# Discrete Mathematics DSBA 2022/2023

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## Instructors

### The lecturer

My name is Evgeny Dashkov. Feel free to contact me via email: edashkov@gmail.com, Telegram, or VK.

### Seminar instructors

Group 221 222 223 224
Teachers Evgeny Dashkov Boris Danilov Telegram Trofimova Anastasia Telegram
Teaching Assistants Arseny Bolotnikov Telegram Daria Ivanova Telegram Egor Kornelyuk Telegram Marianna Kouis Telegram
Lecturer’s Assistant Alena Chislova Telegram

## 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 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.

## Problem sets

### Homework problems

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
HW 5 March 26 March 26 March 26 March 26

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

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;

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

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

1. Anderson J. A., Discrete Mathematics With Combinatorics. Prentice Hall, 2003.
2. Biggs N. L., Discrete mathematics. 2nd ed., New York; Oxford: Oxford University Press, 2004.
3. Gavrilov G. P., Sapozhenko A. A. Problems and Exercises in Discrete Mathematics. Kluwer Texts in the Mathematical Sciences 14. Springer, 1996.
4. Lehman E., Thomson Leighton F., Meyer A. R. Mathematics for Computer Science, 2017.
5. Lovasz L., Vesztergombi K. Discrete Mathematics. Lecture Notes; Yale University, 1999.
6. Melnikov O., Sarvanov V., Tyshkevich R., Yemelichev V., Zverovich I. Exercises in Graph Theory. Kluwer Texts in the Mathematical Sciences 19. Springer, 1998.
7. Rosen K. H. Discrete Mathematics and Its Applications. McGraw-Hill, 1999.
8. Stein C., Drysdale R. L., Bogart K. Discrete mathematics for computer scientists. Addison-Wesley, 2010.
9. 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.

1. Виноградов И. М. Основы теории чисел. 9-е изд., М.: Наука, 1981.
2. Вялый М., Подольский В., Рубцов А., Шварц Д., Шень А. Лекции по дискретной математике.
3. Гаврилов Г. П., Сапоженко А. А. Задачи и упражнения по дискретной математике. 3-е изд., М.: ФИЗМАТЛИТ, 2004.
4. Дашков Е. В. Введение в математическую логику. Множества и отношения. М.: МФТИ, 2019.
5. Зубков А. М., Севастьянов Б. А., Чистяков В. П. Сборник задач по теории вероятностей. 2-е изд., М.: Наука, 1989.
6. Мельников О. И. Теория графов в занимательных задачах. 5-е изд., М.: Книжный дом "ЛИБРОКОМ", 2013.
7. Шень А., Математическая индукция. 5-е изд, М.: МЦНМО, 2016.