + 0.4*O&amp;lt;sub&amp;gt;Exam&amp;lt;/sub&amp;gt;&lt;br /&gt;
with the usual (arithmetical) rounding rule.&lt;br /&gt;
&lt;br /&gt;
[https://docs.google.com/spreadsheets/d/1MPWVIkgxyotHU-P5cE7Gik4C6RTWxTnAVK8Btl7Fw3Y/edit?usp=sharing &#039;&#039;&#039;Table with grades&#039;&#039;&#039;]&lt;br /&gt;
&lt;br /&gt;
== Lectures and Seminars ==&lt;br /&gt;
*[https://www.dropbox.com/s/a3im5ruldcdsoy7/%D0%A1%D1%82%D0%BE%D1%85%D0%B0%D0%BD%D0%B0%D0%BB%D0%B8%D0%B7_%20%D0%BB%D0%B5%D0%BA%D1%86%D0%B8%D1%8F%201%20%282%29.pdf?dl=0 &#039;&#039;&#039;Lecture 05.09&#039;&#039;&#039;]&lt;br /&gt;
* [https://www.dropbox.com/s/4q3l1u6os9jtqml/Lecture_12_09.pdf?dl=0 &#039;&#039;&#039;Lecture 12.09&#039;&#039;&#039;]&lt;br /&gt;
* [https://www.dropbox.com/s/pjrtvkia3zu8tx6/Lecture_19_09.pdf?dl=0 &#039;&#039;&#039;Lecture 19.09&#039;&#039;&#039;]&lt;br /&gt;
* [https://www.dropbox.com/s/gqsttggpwiz7040/Seminar_19_09_stochan.pdf?dl=0 &#039;&#039;&#039;Seminar 19.09&#039;&#039;&#039;]&lt;br /&gt;
* [https://www.dropbox.com/s/3asrxd56bbljkii/Martingales.pdf?dl=0 &#039;&#039;&#039;Lecture-Seminar 26.09, part 1 (Martingales)&#039;&#039;&#039;]&lt;br /&gt;
* [https://www.dropbox.com/s/vqvzh7vb1cq96l7/Gaussian%20Process.pdf?dl=0 &#039;&#039;&#039;Lecture-Seminar 26.09, part 2 (Wiener process)&#039;&#039;&#039;]&lt;br /&gt;
* [https://www.dropbox.com/s/kpndh6fpnn8jpbe/%D0%A1%D1%82%D0%BE%D1%85%D0%B0%D0%BD%D0%B0%D0%BB%D0%B8%D0%B7_%20%D0%BB%D0%B5%D0%BA%D1%86%D0%B8%D1%8F%203%20.pdf?dl=0 &#039;&#039;&#039;Lecture 03.10&#039;&#039;&#039;]&lt;br /&gt;
* [https://www.dropbox.com/s/pqhvmrupzbh6rs0/Seminar_03_10.pdf?dl=0 &#039;&#039;&#039;Seminar 03.10&#039;&#039;&#039;]&lt;br /&gt;
*[https://www.dropbox.com/s/18xv3jlbw5mfrnj/%D0%A1%D1%82%D0%BE%D1%85%D0%B0%D0%BD%D0%B0%D0%BB%D0%B8%D0%B7_%20%D0%BB%D0%B5%D0%BA%D1%86%D0%B8%D1%8F%204%20%282%29.pdf?dl=0 &#039;&#039;&#039;Lecture 17.10&#039;&#039;&#039;]&lt;br /&gt;
*[https://www.dropbox.com/s/jgndwtup4v3jlgc/Seminar_30_10.pdf?dl=0 &#039;&#039;&#039;Seminar 31.10&#039;&#039;&#039;]&lt;br /&gt;
&lt;br /&gt;
==Homeworks ==&lt;br /&gt;
*[https://www.dropbox.com/s/k1adzfss7hdg39z/HW_1_stochan_2020.pdf?dl=0 &#039;&#039;&#039;Homework №1, deadline: 10.10.2020, 23:59&#039;&#039;&#039;]&lt;br /&gt;
*[https://www.dropbox.com/s/pm9ffkzt66ax2lb/HW_2_stochan_2020.pdf?dl=0 &#039;&#039;&#039;Homework №2, deadline: 17.11.2020, 23:59&#039;&#039;&#039;]&lt;br /&gt;
&lt;br /&gt;
==Midterm ==&lt;br /&gt;
Midterm will take place on Saturday, 07.11.2020, at 11:10. You are allowed to use your lectures and seminar notes, or any other notes or books, but NOT the laptops, mobile phones and other devices. Midterm will take 1.5 hours and it will contain 6 problems. Solving any 5 of them will give you the maximal grade. &lt;br /&gt;
