Mathematical Logic

Lecturer:

Tutor:

Supervisor:

Department of Mathematics

Synopsis:

Sets and relations. Cardinality. Binary relations, graphs, trees. Ordering, equivalence. Strings over finite alphabet. Propositional algebra, tautology, contradiction. Satisfiability, tautological equivalence. Propositional logical connectives. Disjunctive and conjunctive normal forms. Logical network algebra. Resolution in propositional logic. Deduction, concept of proof. Predicate logic. Predicate algebra, interpretation.ements method. Constructing finite elements. Random variables, elementary statistics. Simle tests on parameters. Empirical distribution function, histogram. Testing hypotheses.

Requirements:

Syllabus of lectures:

1. Sets and relations. Cardinality

2. Binary relations, graphs, trees

3. Ordering, equivalence

4. Strings over finite alphabet

5. Propositional algebra, tautology, contradiction

6. Satisfiability, tautological equivalence

7. Propositional logical connectives

8. Disjunctive and conjunctive normal forms

9. Logical network algebra

10. Resolution in propositional logic

11. Deduction, concept of proof

12. Predicate logic

13. Predicate algebra, interpretation

Syllabus of tutorials:

1. Sets and relations. Cardinality

2. Binary relations, graphs, trees

3. Ordering, equivalence

4. Strings over finite alphabet

5. Propositional algebra, tautology, contradiction

6. Satisfiability, tautological equivalence

7. Propositional logical connectives

8. Disjunctive and conjunctive normal forms

9. Logical network algebra

10. Resolution in propositional logic

11. Deduction, concept of proof

12. Predicate logic

13. Predicate algebra, interpretation

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: