Discrete Mathematics for KM

Lecturer:

Marie Demlová (gar.)

Tutor:

Marie Demlová (gar.), Jiřina Scholtzová

Supervisor:

Department of Mathematics

Synopsis:

The course covers the basics of mathematical logic and graph theory;

it is intended for the students of „Cybernetics and measurement“ and

contains formal syntax of propositional logic, tautological

equivalence, CNF and DNF, resolution method in propositional logic and

predicate logic. The main topics of graph theory are directed and

undirected graphs, trees, Euler and Hamilton graphs. A brief

introduction to group theory ends the course.

Requirements:

The requirement for receiving the credit is an active participation in the tutorials.

Syllabus of lectures:

1. Formal syntax of propositional logic, truth valuation

2. Semantical consequence, tautological equivalence

3. CNF and DNF, Boolean calculus

4. Resolution method in propositional logic

5. Introduction of predicate logic, quantifiers

6. Interpretation of predicate logic

7. Directed and undirected graphs

8. Trees, directed trees (arborescence)

9. Euler trials and applications

10. Hamilton paths and applications

11. Colorability of graphs, cliques in graphs

12. Binary operations and their properties

13. Semigroups and monoids

14. Groups, their basic properties

Syllabus of tutorials:

1. Formal syntax of propositional logic, truth valuation

2. Semantical consequence, tautological equivalence

3. CNF and DNF, Boolean calculus

4. Resolution method in propositional logic

5. Introduction of predicate logic, quantifiers

6. Interpretation of predicate logic

7. Directed and undirected graphs

8. Trees, directed trees (arborescence)

9. Euler trials and applications

10. Hamilton paths and applications

11. Colorability of graphs, cliques in graphs

12. Binary operations and their properties

13. Semigroups and monoids

14. Groups, their basic properties

Study Objective:

Study materials:

1. M. Demlová: Mathematical Logic. ČVUT Praha, 1999.

Note:

Further information:

No time-table has been prepared for this course

The course is a part of the following study plans:

• Cybernetics and Measurements- structured studies (compulsory elective course)