Introduction to Discrete Mathematics

Garant předmětu:

Lecturer:

Tutor:

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

formal construction of propositional calculus.

Requirements:

Grammar school knowledge.

Syllabus of lectures:

1.Basic combinatorics, Binomial Theorem.

2. Inclusion and Exclusion Principle and applications.

3. Basics from graph theory, connected graphs.

4. Eulerian graphs, trees and their properties.

5. Weighted tree, minimal spanning tree.

6. Bipartite graph, matching in bipartite graphs.

7. Binary relation, equivalence.

8. Ordering, minimal and maximal elements.

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

10. Uncountable sets, Cantor Theorem.

11. Well-formed formula in propositional calculus.

12. Logical consequence, boolean functions.

13. Disjunctive and conjunctive normal forms, satisfiable sets, resolution method.

14. Well-formed formula in predicate calculus.

Syllabus of tutorials:

1.Basic combinatorics, Binomial Theorem.

2. Inclusion and Exclusion Principle and applications.

3. Basics from graph theory, connected graphs.

4. Eulerian graphs, trees and their properties.

5. Weighted tree, minimal spanning tree.

6. Bipartite graph, matching in bipartite graphs.

7. Binary relation, equivalence.

8. Ordering, minimal and maximal elements.

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

10. Uncountable sets, Cantor Theorem.

11. Well-formed formula in propositional calculus.

12. Logical consequence, boolean functions.

13. Disjunctive and conjunctive normal forms, satisfiable sets, resolution method.

14. Well-formed formula in predicate calculus.

Study Objective:

The aim of this subject is to develop logical reasoning and to analyze logical structure of propositions.

The basics form combinatorics, graph and set theories are included as well.

Study materials:

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

Note:

Further information:

http://math.feld.cvut.cz/bohata/zdmd.html

No time-table has been prepared for this course

The course is a part of the following study plans:

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