Discrete mathematics and logics

Lecturer:

Jiří Velebil

Tutor:

Jiří Velebil

Supervisor:

Department of Mathematics

Synopsis:

The course covers basics of logic, both propositional and predicate for computer scientists. Mathematical induction is presented as a tool for proofs and for defining new entities. Next topics are binary relations, equivalence, ordering, Euklid's algorithm, relation mod n, congruence classes as examples of groups, rings and fields. The final topic is solving difference equations.

Requirements:

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

Syllabus of lectures:

1. Semantical consequence and tautological equivalence in propositional logic.

2. CNF and DNF, Boolean calculus.

3. Predicate logic, interpretation.

4. Semantical consequence and tautological equivalence in predicate logic.

5. Mathematical induction.

6. Binary relations.

7. Equivalence and partial order.

8. Integers, Euclid's algorithm.

9. Relation mod n on the set of integers.

10. Congruence classes.

11. Semigroups, monoids, groups.

12. Rings and fields.

13. Homogeneous linear difference equations.

14. Nonhomogeneous linear difference equations.

Syllabus of tutorials:

1. Semantical consequence and tautological equivalence in propositional logic.

2. CNF and DNF, Boolean calculus.

3. Predicate logic, interpretation.

4. Semantical consequence and tautological equivalence in predicate logic.

5. Mathematical induction.

6. Binary relations.

7. Equivalence and partial order.

8. Integers, Euclid's algorithm.

9. Relation mod n on the set of integers.

10. Congruence classes.

11. Semigroups, monoids, groups.

12. Rings and fields.

13. Homogeneous linear difference equations.

14. Nonhomogeneous linear difference equations.

Study Objective:

Study materials:

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

Note:

Time-table for winter semester 2011/2012:

Time-table is not available yet

Time-table for summer semester 2011/2012:

Time-table is not available yet

The course is a part of the following study plans:

• Computer Technology- structured studies (compulsory course)