Algebra 2 (NMAI076) - Spring term 2025
Lecture: Thursday 12:20 - 13:50, lecture room S8
Exercises: Thursdays 14:00 - 15:30 on
odd weeks, lecture room S1
Evaluation:
To obtain the credit (
Zápočet) for the course you need to score at least 54 out of 90 points. Points can be obtained from 3 homework assigments (3*30 points).
The final 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:
- Homomorphisms (group homomorphism, quotient groups, ring homomorphisms, ideals, classification of finite fields)
- Number fields (ring and field extensions, algebraic elements, and finite degree extensions)
- Algorithms in polynomial arithmetic (fast polynomial multiplication and division, decomposition)
- Other algebraic structures (lattices and Boolean algebras)
Overview:
| Date |
Topics |
Lecture notes |
Homework |
| 20/02 | Group homomorphisms and isomorphisms, invariants, classifications
Ex: Examples | Section 1 | |
| 27/02 | Quotient groups
Homomorphism theorem and isomorphism theorems | Section 2 | |
| 06/03 | Ideals, Principal Ideal Domains
Ex: Quotient groups, sums and intersections of Ideals | Section 3 | HW1
due 20.03. |
| 13/03 | | | |
| 20/03 |
Ex: | | |
| 27/03 | | | |
| 03/04 |
Ex: | | |
| 10/04 | | | |
| 17/04 |
Ex: | | |
| 24/04 | | | |
01/05 | International Workers' Day | | |
08/05 | V day | | |
| 15/05 |
Ex: | | |
| 22/05 | | | |
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.