*[https://www.dropbox.com/s/dwzwwuv6ed5i6lq/Questions_stochan_midterm.pdf?dl=0 &#039;&#039;&#039;List of topics&#039;&#039;&#039;]&lt;br /&gt;
&lt;br /&gt;
== Recommended literature (1st term) ==&lt;br /&gt;
*http://www.statslab.cam.ac.uk/~james/Markov/ - Cambridge lecture notes on discrete-time Markov Chains&lt;br /&gt;
*https://link.springer.com/book/10.1007%2F978-3-319-97704-1 - book by E. Moulines et al, you are mostly interested in chapters 1,2,7 and 9 (book is accessible for download through HSE network)&lt;br /&gt;
*https://link.springer.com/book/10.1007%2F978-3-319-62226-2 - Stochastic Calculus by P. Baldi, good overview of conditional probabilities and expectations (part 4, also accessible through HSE network)&lt;br /&gt;
*https://link.springer.com/book/10.1007%2F978-1-4419-9634-3 - Probability for Statistics and Machine Learning by A. Dasgupta, chapter 19 (MCMC), also accessible through HSE network&lt;/div&gt;</summary>
		<author><name>Smomitya</name></author>
	</entry>
	<entry>
		<id>https://wiki.cs.hse.ru/index.php?title=Stochastic_analysis_2020_2021&amp;diff=46999</id>
		<title>Stochastic analysis 2020 2021</title>
		<link rel="alternate" type="text/html" href="https://wiki.cs.hse.ru/index.php?title=Stochastic_analysis_2020_2021&amp;diff=46999"/>
		<updated>2020-11-07T00:41:21Z</updated>

		<summary type="html">&lt;p&gt;Smomitya: Добавлена таблица с оценками&lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;== Lecturers and Seminarists ==&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot; style=&amp;quot;text-align:center&amp;quot;&lt;br /&gt;
|-&lt;br /&gt;
|| Lecturer || [https://www.hse.ru/staff/anaumov Naumov Alexey ] || [anaumov@hse.ru] || T924&lt;br /&gt;
|-&lt;br /&gt;
|| Lecturer || [https://www.hse.ru/org/persons/93130881 Belomestny Denis ] || [dbelomestny@hse.ru] || T926&lt;br /&gt;
|- &lt;br /&gt;
|| Seminarist || [https://www.hse.ru/org/persons/219484540 Samsonov Sergey] || [svsamsonov@hse.ru] || T926&lt;br /&gt;
|-&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
== About the course ==&lt;br /&gt;
This page contains materials for Stochastic Analysis course in 2020/2021 year, mandatory one for 1st year Master students of the Statistical Learning Theory program (HSE and Skoltech).&lt;br /&gt;
&lt;br /&gt;
== Grading == &lt;br /&gt;
The final grade consists of 3 components (each is non-negative real number from 0 to 10, without any intermediate rounding) :&lt;br /&gt;
* O&amp;lt;sub&amp;gt;HW&amp;lt;/sub&amp;gt; for the hometasks&lt;br /&gt;
