# Discrete Mathematics DSBA 2024/2025

## Содержание

## Instructors

### The lecturer

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

My Assistant (the person responsible for the tables etc.): Elizaveta Levshina.

### Seminar Instructors and Teaching Assistants

Group | 241 | 242 | 243 | 244 | 245 | 246 | |
---|---|---|---|---|---|---|---|

Teachers | Evgeny Dashkov | Boris Danilov | Diego Buitrago | ||||

Teaching Assistants | Sergei Budygin | Zakhar Zinkin | Sergey Savin | Ivan Mashkarin | Maxim Titov | Maria Krotova |

### Whom should I ask?

If you have a question or comment concerning the mathematical content of our course, it is best to post it to our student chat. Alternatively, you may address your question to your Teaching Assistant, Seminar Instructor or the Lecturer (say, if your question discloses an important idea for a HW problem). It is much better to ask and get to know than not to ask and remain ignorant. **Please do not hesitate to ask your mathematical questions!**

If you need a more detailed consultation concerning the course's mathematics, please be informed that our Teaching Assistants usually hold periodic consultations while the Seminar Instructors and Lecturer have some designated time for counseling students. Still, the best thing to do is to arrange a consultation in advance via a personal communication.

Homework-grading related questions should be directed to your teaching assistant first; then to your seminar instructor and to the lecturer just in case of any disagreement.

Organizational, administrative, legal or paperwork questions must be addressed to the Student Service Center, Study Office or other relevant offices first and foremost. If you have been redirected to us with such a question nevertheless, please contact the Lecturer's Assistant first.

## Current performance

## 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’. These sets may be subdivided further for students’ convenience.

A student may be required to 'defend' (i.e., 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. The examination takes about 120 minutes. Some problems of the exam are labeled as ‘bonus’; the others are ‘ordinary’.

## 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.

## Exam 2

A written examination is held past Module 3. 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’.

## Bonus activities

Throughout the course, the students may be graded for a variety of ‘bonus activities’ (like quizzes, etc.) either offline or online.

## Course materials

Course chat. This is our primary outlet for course announcements, questions, and discussions. **Please join it!**

### Lecture notes

A Russian translation by volunteering students (you are welcome to join their ranks)

### Classes recordings

### Lecture video archive

### Other resources

- We have a dedicated server to hold an online meeting if we need one.

## Problem sets

### Class problems

### Assignment deadlines

Home problem set | Deadline | ||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|

241 | 242 | 243 | 244 | 245 | 246 | ||||||

HW1a | Sep 19 | Sep 19 | Sep 19 | Sep 24 | Sep 24 | Sep 24 |

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

## Assessment and Grading

### Homework

The homework is graded in two batches: one (HW_A) includes everything to be submitted in Module1 and the other (HW_B) includes all the rest. For each problem, either ordinary or bonus, the student is given a score from 0 to 1 point (in fractional values) according to the progress he made.

Grade HW_A is computed the following way (before rounding):

HW_A = 8 * ord + 2 * adv, where

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

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

Grade HW_B is computed similarly but for its respective period of Modules 2 and 3.

### Exam1 and the Interim Assessment

Each problem solution in the exam is graded with a fractional score from 0 to 1 point, and the entire exam with the value (before rounding)

Exam1 = 8 * ord + 2 * adv, where

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

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

The Interim grade 1 is computed past Module 1 and equals:

Interim1 = round(0.5 * HW_A + 0.5 * Exam1).

(Here and everywhere, rounding is according to arithmetic rules.)

### Colloquium

For each of the 'definition' two questions, the student is given a score from 0 to 2 points, and from 0 to 4 points for the ‘proof’ question (all in fractional values). The Colloq grade is computed the following way (before rounding):

Colloq = 10 * (the sum of points given) / 8.

### Bonuses

Each student is given a score according to his progress in bonus activities, which results in the grade

Bonus = 10 * #(points given) / #(points possible).

The number of possible points varies but it is between 1 and 25 usually.

### Exam2, the Second Interim, and the Final Assessment

Each problem solution in exam is graded with a fractional score from 0 to 1 point, and the entire exam with the value (before rounding)

Exam2 = 8 * ord + 2 * adv, where

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

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

The Interim grade 2 is computed past Module 3 and equals:

Interim2 = round(0.295 * HW_B + 0.295 * Colloq + 0.06 * Bonus + 0.35 * Exam2).

The final grade for the course is

Final = round(0.3 * Interim1 + 0.7 * Interim 2)

Generally, **nobody is exempt from the examinations**.

## Exam retaking

Examinations 1 and 2 are subject to be retaken if either the Interim1 or Final grade, respectively, is unsatisfactory (i.e., < 4). Retaking an exam is similar to the regular examination. The resulting grade is substituted for that of the latter (that is, retake grade is assigned to the variable Exami in the respective formula, whose value is then reevaluated). Those whose Interim or Final grade is still unsatisfactory after the first retake will have a (tough) choice to make.

Please take into account the following regulation according to the *ПОПАТКУС*:

On the first and second retake the cumulative course grade is taken into consideration. In case of receiving an unsatisfactory final grade after the first retake, the student may refuse to participate in the second retake and repeat the course according to the individual curricula. Cumulative grade is formed again as a result of repeated course. After the completion of the repeated course, the student is given a second retake only, from which the student has previously refused.

The 'cumulative grade' here means all the variables in the grading formulas except Exami, which are the only ones to be retaken. The 'second retake' is similar to the first one and it is evaluated according to the same formula with the same values of 'cumulative' variables. This poses an obvious risk for anyone whose 'cumulatives' are low!

## 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.
- Lehman E., Thomson Leighton F., Meyer A. R. Mathematics for Computer Science, 2017.
- 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.
- 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.
- 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.
- Шень А., Математическая индукция. 5-е изд, М.: МЦНМО, 2016.