Discrete Mathematics and Graphs
Code  Completion  Credits  Range  Language 

BE5B01DMG  Z,ZK  5  3P+1S 
 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), ISBN10: 0387745270
[2] Richard Johnsonbaugh: Discrete Mathematics, Prentice Hall, 4th edition (1997), ISBN 0135182425
 Note:
 Further information:
 https://math.feld.cvut.cz/0educ/BE5B01DMG.html
 Timetable 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
Mon Tue Fri Thu Fri  Timetable for summer semester 2019/2020:
 Timetable is not available yet
 The course is a part of the following study plans:

 Electrical Engineering and Computer Science (EECS) (compulsory course in the program)
 Electrical Engineering and Computer Science (EECS) (compulsory course in the program)