* O&amp;lt;sub&amp;gt;Mid-term&amp;lt;/sub&amp;gt; for the midterm exam&lt;br /&gt;
* O&amp;lt;sub&amp;gt;Exam&amp;lt;/sub&amp;gt; for the final exam  &lt;br /&gt;
The formula for the final grade is &lt;br /&gt;
* O&amp;lt;sub&amp;gt;Final&amp;lt;/sub&amp;gt; = 0.3*O&amp;lt;sub&amp;gt;HW&amp;lt;/sub&amp;gt; + 0.3*O&amp;lt;sub&amp;gt;Mid-term&amp;lt;/sub&amp;gt; + 0.4*O&amp;lt;sub&amp;gt;Exam&amp;lt;/sub&amp;gt;&lt;br /&gt;
with the usual (arithmetical) rounding rule.&lt;br /&gt;
[https://docs.google.com/spreadsheets/d/1MPWVIkgxyotHU-P5cE7Gik4C6RTWxTnAVK8Btl7Fw3Y/edit?usp=sharing &#039;&#039;&#039;Table with grades&#039;&#039;&#039;]&lt;br /&gt;
&lt;br /&gt;
== Lectures and Seminars ==&lt;br /&gt;
*[https://www.dropbox.com/s/a3im5ruldcdsoy7/%D0%A1%D1%82%D0%BE%D1%85%D0%B0%D0%BD%D0%B0%D0%BB%D0%B8%D0%B7_%20%D0%BB%D0%B5%D0%BA%D1%86%D0%B8%D1%8F%201%20%282%29.pdf?dl=0 &#039;&#039;&#039;Lecture 05.09&#039;&#039;&#039;]&lt;br /&gt;
* [https://www.dropbox.com/s/4q3l1u6os9jtqml/Lecture_12_09.pdf?dl=0 &#039;&#039;&#039;Lecture 12.09&#039;&#039;&#039;]&lt;br /&gt;
* [https://www.dropbox.com/s/pjrtvkia3zu8tx6/Lecture_19_09.pdf?dl=0 &#039;&#039;&#039;Lecture 19.09&#039;&#039;&#039;]&lt;br /&gt;
* [https://www.dropbox.com/s/gqsttggpwiz7040/Seminar_19_09_stochan.pdf?dl=0 &#039;&#039;&#039;Seminar 19.09&#039;&#039;&#039;]&lt;br /&gt;
* [https://www.dropbox.com/s/3asrxd56bbljkii/Martingales.pdf?dl=0 &#039;&#039;&#039;Lecture-Seminar 26.09, part 1 (Martingales)&#039;&#039;&#039;]&lt;br /&gt;
* [https://www.dropbox.com/s/vqvzh7vb1cq96l7/Gaussian%20Process.pdf?dl=0 &#039;&#039;&#039;Lecture-Seminar 26.09, part 2 (Wiener process)&#039;&#039;&#039;]&lt;br /&gt;
* [https://www.dropbox.com/s/kpndh6fpnn8jpbe/%D0%A1%D1%82%D0%BE%D1%85%D0%B0%D0%BD%D0%B0%D0%BB%D0%B8%D0%B7_%20%D0%BB%D0%B5%D0%BA%D1%86%D0%B8%D1%8F%203%20.pdf?dl=0 &#039;&#039;&#039;Lecture 03.10&#039;&#039;&#039;]&lt;br /&gt;
* [https://www.dropbox.com/s/pqhvmrupzbh6rs0/Seminar_03_10.pdf?dl=0 &#039;&#039;&#039;Seminar 03.10&#039;&#039;&#039;]&lt;br /&gt;
*[https://www.dropbox.com/s/18xv3jlbw5mfrnj/%D0%A1%D1%82%D0%BE%D1%85%D0%B0%D0%BD%D0%B0%D0%BB%D0%B8%D0%B7_%20%D0%BB%D0%B5%D0%BA%D1%86%D0%B8%D1%8F%204%20%282%29.pdf?dl=0 &#039;&#039;&#039;Lecture 17.10&#039;&#039;&#039;]&lt;br /&gt;
*[https://www.dropbox.com/s/jgndwtup4v3jlgc/Seminar_30_10.pdf?dl=0 &#039;&#039;&#039;Seminar 31.10&#039;&#039;&#039;]&lt;br /&gt;
&lt;br /&gt;
==Homeworks ==&lt;br /&gt;
*[https://www.dropbox.com/s/k1adzfss7hdg39z/HW_1_stochan_2020.pdf?dl=0 &#039;&#039;&#039;Homework №1, deadline: 10.10.2020, 23:59&#039;&#039;&#039;]&lt;br /&gt;
