# MAT-60056 Algebra, 5 cr

#### Lisätiedot

This is an English version of the Algebra 1B course MTTMA3B. The course will be lectured in English every second year.

Mika Mattila

#### Opetus

 Toteutuskerta Periodi Vastuuhenkilö Suoritusvaatimukset MAT-60056 2019-01 3 Mika Mattila Final exam.

#### Osaamistavoitteet

After passing the course the student - possesses an ability of abstract thinking - recognizes and understands basic algebraic structures such as groups, rings and fields - understands the content of the fundamental theorems of abstract algebra and is able to prove them if necessary

#### Sisältö

 Sisältö Ydinsisältö Täydentävä tietämys Erityistietämys 1. GROUP THEORY: Groups, subgroups, group homomorphisms and isomorphisms. Normal subgroups and quotient groups. Congruence gruops, cyclic groups, permutation groups, matrix groups, dihedral groups. 2. RINGS AND FIELDS: Rings, subrings, integral domains and fields, ideals, polynomials of one variable. Quotient rings, field extensions. Matrix rings, field of fractions.

#### Ohjeita opiskelijalle osaamisen tasojen saavuttamiseksi

Active participation in the weekly exercise sessions is very much recommended. It will also result as a significant number of bonus points that will be taken into account in the grading of the course.

#### Arvosteluasteikko:

Numerical evaluation scale (0-5)

#### Oppimateriaali

 Tyyppi Nimi Tekijä ISBN URL Lisätiedot Tenttimateriaali Book Fundamental Structures of Algebra & Discrete Mathematics Foldes, S. Wiley 1994. Yes Book Johdatus Abstraktiin Algebraan J. Häsä & J. Rämö Alternative Finnish material No

#### Esitietovaatimukset

 Opintojakso P/S Selite MAT-01366 Mathematics 3 Mandatory MAT-01566 Mathematics 5 Advisable MAT-02106 Multivariable Calculus Advisable

#### Vastaavuudet

 Opintojakso Vastaa opintojaksoa Selite MAT-60056 Algebra, 5 cr MAT-41156 Algebra 1, 5 cr MAT-60056 Algebra, 5 cr MAT-60050 Algebra, 5 cr

 Päivittäjä: Kunnari Jaana, 05.03.2019