MATA221 Algebra 1: Groups (5 cr)
Study level:
Intermediate studies
Grading scale:
0-5
Language:
English, Finnish
Responsible organisation:
Department of Mathematics and Statistics
Curriculum periods:
2020-2021, 2021-2022, 2022-2023
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)
Study materials
Kurssimoniste
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
Grading scale:
0-5
Language:
Finnish
Study methods:
Lectures 28 h (in Finnish), 7 sets of exercises
Study materials:
Lecture notes (in Finnish)
Teaching
8/26–8/26/2020 Exam
3/15–5/23/2021 Lectures
5/19–5/19/2021 Exam
6/2–6/2/2021 Exam
x
Exam (5 cr)
Type:
Exam
Grading scale:
0-5
Language:
English, Finnish
Study methods:
Final exam (in Finnish or English)