Algebra in Coding Theory     LS 2018/2019

Course: 470-4202/02: Algebra in Coding Theory   (AvTK)
Teacher: Petr Kovář
Hours: 6 credits (2/2/0/0/2)
Academic year: 2018/2019

Course outline is available in Edison system.

Credit and Exam

A Test will be written at the end of the Summer Term. Course credit "zápočet" will be given to those, who receive at least 15 points out of 30 for the Test.

To pass the exam one has to receive at least 35 points out of 70.

Topics

1. introduction to group theory: symmetries and dihedral groups
2. algebraic structures: groups, definitions, basic properties
3. subgroups, vproperties, examples
4. normal subgroups, Lagrange's Theorem
5. factor groups
6. homomorphisms of groups, defition, examples
7. isomorpsism: motivation, properties, Cayley's Theorem
8. cyclic groups, classifcation
9. permutation groups, definition, cycles, properties and applications
10. product of groups, definition, examples, applications
11. rings and subrings: definition, finite and infinte examples, applications
12. integral domains and fields: definition, properties
13. ideals, factor rings: definition, properties
14. homomorphism of rings, polynomial rings
15. fields, examples and applications
16. Final Test

Suggested reading

• J. Gallian: Contemporary Abstract Algebra, Cengage Learning; 8 edition (2012), ISBN13 978-1133599708. (available in University Library)
• G. Birkhoff, S. Mac Lane: Algebra, Alfa, Bratislava (1974).

Other books might be used, but beware: terminology might differ! (definitions) and at the exams we build on terminology from the lectures.

Office hours

Zastihnete mne nejlépe osobně během konzultačních hodin, případně (po dohodě emailem) on-line přes MS Teams.

Best way to reach me is during my office hours. It is also possible to arrange (ahead via e-mail) an on-line appointment in MS Teams.

Po předchozí domluvě jsou konzultace možné i v jinou dobu. / Or by appointment.

Petr<tečka>Kovar<zavináč>vsb<tečka>cz kancelář EA536, tel. 597 325 972

Upraveno: 09.09.2019