Discrete Math.& Graphs

Course guarantor:

Marie Demlová

Lecturer:

Marie Demlová

Tutor:

Marie Demlová

Supervisor:

Department of Mathematics

Synopsis:

The course introduces basic notions from discrete mathematics directed to those topics useful for electrical engineering studies. The content of the course covers: infinite sets with emphasis to cardianlity of sets, binary relations with emphasis to equivalence relations and partial ordes'; integers, relation modulo n'; basic algebraic structures (includin finite fields of characteristic 2). Furher the course contains basic notions and their applications from graph theory.

Requirements:

None.

Syllabus of lectures:

1. Sets. Cardinality of sets.

2. Binary relalations, equivalence relation, partial order.

3. Integers, Eclid's algorithm and Bezout's theorem

4. Relation modulo n, rezidual classes and operations with them

5. Binary operations, semigroups, groups.

6. Sets with two binary operations, Boolean algebras.

7. Rings of rezidual classes, finite fieldst of rezidual classes over a prime, polynomials

over them.

8. Galois fields GF(2^k).

9. Homomorfisms of algebraic structures.

10. Undirected graphs, directed graphs, trees and spanning trees.

11. Strongly connected and acyclic graphs, topological sort

12.Combinatorics.

13. Asymptotic growth of functions.

Syllabus of tutorials:

1. Sets. Cardinality of sets.

2. Binary relalations, equivalence relation, partial order.

3. Integers, Eclid's algorithm and Bezout's theorem

4. Relation modulo n, rezidual classes and operations with them

5. Binary operations, semigroups, groups.

6. Sets with two binary operations, Boolean algebras.

7. Rings of rezidual classes, finite fieldst of rezidual classes over a prime, polynomials

over them.

8. Galois fields GF(2^k).

9. Homomorfisms of algebraic structures.

10. Undirected graphs, directed graphs, trees and spanning trees.

11. Strongly connected and acyclic graphs, topological sort

12.Combinatorics.

13. Asymptotic growth of functions.

Study Objective:

The aim of the course is to introduce to students basic notions of discrete mathematics that will be used in their studies.

Study materials:

1. Lindsay N. Childs: A Concrete Introduction to Higher Algebra, Springer; 3rd edition (November 26, 2008),

ISBN-10: 0387745270

2. Jiří Demel: Grafy a jejich aplikace, Academia; 2002, ISBN 80-200-0990-6

3. Richard Johnsonbaugh: Discrete Mathematics, Prentice Hall, 4th edition (1997), ISBN 0-13-518242-5

Note:

Further information:

https://moodle.fel.cvut.cz/courses/A8B01DMG

Time-table for winter semester 2025/2026:

Time-table is not available yet

Time-table for summer semester 2025/2026:

Time-table is not available yet

The course is a part of the following study plans:

• Open Electronic Systems (compulsory course in the program)
• Open Electronic Systems (compulsory course in the program)