*[https://www.dropbox.com/s/pm9ffkzt66ax2lb/HW_2_stochan_2020.pdf?dl=0 &#039;&#039;&#039;Homework №2, deadline: 17.11.2020, 23:59&#039;&#039;&#039;]&lt;br /&gt;
&lt;br /&gt;
==Midterm ==&lt;br /&gt;
Midterm will take place on Saturday, 07.11.2020, at 11:10. You are allowed to use your lectures and seminar notes, or any other notes or books, but NOT the laptops, mobile phones and other devices. Midterm will take 1.5 hours and it will contain 6 problems. Solving any 5 of them will give you the maximal grade. &lt;br /&gt;
*[https://www.dropbox.com/s/dwzwwuv6ed5i6lq/Questions_stochan_midterm.pdf?dl=0 &#039;&#039;&#039;List of topics&#039;&#039;&#039;]&lt;br /&gt;
&lt;br /&gt;
== Recommended literature (1st term) ==&lt;br /&gt;
*http://www.statslab.cam.ac.uk/~james/Markov/ - Cambridge lecture notes on discrete-time Markov Chains&lt;br /&gt;
*https://link.springer.com/book/10.1007%2F978-3-319-97704-1 - book by E. Moulines et al, you are mostly interested in chapters 1,2,7 and 9 (book is accessible for download through HSE network)&lt;br /&gt;
*https://link.springer.com/book/10.1007%2F978-3-319-62226-2 - Stochastic Calculus by P. Baldi, good overview of conditional probabilities and expectations (part 4, also accessible through HSE network)&lt;br /&gt;
*https://link.springer.com/book/10.1007%2F978-1-4419-9634-3 - Probability for Statistics and Machine Learning by A. Dasgupta, chapter 19 (MCMC), also accessible through HSE network&lt;/div&gt;</summary>
		<author><name>Smomitya</name></author>
	</entry>
	<entry>
		<id>https://wiki.cs.hse.ru/index.php?title=%D0%90%D0%BB%D0%B3%D0%B5%D0%B1%D1%80%D0%B0_%D0%BD%D0%B0_%D0%9F%D0%9C%D0%98_2016/2017&amp;diff=23016</id>
		<title>Алгебра на ПМИ 2016/2017</title>
		<link rel="alternate" type="text/html" href="https://wiki.cs.hse.ru/index.php?title=%D0%90%D0%BB%D0%B3%D0%B5%D0%B1%D1%80%D0%B0_%D0%BD%D0%B0_%D0%9F%D0%9C%D0%98_2016/2017&amp;diff=23016"/>
		<updated>2017-04-07T20:03:52Z</updated>

		<summary type="html">&lt;p&gt;Smomitya: &lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;== Преподаватели и учебные ассистенты ==&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot; style=&amp;quot;text-align:center&amp;quot;&lt;br /&gt;
|-&lt;br /&gt;
! Группа !! БПМИ161 !! БПМИ162 !! БПМИ163 !! БПМИ164 !! БПМИ165 !! БПМИ166 !! БПМИ167 !! БПМИ168&lt;br /&gt;
|-&lt;br /&gt;
|| Лектор ||colspan=&amp;quot;2&amp;quot;| [http://www.hse.ru/staff/arjanstev Иван Владимирович Аржанцев] ||colspan=&amp;quot;6&amp;quot;| [http://www.hse.ru/org/persons/112929840 Роман Сергеевич Авдеев]&lt;br /&gt;
|- &lt;br /&gt;
