 CZECH TECHNICAL UNIVERSITY IN PRAGUE
STUDY PLANS
2019/2020

# Discrete Math.& Graphs

Code Completion Credits Range Language
A8B01DMG Z,ZK 5 3P+1S Czech
Lecturer:
Marie Demlová (guarantor)
Tutor:
Marie Demlová (guarantor)
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:
http://math.feld.cvut.cz/demlova/teaching/dmg_vyuka.html
Time-table for winter semester 2019/2020:
 06:00–08:0008:00–10:0010:00–12:0012:00–14:0014:00–16:0016:00–18:0018:00–20:0020:00–22:0022:00–24:00 roomT2:C4-363Demlová M.09:15–10:45(lecture parallel1)DejviceCvicebnaroomT2:C4-363Demlová M.11:45–12:30(lecture parallel1parallel nr.101)DejviceCvicebna roomT2:C4-363Demlová M.11:00–11:45(lecture parallel1)DejviceCvicebna
Time-table for summer semester 2019/2020:
Time-table is not available yet
The course is a part of the following study plans:
Data valid to 2020-01-28
For updated information see http://bilakniha.cvut.cz/en/predmet2665106.html