Theory of Groups

Mode of Delivery

Face to Face

Prerequisites and Co-Requisites

None

Recommended Optional Programme Components

Algebra 1

Course Contents

This course provides candidates with in-depth knowledge on groups and subgroups , cyclic groups and cosets,normal subgroups and factor groups, homomorphisms and group action on a set ,symmetric alternating and dihedral groups, categories, direct products and direct sums, free groups and free products, finitely generated Abelian groups, Krull-Schmidt's theorem, Sylow theorems, classification of finite groups, nilpotent and solvable groups, normal and subnormal series.

Weekly Schedule

1) Groups and subgroups
2) Cyclic groups and cosets
3) Normal subgroup and factor groups
4) Homomorphisms and group action on a set
5) Symmetric, Alternating and Dihedral groups
6) Categories
7) Direct products and Direct Sums
8) Midterm examination/Assessment
9) Free groups and free products
10) Finitely generated abelian groups
11) The Krull-Schmidt theorem
12) Sylow theorems
13) Classification of finite groups
14) Nilpotent and solvable groups
15) Normal and subnormal series
16) Final examination

Recommended or Required Reading

Planned Learning Activities and Teaching Methods

1) Lecture
2) Discussion
3) Demonstration
4) Group Study
5) Problem Solving

Assessment Methods and Criteria

Contribution of Semester Studies to Course Grade	40%
Number Percentage Semester Studies Midterm Examination 1 60% Quiz 2 30% Presentation/Seminar 1 10%
Contribution of Final Examination to Course Grade	60%
Total	100%

Language of Instruction

Turkish

Work Placement(s)

Not Required