| Unit name | Group Theory |
|---|---|
| Unit code | MATH33300 |
| Credit points | 20 |
| Level of study | H/6 |
| Teaching block(s) |
Teaching Block 1 (weeks 1 - 12) |
| Unit director | Professor. Tim Burness |
| Open unit status | Not open |
| Pre-requisites |
MATH10005 Introduction to Group Theory and MATH10003 Analysis 1A (or MATH10011 Analysis) One of MATH21800 Algebra 2 or MATH21100 Linear Algebra 2 is desirable, but not essential |
| Co-requisites |
None |
| School/department | School of Mathematics |
| Faculty | Faculty of Science |
Unit Aims
To develop the student's understanding of groups, one of mathematics' most fundamental constructs.
Unit Description
Groups are one of the main building blocks in mathematics. They form the basis of all rings, fields and vector spaces, and many objects studied in analysis and topology have a group-theoretic structure. Also, physicists use groups to describe properties of the fundamental particles of matter. Pure mathematicians use them to study symmetry properties of geometric figures, in problems concerning permutations, to classify sets of objects like points of algebraic curves, and to study collections of matrices as well as in many other uses. The unit will cover the basic parts of the subject and study finite groups in some detail.
Relation to Other Units
This unit develops the material from Introduction to Group Theory. The ideas are carried further in the Level 7 units Representation Theory, Algebraic Topology, and Galois Theory.
Learning Objectives
After taking this unit, students should have gained an understanding of the basic properties of finite groups and an appreciation of the beauties of the subject and the limits of our present understanding.
Transferable Skills
Assimilation and use of novel and abstract ideas.
Lectures and exercises to be done by the students.
90% Examination. 10% Coursework.
Raw scores on the examinations will be determined according to the marking scheme written on the examination paper. The marking scheme, indicating the maximum score per question, is a guide to the relative weighting of the questions. Raw scores are moderated as described in the Undergraduate Handbook.
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