|| Семинарист || [http://www.hse.ru/staff/arjanstev Иван Владимирович Аржанцев] || [http://www.hse.ru/org/persons/63679989 Сергей Александрович Гайфуллин] || [https://www.hse.ru/org/persons/63680045 Полина Юрьевна Котенкова] || [http://www.hse.ru/org/persons/112929840 Роман Сергеевич Авдеев] ||colspan=&amp;quot;2&amp;quot;| [https://www.hse.ru/org/persons/63680045 Полина Юрьевна Котенкова] || [http://www.hse.ru/org/persons/63679989 Сергей Александрович Гайфуллин] ||colspan=&amp;quot;2&amp;quot;| [https://www.hse.ru/org/persons/161646591 Станислав Николаевич Федотов]&lt;br /&gt;
|-&lt;br /&gt;
|| Ассистент || Данила Кутенин || Дарья Мусаткина || Максим Каледин || Вадим Гринберг || Софья Иволгина || Наталья Богданова || Дмитрий Сморчков || Дина Акимова&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
== Расписание консультаций ==&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot;&lt;br /&gt;
|-&lt;br /&gt;
! !! Преподаватель/ассистент !! понедельник !! вторник !! среда !! четверг !! пятница&lt;br /&gt;
|-&lt;br /&gt;
| &amp;lt;center&amp;gt;1&amp;lt;/center&amp;gt; || Иван Владимирович Аржанцев ||  || 17:00&amp;amp;ndash;18:30, каб.&amp;amp;nbsp;603 ||   ||  ||&lt;br /&gt;
|-&lt;br /&gt;
| &amp;lt;center&amp;gt;2&amp;lt;/center&amp;gt; || Роман Сергеевич Авдеев || 15:40&amp;amp;ndash;17:40, ауд.&amp;amp;nbsp;623 ||  ||  || ||&lt;br /&gt;
|-&lt;br /&gt;
| &amp;lt;center&amp;gt;3&amp;lt;/center&amp;gt; || Полина Юрьевна Котенкова || ||  ||  || ||&lt;br /&gt;
|-&lt;br /&gt;
| &amp;lt;center&amp;gt;4&amp;lt;/center&amp;gt; || Сергей Александрович Гайфуллин || || || || ||&lt;br /&gt;
|-&lt;br /&gt;
| &amp;lt;center&amp;gt;5&amp;lt;/center&amp;gt; || Станислав Николаевич Федотов || || || || || &lt;br /&gt;
|-&lt;br /&gt;
| &amp;lt;center&amp;gt;6&amp;lt;/center&amp;gt; || Данила Кутенин || 15:10&amp;amp;ndash;16:30, ауд.&amp;amp;nbsp;623 || || || || &lt;br /&gt;
|-&lt;br /&gt;
| &amp;lt;center&amp;gt;7&amp;lt;/center&amp;gt; || Дарья Мусаткина || || 13:30&amp;amp;ndash;15:00, ауд.&amp;amp;nbsp;306 || || || &lt;br /&gt;
|-&lt;br /&gt;
| &amp;lt;center&amp;gt;8&amp;lt;/center&amp;gt; || Максим Каледин || || || || || 12:10&amp;amp;ndash;13:40, ауд.618 &lt;br /&gt;
|-&lt;br /&gt;
| &amp;lt;center&amp;gt;9&amp;lt;/center&amp;gt; || Вадим Гринберг || || || 15:10&amp;amp;ndash;16:30, ауд.&amp;amp;nbsp;?? || || &lt;br /&gt;
|-&lt;br /&gt;
| &amp;lt;center&amp;gt;10&amp;lt;/center&amp;gt; || Софья Иволгина ||16:40&amp;amp;ndash;18:00, ауд.&amp;amp;nbsp;?? || || || || &lt;br /&gt;
|-&lt;br /&gt;
| &amp;lt;center&amp;gt;11&amp;lt;/center&amp;gt; || Наталья Богданова || || || || ||&lt;br /&gt;
|-&lt;br /&gt;
| &amp;lt;center&amp;gt;12&amp;lt;/center&amp;gt; || Дмитрий Сморчков || 16:40&amp;amp;ndash;18:00, ауд.&amp;amp;nbsp;??  ||  ||  ||  || &lt;br /&gt;
