M3150 Algebra II

Faculty of Science
Autumn 2022
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
Thu 8:00–9:50 M6,01011
  • Timetable of Seminar Groups:
M3150/01: Wed 16:00–17:50 M2,01021, P. Francírek
Prerequisites (in Czech)
M2150 Algebra I || MUC32 Algebra
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
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, and lattice theory;
* 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).
  • Groups (normal subgroups, quotient groups, group actions, center of a group and inner automorphisms, Sylow's theorems).
  • Rings and polynomials (ideals, quotient rings, fields, localization, field of quotients, field extensions, finite fields, rudiments of Galois theory).
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. Vyd. 1. Praha: Ministerstvo školství, mládeže a tělovýchovy ČSR, 1989, 84 s. info
  • DUMMIT, David Steven and Richard M. FOOTE. Abstract algebra. 3rd ed. Hoboken, N.J.: John Wiley & Sons, 2004, xii, 932. ISBN 0471433349. 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
Study Materials
The course is taught annually.
Listed among pre-requisites of other courses
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 2014, Autumn 2015, Autumn 2016, autumn 2017, Autumn 2018, Autumn 2019, Autumn 2020, autumn 2021, Autumn 2023, Autumn 2024.
  • Enrolment Statistics (Autumn 2022, recent)
  • Permalink: https://is.muni.cz/course/sci/autumn2022/M3150