Introduction to Discrete Mathematics

Course guarantor:

Jaroslav Tišer

Lecturer:

Jaroslav Tišer

Tutor:

Jaroslav Tišer

Supervisor:

Department of Mathematics

Synopsis:

No advanced knowleges of mathematics are required at the beginning of this course. Using illustrative examples we build sufficient understanding of combinatorics, set and graph theory. Then we proceed to a brief formal construction of predicate calculus.

Requirements:

Grammar school knowledge.

Syllabus of lectures:

1.Basic combinatorics, Binomial Theorem.

2. Inclusion and Exclusion Pronciple and applications.

3. Cardinality of sets, countable set and their properties.

4. Uncoutable sets, Cantor Theorem.

5. Binary relation, equivalence.

6. Ordering, minimal and maximal elements.

7. Basic from graph theory, connected graphs.

8. Eulerian graphs and their characterizartion.

9. Trees, basic properties.

10. Weighted tree, minimal spanning tree.

11. Bipartite graph, matching in bipartite graphs.

12. Well-formed formula in propositional calculus.

13. Well-formed formula in predicate calculus.

14. Reserve.

Syllabus of tutorials:

1.Basic combinatorics, Binomial Theorem.

2. Inclusion and Exclusion Pronciple and applications.

3. Cardinality of sets, countable set and their properties.

4. Uncoutable sets, Cantor Theorem.

5. Binary relation, equivalence.

6. Ordering, minimal and maximal elements.

7. Basic from graph theory, connected graphs.

8. Eulerian graphs and their characterizartion.

9. Trees, basic properties.

10. Weighted tree, minimal spanning tree.

11. Bipartite graph, matching in bipartite graphs.

12. Well-formed formula in propositional calculus.

13. Well-formed formula in predicate calculus.

14. Reserve.

Study Objective:

The aim of this subject is the basics of combinatorics, graph and set theories and to develop logical reasoning in predicate calculus.

Study materials:

K.H. Rosen: Discrete mathematics and its applications, 7th edition, McGraw-Hill, 2012.

Note:

Further information:

https://math.fel.cvut.cz/en/people/tiser/vyuka.html

Time-table for winter semester 2024/2025:

	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	roomT2:C4-155 Tišer J. 14:30–16:00 (lecture parallel1 parallel nr.103) Dejvice roomT2:C4-155 Tišer J. 16:15–17:45 (lecture parallel1 parallel nr.101) Dejvice roomT2:C4-155 Tišer J. 14:30–16:00 (lecture parallel1 parallel nr.108) Dejvice roomT2:C4-155 Tišer J. 16:15–17:45 (lecture parallel1 parallel nr.109) Dejvice
Tue	roomT2:C3-54 09:15–10:45 (lecture parallel1 parallel nr.106) Dejvice roomT2:C3-54 Tišer J. 11:00–12:30 (lecture parallel1 parallel nr.102) Dejvice roomT2:C3-54 Tišer J. 16:15–17:45 (lecture parallel1 parallel nr.104) Dejvice roomT2:C3-54 Tišer J. 11:00–12:30 (lecture parallel1 parallel nr.105) Dejvice roomT2:C3-54 Tišer J. 16:15–17:45 (lecture parallel1 parallel nr.107) Dejvice roomT2:D3-309 Tišer J. 14:30–16:00 (lecture parallel1) Dejvice
Wed	roomT2:C4-155 09:15–10:45 (lecture parallel1 parallel nr.110) Dejvice roomT2:C4-155 09:15–10:45 (lecture parallel1 parallel nr.111) Dejvice
Thu
Fri

Time-table for summer semester 2024/2025:

Time-table is not available yet

The course is a part of the following study plans:

• Software Engineering and Technology (compulsory course in the program)
• Software Engineering and Technology (compulsory course in the program)
• Software Engineering and Technology (compulsory course in the program)
• Software Engineering and Technology (compulsory course in the program)
• Software Engineering and Technology (compulsory course in the program)
• Software Engineering and Technology (compulsory course in the program)