# Unit information: Group Theory in 2022/23

Unit name Group Theory MATH33300 20 H/6 Teaching Block 1 (weeks 1 - 12) Dr. Tointon Not open MATH10010 Introduction to Proofs and Group Theory None None School of Mathematics Faculty of Science

## Unit Information

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 various specific classes of 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.

## Your learning on this unit

Learning Objectives

After taking this unit, students should have gained an understanding of the basic properties of groups, and an appreciation of the beauties of this active, exciting and growing subject.

Transferable Skills

Assimilation and use of novel and abstract ideas.

## How you will learn

The unit will be taught through a combination of

• Face-to-face lectures
• Lecture notes
• Exercise sheets to be worked on independently
• Weekly synchronous support sessions
• Weekly synchronous drop-in sessions with the unit director

## How you will be assessed

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.

## Resources

If this unit has a Resource List, you will normally find a link to it in the Blackboard area for the unit. Sometimes there will be a separate link for each weekly topic.

If you are unable to access a list through Blackboard, you can also find it via the Resource Lists homepage. Search for the list by the unit name or code (e.g. MATH33300).

How much time the unit requires
Each credit equates to 10 hours of total student input. For example a 20 credit unit will take you 200 hours of study to complete. Your total learning time is made up of contact time, directed learning tasks, independent learning and assessment activity.