Adaptation DM 20-21
Содержание
General Information
The main goal of the Discrete Mathematics Adaptation Course is to help students keep up with the course curriculum by discussing the most important and challenging topics in detail. The second very important goal of the course is to teach students to work competently with mathematical definitions and proofs, correctly logically build solutions to problems and prove statements. The topics of the course are coordinated with the "basic" course of the DSBA and SE program, but its study will also be useful for the direction of AMI. The approximate order of topics is sets and logic, combinatorics, functions and relations, graphs, the beginning of number theory, the foundations of probability theory, generating functions.
Schedule
The classes are organised online on Fridays at 18:00.
Course materials
First semester
| Date | Topic | Problem Set | Class note | Video |
|---|---|---|---|---|
| 25.09.20 | Statements, connectives, quantifiers | PS 1 | ||
| 2.10.20 | Logics and inductive definitions | The same PS | ||
| 9.10.20 | Mathematical Induction. Formal Proofs. | PS 3 | ||
| 16.10.20 | Divisibity. | PS 4 | Notes 4 | Video 4 |
| 23.10.20 | Divisibility. Great common dividers. | PS 5 | [ Notes 5] | Video 5 |
| 30.10.20 | The Euclidean algorithm. Bezout equations. | PS 6 | Notes 6 | Video 6 |
| 6.11.20 | Euler's and Fermat's Little Theorems | PS 7 | Notes 7 | Video 7 |
| 13.11.20 | Bezout equalities and sotition of congruences | PS 8 | Notes 8 | Video 8 |
| 20.11.20 | Logics, induction and number theory | PS 9 | Notes 9 | Video 9 |
| 27.11.20 | Revisiting inverse elements and Sets. Cartesian product | PS 10 | Notes 10 | [Video 10] |
| 4.12.20 | Sets. Proofs of equalities. Relations. Compositions | PS 11 | Notes 11 | [Video 11] |
| 11.12.20 | Relations, image and preimage. Construction of counterexamples | PS 12 | Notes 12 | Video 12 |
| 18.12.20 | Functions, their properties. | PS 13 | Notes 13 | Video 13 |
| 15.01.21 | Equivalent sets, bijections, cardinalities. | PS 14 | Notes 14 | Video 14 |
| 22.01.21 | More about cardinalities. | PS 15 | Notes 15 | Video 15 |
| 29.01.21 | Definition of functions and consruction of proofs | PS 16 | Notes 16 | Video 16 |
| 5.02.21 | Countable sets. | PS 17 | Notes 17 | [ Video 17] |
| 12.02.21 | Combinatirics: binomial coefficients. | PS 18 | Notes 18 | Video 18 |
| 19.02.21 | Pigeonhole principle and Pascal's triangular. | PS 19 | Notes 19 | [ Video 19] |
| 26.02.21 | Proof of equalities with binomial coefficients. Generalized binomial coefficients. | PS 20 | Notes 20 | Video 20 |
Homeworks
Semester 1
Homework 1 (Logics and Induction), Deadline 7th November extended to 26th November
Homework 2 (Number Theory), Deadline 7th December
Homework 3 (Set Theory and Relations), Deadline 20th December
Semester 2
Homework 1 (Combinatorics), Deadline 1st March
References
Grading and Results
Final grade = 1/2*Homework 1 + 1/2*Homework 2 + Bonus points
Bonus point number is between 0 to 20. Such points may be given for a variety of auxiliary activities.
