# Unit information: Introduction to Group Theory in 2016/17

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Unit name Introduction to Group Theory MATH10005 10 C/4 Teaching Block 2 (weeks 13 - 24) Professor. Rickard Not open A in A Level Mathematics None School of Mathematics Faculty of Science

## Description including Unit Aims

In the past, certain systems studied in various parts of mathematics have turned out to have common features, and these have been formalised into the definition of a group. Some of the earliest examples arose in connection with the solution of polynomial equations by formulae, and involved what we would now call groups of permutations. Other examples arise in trying to pin down mathematically what it means to say that a geometrical figure is symmetric and to quantify just how symmetric it is. It makes sense to study in one go all the systems which have the same general features. We shall start from the formal definition of a group and derive important general results from it using careful mathematical reasoning, but throughout there will be an emphasis on particular examples in which calculations can be performed relatively easily. The unit aims to introduce students to basic material in group theory, including examples of groups, group homomorphisms, subgroups, quotient groups, basic theorems on groups (such as Lagrange’s Theorem, Fermat’s Little theorem, 1st Isomorphism Theorem) and their applications.

## Intended Learning Outcomes

At the end of the unit, the students should:

• be able to understand and write clear mathematical statements and proofs;
• be able to demonstrate facility in working with various specific examples of groups;
• be able to solve standard types of problems in introductory group theory;
• understand and be able to apply the basic concepts and results presented throughout the unit.

## Teaching Information

Lectures, supported by lecture notes with problem sets and model solutions, and small group tutorials. Formative assessment will be provided by problem sheets with questions that will be set by the instructor and marked by the students’ tutors.

## Assessment Information

The final assessment mark will be based on a 1 ½-hour written examination.