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PřF:M3150 Algebra II - Course Information

## M3150 Algebra II

**Faculty of Science**

Autumn 2019

**Extent and Intensity**- 2/2/0. 4 credit(s) (příf plus uk k 1 zk 2 plus 1 > 4). Type of Completion: zk (examination).
**Teacher(s)**- prof. RNDr. Radan Kučera, DSc. (lecturer)

Mgr. Pavel Francírek, Ph.D. (seminar tutor) **Guaranteed by**- prof. RNDr. Radan Kučera, DSc.

Department of Mathematics and Statistics - Departments - Faculty of Science

Supplier department: Department of Mathematics and Statistics - Departments - Faculty of Science **Timetable**- Fri 8:00–9:50 M6,01011
- Timetable of Seminar Groups:

*P. Francírek* **Prerequisites**(in Czech)-
**M2150**Algebra I

Zvládnutí základů matematiky a kurzu Algebra I. **Course Enrolment Limitations**- The course is also offered to the students of the fields other than those the course is directly associated with.
**fields of study / plans the course is directly associated with**- Mathematics (programme PřF, B-MA)

**Course objectives**- The aim of this course is to give students the necessary algebraic background, which is assumed in some advanced courses.
**Learning outcomes**- At the end of this course, students should be able to:

* define basic notions of group theory, ring theory, field theory, lattice theory, and universal algebra;

* explain learned theoretical results;

* apply learned methods to concrete exercises. **Syllabus**- Lattices (semilattices and lattices - two approaches, modular and distributive lattices, Boolean algebras, representation of finite distributive lattices and Boolean algebras).
- Rings and polynomials (ideals, factorrings, fields, field of quotients, extensions, finite fields, symmetric polynomials).
- Universal algebra (subalgebras, homomorphisms, congruences and factoralgebras, products, terms, varieties, free algebras, Birkhoff's theorem).

**Literature**- ROSICKÝ, Jiří.
*Algebra*. 4., přeprac. vyd. Brno: Masarykova univerzita, 2002. 133 s. ISBN 80-210-2964-1. info - BICAN, Ladislav and Jiří ROSICKÝ.
*Teorie svazů a univerzální algebra*. 1. vyd. Praha: Ministerstvo školství, mládeže a tělovýchovy ČSR, 1989. 84 s. info - PROCHÁZKA, Ladislav.
*Algebra*. 1. vyd. Praha: Academia, 1990. 560 s. info

- ROSICKÝ, Jiří.
**Teaching methods**- Lectures: theoretical explanation. Exercises: solving problems with the aim to understand basic concepts and theorems, homework.
**Assessment methods**- Examination consists of two parts: a written test and an oral examination. To pass the written part, which consists of 7 exercises, it is necessary to get at least 50% of points (50 points of 100). The students successful in the written part have to show in the following oral part that they are able to define the used notions and to work with them, to formulate the explained statements and to prove the easier of them.
**Language of instruction**- Czech
**Further comments (probably available only in Czech)**- Study Materials

The course is taught annually. **Listed among pre-requisites of other courses****Teacher's information**- http://www.math.muni.cz/~kucera

- Enrolment Statistics (Autumn 2019, recent)
- Permalink: https://is.muni.cz/course/sci/autumn2019/M3150