Group Theory | Makerere University Courses

Course Code:

MTH 2201

Course Credit Units:

Semester:

Semester 2

Year of Study:

Year 2

Undergraduate or Graduate Level:

Undergraduate Level

College:

College of Natural Sciences

School:

School of Physical Sciences

Department:

Mathematics

Course Discipline:

mathematics

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 prove Sylow’s theorems
Define simple and soluble groups.

File Attachments:

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