Algebra
| Code | Completion | Credits | Range |
|---|---|---|---|
| 01ALGE | Z,ZK | 6 | 4+1 |
- Garant předmětu:
- Zuzana Masáková
- Lecturer:
- Zuzana Masáková
- Tutor:
- Zuzana Masáková
- Supervisor:
- Department of Mathematics
- Synopsis:
-
Firstly, the Peano axioms are treated in detail. Elements of the set theory cover only: equivalence and subvalence, the Cantorov-Bernstein theorem, the axiom of choice and equivalent statements, definition of ordinals and cardinals. Further standard algebraic structures are addressed: semigroups, monoids, groups, rings, integral domains, principal ideal domains, fields, lattices. Independent chapters are devoted to divisibility in integral domains and to finite fields.
- Requirements:
-
01LAA2
- Syllabus of lectures:
-
1. Binary relations, equivalence, ordering
2. The Peano axioms for the natural numbers, principle of recursive definition
3. Equivalence and subvalence of sets, the transfinite induction
4. The axiom of choice and equivalent statements
5. Ordinals and cardinals
6. Semigroups, monoids
7. Groups
8. Rings, integral domains, principal ideal domains, fields
9. Divisibility in integral domains
10. Finite fields
11. Lattices
- Syllabus of tutorials:
- Study Objective:
-
Knowledge: elements of the set theory - equivalence and subvalence, the axiom of choice and equivalent statements, ordinals and cardinals; basics of algebra - the Peano axioms, monoids, groups, rings, integral domains, principal ideal domains, fields
Skills: using algebraic structures, applying these structures along with some elements of the set theory in other fields of mathematics
- Study materials:
-
Key references:
[1] Mareš J.: Algebra. Úvod do obecné algebry, 3. vydání. ČVUT, Praha, 1999.
Recommended references:
[2] Mac Lane S., Birkhoff G.: Algebra. Springer, New York, 2005.
[3] Lang S.: Algebra. Springer, New York, 2005.
- Note:
- Time-table for winter semester 2023/2024:
- Time-table is not available yet
- Time-table for summer semester 2023/2024:
- Time-table is not available yet
- The course is a part of the following study plans:
-
- BS Matematické inženýrství - Matematické modelování (compulsory course of the specialization, elective course)
- BS Matematické inženýrství - Matematická fyzika (elective course)
- BS Matematické inženýrství - Aplikované matematicko-stochastické metody (elective course)
- BS Informatická fyzika (elective course)
- BS Aplikace softwarového inženýrství (elective course)
- BS Aplikovaná informatika (elective course)
- BS jaderné inženýrství B (elective course)
- BS Jaderné inženýrství C (elective course)
- BS Dozimetrie a aplikace ionizujícího záření (elective course)
- BS Experimentální jaderná a částicová fyzika (elective course)
- BS Inženýrství pevných látek (elective course)
- BS Diagnostika materiálů (elective course)
- BS Fyzika a technika termojaderné fúze (elective course)
- BS Fyzikální elektronika (elective course)
- BS Jaderná chemie (elective course)
- Aplikovaná algebra a analýza (compulsory course in the program)
- Matematické inženýrství - Matematická fyzika (elective course)
- Matematické inženýrství - Matematická informatika (PS)
- Matematické inženýrství - Matematické modelování (PS)