# MAT-60056 Algebra, 5 cr

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

Mika Mattila

#### Lessons

 Implementation Period Person responsible Requirements MAT-60056 2019-01 3 Mika Mattila Final exam.

#### Learning Outcomes

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

#### Content

 Content Core content Complementary knowledge Specialist knowledge 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.

#### Instructions for students on how to achieve the learning outcomes

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.

#### Assessment scale:

Numerical evaluation scale (0-5)

#### Study material

 Type Name Author ISBN URL Additional information Examination material Book An Introduction to Essential Algebraic Structures M.R. Dixon, L.A. Kurdachenko and I.Y. Subbotin No Book Johdatus Abstraktiin Algebraan J. Häsä & J. Rämö Alternative Finnish material No

#### Prerequisites

 Course Mandatory/Advisable Description MAT-01366 Mathematics 3 Mandatory MAT-01566 Mathematics 5 Advisable MAT-02106 Multivariable Calculus Advisable

#### Correspondence of content

 Course Corresponds course Description MAT-60056 Algebra, 5 cr MAT-41156 Algebra 1, 5 cr MAT-60056 Algebra, 5 cr MAT-60050 Algebra, 5 cr

 Updated by: Kunnari Jaana, 05.03.2019