Unit information: Group Theory in 2020/21

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	Dr. Tointon
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

Description including Unit Aims

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.

Intended Learning Outcomes

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.

Teaching Information

The unit will be taught through a combination of

• synchronous online and, if subsequently possible, face-to-face lectures
• asynchronous online materials, including narrated presentations and worked examples
• guided asynchronous independent activities such as problem sheets and/or other exercises
• synchronous weekly group problem/example classes, workshops and/or tutorials
• synchronous weekly group tutorials
• synchronous weekly office hours

Assessment Information

90% Timed, open-book 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.

If you fail this unit and are required to resit, reassessment is by a written examination in the August/September Resit and Supplementary exam period.

Reading and References

Recommended

• M. A. Armstrong, Groups and Symmetry, Springer, 1988
• J. F. Humphreys, A Course in Group Theory, Oxford University Press, 1996
• H. E. Rose, A Course on Finite Groups, Springer, 2009