# Algebra 1 (NMAI062) - Winter term 2021/22

## Please register to the **!!** Moodle course **!!**

**Lecture notes**
**Lecture**: Wednesday 10:40 - 12:10, lecture room S4

**Exercise classes**: Tuesdays 15:40 - 17:10, lecture room S10, given by

Kevin Berg
(

current covid regulations)

**Evaluation:**
To get ''Zápočet'' (i.e. to pass the exercise classes) you need to score at least 60/100 points. These can be obtained from 3 homework assignments (3*30 points), or weekly quizzed (10 points), which will be posted on the

Moodle course
The final grade will be determined by a written exam. Admission to the exam requires passing the exercise class.

**Syllabus:**This course aims to give an introduction to algebra for computer science students. It will cover the following topics:

- Number theory: prime factorization, congruences, Euler's theorem and RSA, the Chinese remainder theorem
- Polynomials: rings and integral domains, polynomial rings, irreducibility, GCD, the Chinese remainder theorem and interpolation, the construction of finite fields and applications (error correcting codes, secret sharing,...)
- Group theory: permutation groups, subgroups, Langrange's theorem, group actions and Burnsides's theorem, cyclic groups, discrete logarithm and applications in cryptography

**Literature**:The course has its own

lecture notes, which are based on

David Stanovsky's material from last year, and will be constantly updated during the semester. Complementary resources are for instance

- J. Rotman,
*A First Course in Abstract Algebra* (available in our library),
- C. Pinter
*A Book of Abstract Algebra* (freely available online),
- or any other undergraduate level textbook on abstract algebra.

**Consultation:**
If you have open 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.