MAT-60056 Algebra, 5 cr

Additional information

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

Person responsible

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   Fundamental Structures of Algebra & Discrete Mathematics   Foldes, S.       Wiley 1994.   Yes   
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