|-&lt;br /&gt;
| &amp;lt;center&amp;gt;13&amp;lt;/center&amp;gt; || Дина Акимова ||  ||  || 16:40&amp;amp;ndash;17:40, ауд.&amp;amp;nbsp;501  ||  || &lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
== Информация для пилотного потока ==&lt;br /&gt;
&lt;br /&gt;
== Информация для основного потока ==&lt;br /&gt;
&lt;br /&gt;
=== Порядок формирования оценок ===&lt;br /&gt;
&lt;br /&gt;
Накопленная оценка вычисляется по следующей формуле:&lt;br /&gt;
&lt;br /&gt;
O&amp;lt;sub&amp;gt;накопленная&amp;lt;/sub&amp;gt; = 0,6 * O&amp;lt;sub&amp;gt;дз&amp;lt;/sub&amp;gt; + 0,4 * O&amp;lt;sub&amp;gt;к/р&amp;lt;/sub&amp;gt;,&lt;br /&gt;
&lt;br /&gt;
где O&amp;lt;sub&amp;gt;дз1&amp;lt;/sub&amp;gt; &amp;amp;mdash; оценка за домашние задания, O&amp;lt;sub&amp;gt;к/р&amp;lt;/sub&amp;gt; &amp;amp;mdash; оценка за контрольную работу.&lt;br /&gt;
&lt;br /&gt;
Итоговая оценка выражается через накопленную и оценку за экзамен следующим образом:&lt;br /&gt;
&lt;br /&gt;
O&amp;lt;sub&amp;gt;итоговая&amp;lt;/sub&amp;gt; = 0,5 * O&amp;lt;sub&amp;gt;накопленная&amp;lt;/sub&amp;gt; + 0,5 * О&amp;lt;sub&amp;gt;экз&amp;lt;/sub&amp;gt;.&lt;br /&gt;
&lt;br /&gt;
Округление производится только для итоговой оценки. Способ округления &amp;amp;mdash; арифметический.&lt;br /&gt;
&lt;br /&gt;
=== Краткое содержание лекций ===&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;Лекция 1&#039;&#039;&#039; (3.04.2017). Бинарные операции. Полугруппы, моноиды, группы, коммутативные (абелевы) группы. Порядок группы. Примеры групп. Подгруппы. Описание всех подгрупп в группе целых чисел по сложению. Циклические подгруппы. Порядок элемента группы. Связь между порядком элемента и порядком порождаемой им циклической подгруппы.&lt;br /&gt;
&lt;br /&gt;
=== Домашние задания ===&lt;br /&gt;
&lt;br /&gt;
[https://www.dropbox.com/s/fumjcyiubckxgem/A_16-17_Stream2_Homework1.pdf?dl=0 &#039;&#039;&#039;Домашнее задание 1&#039;&#039;&#039;]&lt;br /&gt;
&lt;br /&gt;
== Ведомости текущего контроля ==&lt;br /&gt;
&lt;br /&gt;
== Литература ==&lt;br /&gt;
&lt;br /&gt;
* Э.Б.&amp;amp;nbsp;Винберг. Курс алгебры. М.: Факториал Пресс, 2002.&lt;br /&gt;
* А.И.&amp;amp;nbsp;Кострикин. Введение в алгебру. Основы алгебры. М.: Наука. Физматлит, 1994.&lt;br /&gt;
* А.И.&amp;amp;nbsp;Кострикин. Введение в алгебру. Основные структуры алгебры. М.: Наука. Физматлит, 2000.&lt;br /&gt;
* Сборник задач по алгебре под редакцией А.Н.&amp;amp;nbsp;Кострикина. Новое издание. М.: МЦНМО, 2009.&lt;/div&gt;</summary>
		<author><name>Smomitya</name></author>
	</entry>
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