Mathematics 5D

Lecturer:

Tutor:

Supervisor:

Department of Mathematics

Synopsis:

Sets and relations. Equivalence, ordered sets. Mathematical induction, BNF. Lattices, Boolean algebras, homomorphisms. Binary operations. Homomorphisms, free algebras. Rings and fields, cosets. Matrix algebras over fields. Predicate calculus. Resolution in propositional calculus. Normal formulas. Resolution in predicate calculus. Predicate algebras with more syntactics types.

Requirements:

Syllabus of lectures:

1. Sets and relations

2. Equivalence, ordered sets

3. Mathematical induction, BNF

4. Lattices, Boolean algebras, homomorphisms

5. Binary operations

6. Homomorphisms, free algebras

7. Rings and fields, cosets

8. Matrix algebras over fields

9. Predicate calculus

10. Resolution in propositional calculus

11. Normal formulas

12. Resolution in predicate calculus

13. Predicate algebras with more syntactics types

Syllabus of tutorials:

1. Sets and relations

2. Equivalence, ordered sets

3. Mathematical induction, BNF

4. Lattices, Boolean algebras, homomorphisms

5. Binary operations

6. Homomorphisms, free algebras

7. Rings and fields, cosets

8. Matrix algebras over fields

9. Predicate calculus

10. Resolution in propositional calculus

11. Normal formulas

12. Resolution in predicate calculus

13. Predicate algebras with more syntactics types

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:

• Výpočetní technika-bakalářský blok (compulsory course)
• Výpočetní technika-bakalářský blok (compulsory course)