Discrete Mathematics DSBA2020/2021

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We shall have the final exam at the end of the 3rd Module.


Please follow this link for the Colloquium Rules and Question List.

The Colloquium schedule is as follows:

  • Group #201 - 16:20 MSK, December, 10
  • Group #202 - 18:10 MSK, December, 10
  • Group #203 - 16:20 MSK, December, 11
  • Group #204 - 16:20 MSK, December, 9

The links to the conferences will be published later.


We shall have a written test on November, 24. The test is scheduled for 6:10 pm MSK. You are supposed to send you work via a Google-form.

Current Results

You can check your progress up to now via the DM1 Register Online.

Homework Deadlines

For Group 201:

  • HW 1, Tasks 1--5: September 18
  • HW 1, Tasks 6--9: September 25

For Group 202:

  • HW 1, Tasks 1--3: September 15
  • HW 1, Tasks 4--5: September 22
  • HW 1, Tasks 7--9: September 28
  • HW 2, Tasks 1--3: October 13
  • HW 2, Tasks 4--9: October 27
  • HW 2, Tasks 10--12: November, 2
  • HW 2, Tasks 13--22: November, 19

For Group 203:

  • HW 1, Tasks 1--3: September 15
  • HW 1, Tasks 4--5: September 22
  • HW 1, Tasks 7--9: September 28
  • HW 2, Tasks 1--3: October 13
  • HW 2, Tasks 4--9: October 27
  • HW 2, Tasks 10--11: November, 2
  • HW 2, Tasks 12--22: November, 19

For Group 204:

  • HW 1, Tasks 1--3: September 16
  • HW 1, Tasks 4: September 23
  • HW 1, Tasks 5-6: September 30
  • HW 1, Tasks 7-9: October 7
  • HW 2, Tasks 1-3: October 14
  • HW 2, Tasks 4-10: October 23
  • HW 2, Tasks 11-15: November 7
  • HW 2, Tasks 16, 17, 21, 22: November 15
  • HW 2, Tasks 18-20: November 19
  • HW 3, Tasks 1-5: December 2

Course Materials

Lecture Notes

You can find some useful materials (including the Lecture Notes) here.

Problem sets

Class Problems Homework Assignments
cw1 hw1
cw2 hw2
cw3 ---
cw4 ---
cw5 ---
cw6 hw3
cw7 ---



Lecture 8: The Extended Euclidean Algorithm; solving linear Diophantine equations in two variables.

Lecture 9: Solving linear congruence; the Chinese Remainder Theorem; practical solving of simultaneous congruences.

Lecture 10: Sets: an axiomatic approach; elementhood relation; set inclusion and equality; the Axioms of Foundation and Equality; the "Substitution Principle"; set construction principles; grouping a few sets together; singletons; specifying a subset; the empty set; powersets; the union of two sets (and a more general case); the intersection and difference of two sets.

Lecture 11: Expressing inclusion in terms of equality; set algebra identities (with application examples); (Kuratowski's) ordered pair; pair equality criterion; Cartesian product; ordered tuples; Cartesian power.

Lecture 12: Binary relation between two sets; the domain, range, and field of a relations; relation diagram; relation on a set; the identity relation; the converse relation; the converse of the converse and of the union of relations; the composition of two relations; composition associativity; the converse of the composition; the composition with the identity; set image and pre-image under a relation.

Seminars by Evgeny Dashkov

Seminar 11. Sets.

Seminar 12. Set algebra identities. Cartesian product.


Although we had no regular recording of lectures or seminars until Module 2, a few videos on selected topics are available.

Video 1

An equivalence proof for the Strong Induction, Mathematical Induction and Least Number Principles.

Watch it!

Video 2

The definition of the greatest common divisor (GCD); the uniqueness and existence theorem.

Watch it!

Video 3

A compensatory seminar for Group 201. The main topics are GCD and LCM.

Watch it!

Video 4

A supplementary material partly covered at the extra class with groups 202 and 203 on October, 30. The main topics are common divisors and common multiples, solutions to exercises 4, 5, 7-9 from the classwork sheet #4.

Watch it! and get the whiteboard!

Other Resources

  • We encourage everyone to join Google Classroom for this course: there is a global classroom for everyone and group-specific classrooms. Connect using class codes below:
For all groups Group 201 Group 202 Group 203 Group 204
civetu3 7pmgfzr nf3kg65 36dtkir 76a5te5


The Lecturer

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

Technical Support

My name is Boris Danilov. Please, address me all issues and questions related to distant learning technologies that we use in our course. My contacts: brdanilov@gmail.com, Telegram @brdann .

Seminar Instructors

  • Group 201: Evgeny Dashkov
  • Group 202: Boris Danilov
  • Group 203: Boris Danilov
  • Group 204: Anastasia Trofimova

Teaching Assistants

Recommended Reading

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.

Grading System

Intermediate grade-2 = (1/3) test-1 + (1/3) colloquium-2 + (1/3) homework-2.

Cumulative grade-3 = (3/10) test-1 + (3/10) colloquium-2 + (4/10) homework-3.

Final grade-3 = min(10, (7/10) cumulative grade-3 + (3/10) final exam + (1/10) bonus points).

The number in a grade’s name is the number of the module when grading takes place. The grade homework-n is the normalized average grade for the homework in Modules from 1 to n. The Intermediate and Final grades are subject to rounding half up to an integer. All the other grades are reported with the greatest precision available.

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