PřF:M7230 Galois Theory - Course Information
M7230 Galois TheoryFaculty of Science
Spring 2011 - only for the accreditation
- Extent and Intensity
- 3/0. 3 credit(s) (příf plus uk k 1 zk 2 plus 1 > 4). Type of Completion: zk (examination).
- prof. RNDr. Radan Kučera, DSc. (lecturer)
- Guaranteed by
- prof. RNDr. Radan Kučera, DSc.
Department of Mathematics and Statistics - Departments - Faculty of Science
- 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.
- 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.
- 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
- 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
- Further comments (probably available only in Czech)
- The course is taught once in two years.
The course is taught: every week.