## Discrete Mathematics

### Content:

#### Lectures:

- Sets, cardinality of sets, countable and uncountable sets.
- Binary relations on a set, equivalence.
- Binary relations on a set, partial order.
- Integers, Euclid (extended) algorithms.
- Relation modulo n, congruence classes Zn and operations on Zn.
- Algebraic operations, semigroups, groups.
- Matematical induction and its applications
- Matematical induction as a tool for solving recurrence relations.
- Solving non-homogeneous recurrence equations with constant coefficients.
- Binomial theorem and its applications, properties of combinatorial numbers.
- Combinatorics.
- Reserve.

#### Tutorials:

- Sets, cardinality of sets, countable and uncountable sets.
- Binary relations on a set, equivalence.
- Binary relations on a set, partial order.
- Integers, Euclid (extended) algorithms.
- Relation modulo n, congruence classes Zn and operations on Zn.
- Algebraic operations, semigroups, groups.
- Matematical induction and its applications
- Matematical induction as a tool for solving recurrence relations.
- Solving non-homogeneous recurrence equations with constant coefficients.
- Binomial theorem and its applications, properties of combinatorial numbers.
- Combinatorics.
- Reserve.

### References:

- DLindsay N. Childs: A Concrete Introduction to Higher Algebra, Springer;
3rd edition (November 26, 2008), ISBN-10: 0387745270
- Richard Johnsonbaugh: Discrete Mathematics, Prentice Hall,
4th edition (1997), ISBN 0-13-518242-5