Moodle FEL ČVUT
Discrete Mathematics and Graphs
B261 - Zimní 26/27
Discrete Mathematics and Graphs - BE5B01DMG
| Kredity | 5 |
| Semestry | zimní |
| Zakončení | Zápočet a zkouška |
| Jazyk výuky | angličtina |
| Rozsah výuky | 3P+1S |
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).
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.
Osnovy 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
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
Osnovy 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
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
Literatura
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.
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.
Požadavky
None.