CZECH TECHNICAL UNIVERSITY IN PRAGUE
STUDY PLANS
2020/2021

# Discrete Mathematics and Graphs

Code Completion Credits Range Language
BE5B01DMG Z,ZK 5 3P+1S English
Lecturer:
Tommaso Russo
Tutor:
Tommaso Russo
Supervisor:
Department of Mathematics
Synopsis:

The aim of the course is to introduce students to fundamentals of Discrete Mathematics with focus on electrical engineering. The content of the course covers fundamentals of propositional and predicate logic, infinite sets with focus on the notion of cardinality of sets, binary relations with focus on equivalences and partial orderings; integers, relation modulo; algebraic structures including Boolean algebras. Further, the course covers basics of the Theory of Graphs.

Requirements:

None.

Syllabus of lectures:

1. Foundation of Propositional logic, Boolean calculus

2. Foundation of Predicate logic, quantifiers, interpretation.

3. Sets, cardinality of sets, countable and uncountable sets.

4. Binary relations on a set, equivalence relation, partial order.

5. Integers, Euclid (extended) algorithms.

6. Relation modulo n, congruence classes Zn and operations on Zn.

7. Algebraic operations, semigroups, groups.

8. Sets together with two binary operations, Boolean algebras.

9. Rings of congruence classes Zn, fields Zp.

10. Undirected graphs, trees and spanning trees.

11. Directed graphs, strong connectivity and acyclic graphs.

12. Euler graphs and Hamiltonian graphs, coloring.

13. Combinatorics.

Syllabus of tutorials:

1. Foundations of propositional and predicate logic.

2. Binary relations, equivalence and partial order.

3. Euclid algorithm, relation modulo n, congruence classes modulo n and operations with them.

4. Algebraic operations, semigroups, groups, fields Zp, Boolean algebras.

5. Undirected graphs, trees, spanning trees.

6. Directed graphs, strong connectivity, acyclic graphs.

7. Combinatorics.

Study Objective:

The goal of the course is to introduce students with the basic notions from discrete mathematics, namely logic, basics of set theory, binary relationsand binary operations; basics from graph theory and combinatorics.

Study materials:

[1] Lindsay N. Childs: A Concrete Introduction to Higher Algebra, Springer; 3rd edition (November 26, 2008), ISBN-10: 0387745270

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

Note:
Further information:
https://math.feld.cvut.cz/0educ/BE5B01DMG.html
Time-table for winter semester 2020/2021:
 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:C4-78Russo T.09:15–10:45(lecture parallel1)DejviceT2:C4-78 roomT2:C4-78Russo T.16:15–17:00(lecture parallel1)DejviceT2:C4-78roomT2:C4-78Russo T.17:00–17:45(lecture parallel1parallel nr.101)DejviceT2:C4-78
Time-table for summer semester 2020/2021:
Time-table is not available yet
The course is a part of the following study plans:
Data valid to 2020-09-20
For updated information see http://bilakniha.cvut.cz/en/predmet4355306.html