M3150 Algebra II

Faculty of Science
Autumn 2014
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. Bc. Jaromír Kuben (assistant)
doc. Mgr. Ondřej Klíma, Ph.D. (alternate examiner)
Guaranteed by
Department of Mathematics and Statistics - Departments - Faculty of Science
Supplier department: Department of Mathematics and Statistics - Departments - Faculty of Science
Timetable
Wed 8:00–9:50 M6,01011
• Timetable of Seminar Groups:
M3150/01: Thu 8:00–9:50 M6,01011, R. Kučera
Prerequisites (in Czech)
M2150 Algebra I
Zvládnutí základů matematiky a kurzu Algebra I.
Course Enrolment Limitations
The course is offered to students of any study field.
Course objectives
At the end of this course, students should be able to:
* define basic notions of group theory, ring theory, lattice theory, and universal algebra;
* explain learned theoretical results;
* apply learned methods to concrete exercises.
Syllabus
• Rings and polynomials (ideals, factorrings, fields, field of quotients, extensions, finite fields, symmetric polynomials).
• Lattices (semilattices and lattices - two approaches, modular and distributive lattices, Boolean algebras, representation of finite distributive lattices and Boolean algebras).
• 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
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
The course is also listed under the following terms Autumn 2007 - for the purpose of the accreditation, Autumn 1999, Autumn 2010 - only for the accreditation, Spring 2003, Autumn 2003, Autumn 2004, Autumn 2005, Autumn 2006, Autumn 2007, Autumn 2008, Autumn 2009, Autumn 2010, Autumn 2011, Autumn 2011 - acreditation, Autumn 2012, Autumn 2013, Autumn 2015, Autumn 2016, autumn 2017, Autumn 2018, Autumn 2019, Autumn 2020.
• Enrolment Statistics (Autumn 2014, recent)