#
PřF:M7230 Galois Theory - Course Information

## M7230 Galois Theory

**Faculty of Science**

Spring 2011

**Extent and Intensity**- 3/0. 3 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)
**Guaranteed by**- prof. RNDr. Radan Kučera, DSc.

Department of Mathematics and Statistics - Departments - Faculty of Science **Timetable**- Tue 8:00–10:50 M6,01011
**Prerequisites**(in Czech)- Algebra II (tj. odborná) nebo Algebra 2 (tj. učitelská)
**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, M-MA, specialization Discrete Mathematics)

**Course objectives**- Lecture on Galois theory including some of its applications in algebra and geometry. At the end of this course, students should be able to:

understand main results on Galois theory;

explain basic notions and relations among them. **Syllabus**- Field extension: simple algebraic extension, the degree of extension, algebraic and transcendental extension.
- Constructibility by straightedge and compas: imposibility to construct solution of the following geometric problems posed by the Greeks: doubling the cube, trisecting an angle, squaring the circle (without a proof that "pi" is transcendental).
- Normal and separable extension, linear independence of the embeddings of a field, normal closure, Galois correspondence.
- Solvable and simple groups.
- Solvability of algebraic equations in radicals: radical extensions.
- Unified view on solutions of quadratic, cubic and biquadratic equations, construction of an equation of degree five insolvable in radicals over the field of rational numbers.
- Galois group of cyclotomic fields, constructibility of regular polygons by straightedge and compas.

**Literature**- DUMMIT, David Steven and Richard M. FOOTE.
*Abstract algebra*. 3rd ed. Hoboken, N.J.: John Wiley & Sons, 2004. xii, 932. ISBN 0471433349. info - STEWART, Ian.
*Galois theory*. 2nd ed. London: Chapman & Hall, 1989. xxx, 202 s. ISBN 0-412-34550-1. info - PROCHÁZKA, Ladislav.
*Algebra*. Vyd. 1. Praha: Academia, 1990. 560 s. ISBN 8020003010. info

- DUMMIT, David Steven and Richard M. FOOTE.
**Teaching methods**- Lectures: theoretical explanation with applications in concrete examples.
**Assessment methods**- Examination consists of two parts: written test and oral examination.
**Language of instruction**- Czech
**Further comments (probably available only in Czech)**- Study Materials

The course is taught once in two years.

- Enrolment Statistics (Spring 2011, recent)
- Permalink: https://is.muni.cz/course/sci/spring2011/M7230