Discrete mathematics and logics

The course is a substitute for:

Discrete mathematics and logics (X01DML)

Lecturer:

Tutor:

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. The final grading reflects the performance in both the written and oral part of the examination the student sits for at the end of the course.

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:

Further information:

No time-table has been prepared for this course

The course is a part of the following study plans:

• Computer Technology- structured studies (compulsory course)