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:
  1. Number theory: prime factorization, congruences, Euler's theorem and RSA, the Chinese remainder theorem
  2. 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,...)
  3. 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 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.