Algebra 2 (NMAI076) - Spring term 2026

Practicals: Monday 13:10 - 13:50, lecture room S6
Lecture: Monday 14:00-15:30, lecture room S4

Lecture notes	Czech	English
Algebra 1	alg1_cz	alg1_en
Algebra 2	alg2_cz	alg2_en

Evaluation:
The credit (Zápočet) for the course is obtained through active participation in the Practicals (presentation and discussion of exercises).
The grade will be determined by an oral exam, admission to the exam requires getting ''Zápočet'' first.

Syllabus: This course is a continuation of Algebra 1 and aims to introduce computer science students to some topics from abstract algebra:

1. Homomorphisms (group homomorphism, quotient groups, ring homomorphisms, ideals, classification of finite fields)
2. Number fields (ring and field extensions, algebraic elements, and finite degree extensions)
3. Algorithms in polynomial arithmetic (fast polynomial multiplication and division, decomposition)
4. Other algebraic structures (lattices and Boolean algebras)

Overview:

Date	Topics	Lecture notes
16/02	Group homomorphisms and isomorphisms, invariants	Section 1.1-1.3
23/02	Classification results for groups; Quotient groups, the first isomorphism theorem Pr: Finding homomorphisms/isomorphism between groups	Section 1.4, 2
02/03	Ideals and divisibility, principal ideal domains Pr: first isomorphism theorem, the alternating group An, the 15 puzzle	Section 3
09/03	Ring homomorphisms, isomorphism, isomorphism theorems Pr: Formal power series, basis of ideals	Section 4.1-4.3
16/03	When is a quotient ring a field/domain? Ring and field extensions, the degree of a field extension Pr: Quotients of polynomial rings	Section 4.4, 5
23/03	Algebraic elements, minimal polynomials, degrees of field extensions Pr: ring and field extensions	Section 6
30/03	algebraic numbers form a field; Problems unsolvable by ruler and compass Pr: minimal polynomials, degrees of non-simple extensions	Section 6.3, 7
06/04	Easter Monday
13/04
20/04
27/04
04/05
11/05
18/05

Consultation:
If you have questions, do not hesitate to ask (either in person or via e-mail)! I have no official office hours, but if required, a personal meeting can be arranged. Please make also use of the exercise classes to discuss your questions.