Seminar of applied algebra

Garant předmětu:

Lecturer:

Tutor:

Supervisor:

Department of Mathematics

Synopsis:

Optional course intended to deeper understanding and practice of facts taught in basic general algebra course 01ALGE. The emphasis is given to practical work with algebraic structures on concrete examples.

Requirements:

Basic courses of mathematical analysis and linear algebra (01MAN, 01MAA2-4, 01LAL, 01LAA2).

Syllabus of lectures:

1. Divisibility, integral domains, modular arithmetic, Chinese remainder theorem.

2. Groups, examples of groups, presentation of groups, cryptography.

3. Rings, subrings, ideals, polynomials.

4. Unions, Boolean algebras.

5. Fields, field extensions, Galois theory.

Syllabus of tutorials:

Study Objective:

Knowledge:

Better understanding of some topics taught in general algebra course 01ALGE.

Skills:

Manipulation of concrete algebraic structures, usage of notions from 01ALGE course in practice.

Study materials:

Recommended references:

1. J. Rotman, A First Course in Abstract Algebra: With Applications, Prentice Hall 2006.

2. W. Wickless: A First Graduate Course in Abstract Algebra, CRC Press, 2017.

Note:

Further information:

No time-table has been prepared for this course

The course is a part of the following study plans: