MATA221 Algebra 1: Groups (5 cr)

Study level:
Intermediate studies
0-5
Language:
English, Finnish
Responsible organisation:
Department of Mathematics and Statistics
Curriculum periods:
2020-2021, 2021-2022, 2022-2023, 2023-2024

Description

Basics of abstract algebra: binary operations and homomorphisms, groups

Learning outcomes

After completing the course successfully the student

• is familiar with the concepts of a set equipped with an operation and homomorphism and is able to examine their properties even in an abstract setting
• knows how to find out, whether a set equipped with an operation is a group.
• is able to determine whether a subset of a group is a subgroup, and if the the subgroup is a normal subgroup
• knows how to compute with permutations
• is familiar with the concept of a factor group and especially, knows how to compute with congruence classes
• is able to examine the structure of a group, using for example Lagrange's theorem

Description of prerequisites

Lineaarinen algebra ja geometria 1, modulaariaritmetiikan perusteet (esimerkiksi Algebra 1: Renkaat ja kunnat -kurssin modulaariaritmetiikkaosuus)

Literature

• T.W. Hungerford, Abstract Algebra: an introduction, Brooks/Cole cop. 2014. 3rd ed; ISBN: 9781111569624

Completion methods

Method 1

Description:
Arvosana määräytyy kurssitentistä ja harjoitustehtävistä saatujen pisteiden avulla opetusohjelmassa ilmoitettavan laskutavan mukaisesti.
Evaluation criteria:
course exam and exercises
Time of teaching:
Period 4
Select all marked parts

Method 2

Description:
Hyväksyttyyn suoritukseen riittää puolet lopputentin maksimipistemäärästä.
Evaluation criteria:
final exam
Select all marked parts
Parts of the completion methods
x

Teaching (5 cr)

Type:
Participation in teaching
0-5
Language:
Finnish
Study methods:

Lectures 28 h (in Finnish), 7 sets of exercises

Study materials:

Lecture notes (in Finnish)

x

Type:
Exam