## Discrete Mathematics

### Content:

#### Lectures:

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

#### Tutorials:

1. Sets, cardinality of sets, countable and uncountable sets.
2. Binary relations on a set, equivalence.
3. Binary relations on a set, partial order.
4. Integers, Euclid (extended) algorithms.
5. Relation modulo n, congruence classes Zn and operations on Zn.
6. Algebraic operations, semigroups, groups.
7. Matematical induction and its applications
8. Matematical induction as a tool for solving recurrence relations.
9. Solving non-homogeneous recurrence equations with constant coefficients.
10. Binomial theorem and its applications, properties of combinatorial numbers.
11. Combinatorics.
12. 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

Brief content of lectures Lectures.

Presentations Presentations.

Brief content of tutorials Tutorials.

### Assesment (zapocet):

Requirements: Active participation in tutorials.

During the semester students will be divided into groups of 7, and will be given 6 homeworks. A randomly chosen group will present solution during the next tutorial. The solution will be graded and each member of the group will obtain the same amout of points with maxum gain 5 points.

Midterm: Midterm will be written during the labs in 9th week of semester. Midterm test consists tasks from two parts: 1. binary relations (gain max. 6 points); and 2. solving an equation in rezidue classes (gain max. 9 points). Maximum gain is 15 points.

### Final exam:

A necessary condition is to obtain assesment (zapocet).

Final exam contains written test which consists of 5 problems, maximum gain 80 points, with 105 minutes allowed for solving them.