PřF:M2150 Algebra I - Course Information

M2150 Algebra I

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)
doc. Mgr. Ondřej Klíma, Ph.D. (seminar tutor)
Mgr. Bc. Pavla Glosová (assistant)

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

Mon 18. 2. to Fri 17. 5. Fri 8:00–9:50 M1,01017

• Timetable of Seminar Groups:

M2150/01: Mon 18. 2. to Fri 17. 5. Fri 10:00–11:50 M1,01017, O. Klíma
M2150/02: Mon 18. 2. to Fri 17. 5. Tue 8:00–9:50 M1,01017, O. Klíma
M2150/03: Mon 18. 2. to Fri 17. 5. Tue 12:00–13:50 M1,01017, O. Klíma

Prerequisites (in Czech)

! M2155 Algebra 1

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

there are 9 fields of study the course is directly associated with, display

Course objectives

The aim of the course is to teach students the rudiments of algebra.

Learning outcomes

After passing this course, students should be able to:
* define basic notions of group theory and ring theory;
* explain learned theoretical results;
* apply learned methods to concrete exercises.

Syllabus

• Binary operation on a set, semigroup, (abelian) group; examples of groups and semigroups (numbers, permutations, residue classes, matrices, vectors), basic properties of groups (including powers and order of an element).
• Subgroup (including the subgroup generated by a set).
• Homomorphism and isomorphism of groups (Cayley's theorem, classification of cyclic groups), product of groups.
• Partition of a group, left cosets of a subgroup (Lagrange's theorem and their consequences).
• Quotient groups (normal subgroup, quotient group).
• Center of a group.
• Finite groups, p-groups, classification of finite abelian groups, Sylow's theorems.
• (Commutative) ring, integral domain, fields, their basic properties.
• Subring (including the subring generated by a set).
• Homomorphism and isomorphism of rings.
• Polynomials (basic properties, division of polynomials with remainder, Euclidean algorithm, value of a polynomial in an element, root of a polynomial, multiple roots, connection with the derivative of a polynomial).
• Polynomials over the fields of complex, real and rational numbers and over the ring of integers (irreducible polynomials, computation of roots of a polynomial).

Literature

• ROSICKÝ, Jiří. Algebra. 4., přeprac. vyd. Brno: Masarykova univerzita, 2002, 133 s. ISBN 80-210-2964-1. info

Teaching methods

Lectures: theoretical explanation. Exercises: solving problems with the aim to understand basic concepts and theorems, homework (e-tests).

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 (35 points of 70). 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

Follow-Up Courses

• M3150 Algebra II

Further Comments

Study Materials
The course can also be completed outside the examination period.
The course is taught annually.

Listed among pre-requisites of other courses

• MUC32 Algebra
  !M2150 && !(NOW(M2150))  
• M3150 Algebra II
  M2150 || MUC32  

• Enrolment Statistics (Spring 2019, recent)
  
• Permalink: https://is.muni.cz/course/sci/spring2019/M2150