M2150 Algebra I

Faculty of Science
Spring 2009
Extent and Intensity
2/2/0. 4 credit(s) (fasci plus compl plus > 4). Type of Completion: zk (examination).
Teacher(s)
prof. RNDr. Radan Kučera, DSc. (lecturer)
Mgr. Veronika Trnková (seminar tutor)
Guaranteed by
doc. RNDr. Libor Polák, CSc.
Department of Mathematics and Statistics – Departments – Faculty of Science
Timetable
Tue 8:00–9:50 M1,01017
  • Timetable of Seminar Groups:
M2150/01: Wed 8:00–9:50 M5,01013, V. Trnková
Prerequisites (in Czech)
! M2155 Algebra 1 && ( M1120 Fundamentals of Mathematics || M1125 Fundamentals of Mathematics )
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
At the end of this course, students should be able to:
understand rudiments of group theory and ring theory;
explain basic notions and relations among them.
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 a 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 (normální podgrupa, faktorgrupa).
  • Centrum 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 a 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
Assessment methods
Lecture with a seminar. Examination consists of two parts: written and oral.
Language of instruction
Czech
Follow-Up Courses
Further Comments
The course can also be completed outside the examination period.
The course is taught annually.
Listed among pre-requisites of other courses
The course is also listed under the following terms Spring 2008 - for the purpose of the accreditation, Spring 2011 - only for the accreditation, Autumn 2002, Spring 2003, Spring 2004, Spring 2005, Spring 2006, Spring 2007, Spring 2008, Spring 2010, Spring 2011, Spring 2012, spring 2012 - acreditation, Spring 2013, Spring 2014, Spring 2015, Spring 2016, Spring 2017, spring 2018, Spring 2019, Spring 2020, Spring 2021, Spring 2022, Spring 2023, Spring 2024, Spring 2025.
  • Enrolment Statistics (Spring 2009, recent)
  • Permalink: https://is.muni.cz/course/sci/spring2009/M2150