Course Code:

MTH 2201

Course Credit Units:

3

Semester:

Semester 2

Year of Study:

Year 2

Undergraduate or Graduate Level:

Undergraduate Level

Academic Programs:

School:

Course Description & Objectives:

This course is meant to develop the ability to think abstractly, make conjectures and construct rigorous mathematical proofs. It brings to light the basic philosophy, purpose and history behind the development of groups as abstract algebraic structures. It makes one understand how mappings can preserve algebraic structure, and through such mappings, learn how to determine when two seemingly different algebraic structures turn out to be the same (isomorphic).

Learning Outcomes:

By the end of this course, the student should be able to**:**

- distinguish a group from other algebraic structures
- draw a Cayley table for any group
- state and prove the Lagrange’s theorem
- define cyclic groups and Abelian groups
- define conjugacy, centralizers, the centre, normalizers and normal subgroups
- state and prove the Isomorphism theorems
- state and prove the fundamental theorem of finite Abelian groups
- state and use Sylow’s theorems
- define simple and soluble groups.
- define a ring, a field, an integral domain.
- apply concepts in Abstract Algebra to Number Theory

construct proofs in this area.