Discrete Mathematics and Graphs

Garant předmětu:

Jan Hamhalter

Přednášející:

Jan Hamhalter

Cvičící:

Jan Hamhalter

Předmět zajišťuje:

katedra matematiky

Anotace:

The aim of the course is to introduce students to fundamentals of Discrete Mathematics with focus on application to electrical engineering and computer science. The content of the course covers fundamentals of propositional logic, infinite sets with focus on the notion of cardinality of sets, binary relations with focus on equivalence, numer theory (divisibility, Diophantic equations, prime numbers, Fermat theorem) , basic algebraic structures (monoids, groups, applications to number theory), elements of combinatorics, elements of graph theory (connected graphs, trees, Euler graphs).

Požadavky:

None.

Osnova přednášek:

1. Foundation of Propositional logic, basic methods of proofs

2. Quantifiers

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

4. Binary relations on a set, equivalence relation, equivalence classes

5. Divisibility, Euclid algorithm, Diophantine equations

6. Primes, fundamental theorem of arithmetics, position systems

7. congruence classes, Zn and operations on Zn, Fermat theorem

8. Algebraic operations, monoids, semigroups, groups.

8. Lagrange theorem, order of element.

9. Application of algebra to number theory.

10. Combinatorics - categories, combinatorial numbers.

11. Exclusion-inclusion principle

12. Graphs, trees and spanning trees.

13. Euler graphs

Osnova cvičení:

1. Foundation of Propositional logic, basic methods of proofs

2. Quantifiers

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

4. Binary relations on a set, equivalence relation, equivalence classes

5. Divisibility, Euclid algorithm, Diophantine equations

6. Primes, fundamental theorem of arithmetics, position systems

7. congruence classes, Zn and operations on Zn, Fermat theorem

8. Algebraic operations, monoids, semigroups, groups.

8. Lagrange theorem, order of element.

9. Application of algebra to number theory.

10. Combinatorics - categories, combinatorial numbers.

11. Exclusion-inclusion principle

12. Graphs, trees and spanning trees.

13. Euler graphs

Cíle studia:

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

Studijní materiály:

basic source:

[1] Jan Hamhalter: Discrete Mathematics and Graphs, Lecture notes, FEE CVUT. Available online at

https://math.fel.cvut.cz/en/people/hamhalte/discrete-mathematics-and-graphs

further reading:

[DP] N.Donaldson, A.Pantano: An Introduction to Abstract Mathematics, Lecture Notes available online

[De] M.Demlova, Discrete Mathematics and Graphs, Lecture Notes FEE CTU.

Poznámka:

Další informace:

https://math.fel.cvut.cz/en/people/hamhalte/discrete-mathematics-and-graphs

Rozvrh na zimní semestr 2025/2026:

	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
Po	místnost T2:C2-82 Hamhalter J. 09:15–10:45 (přednášková par. 1) Dejvice T2:C2-82
Út
St	místnost T2:C2-82 Hamhalter J. 16:15–17:00 (přednášková par. 1) Dejvice T2:C2-82místnost T2:C2-82 Hamhalter J. 17:00–17:45 (přednášková par. 1 paralelka 101) Dejvice T2:C2-82
Čt
Pá

Rozvrh na letní semestr 2025/2026:

Rozvrh není připraven

Předmět je součástí následujících studijních plánů:

• Electrical Engineering and Computer Science (EECS) (povinný předmět programu)
• Electrical Engineering and Computer Science (EECS) (povinný předmět programu)