Algebra
| Code | Completion | Credits | Range | Language |
|---|---|---|---|---|
| 01ALG | ZK | 4 | 4+0 | Czech |
- Garant předmětu:
- Lecturer:
- Tutor:
- Supervisor:
- Department of Mathematics
- Synopsis:
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After an introduction into the set theory standard algebraic structures are dealt with: groups, rings, fields, modules, linear algebras, lattices, Boolean algebras, rings of polynomials over commutative fields.
- Requirements:
- Syllabus of lectures:
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Axiom system for set theory, relations, ordering, equivalence and subvalence of sets, isomorphism of linearly ordered sets, well-ordering, axiom of choice, Zorn's lemma, ordinals and cardinals. Semigroups, groups, cyclic groups, congruences, factorgroupoids, homomorphism, normal subgroups, permutation groups, direct product. Rings, integral domains, fields, congruences, factorrings, homomorphism, ideals, modules, linear algebras, field of quotients, characteristic, prime field, polynomial rings, finite fields. Lattices, complete lattices, ideals, filters, distributive and modular lattices, Boolean algebras.
- Syllabus of tutorials:
- Study Objective:
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nd to introduce them into the methods used in the general algebra.
- Study materials:
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Povinná
S. Mac Lane, G. Birkhoff: Algebra. Macmillan Com. New York 1968. (Selected chapters.)
Doporučená
R. Solomon: Abstrct Algebra. American Math.Soc. Belmont 2003.
- Note:
- Further information:
- No time-table has been prepared for this course
- The course is a part of the following study plans:
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- 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 (compulsory course of the specialization, 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)