Courses / Module

GROUPS

Module code: MT316A
Credits: 5
Semester: 1
Department: MATHEMATICS AND STATISTICS
International:

	Overview
	Module Objective: To give a gentle introduction to groups. Definitions and examples: the integers, the integers mod n, permutation groups, finite groups of symmetries (for example dihedral groups). Mappings: group homomorphisms and isomorphisms, kernel and image definitions, examples. Subgroups: examples, orders of elements and groups, Lagrange's Theorem. Conjugacy, normal subgroups, quotient groups. Groups of matrices: examples (to include GL(n), O(n), and SO(n)), geometry of corresponding linear transformations, Euclidean isometries.

Overview

Module Objective:
To give a gentle introduction to groups.

Definitions and examples: the integers, the integers mod n, permutation groups, finite groups of symmetries (for example dihedral groups). Mappings: group homomorphisms and isomorphisms, kernel and image definitions, examples. Subgroups: examples, orders of elements and groups, Lagrange's Theorem. Conjugacy, normal subgroups, quotient groups. Groups of matrices: examples (to include GL(n), O(n), and SO(n)), geometry of corresponding linear transformations, Euclidean isometries.

	Learning Outcomes
	On successful completion of the module, students should be able to: State the axioms defining a group and any definitions or theorems given in the course. Decide whether given examples satisfy these definitions. Prove simple results using definitions and theorems given in the course. Perform calculations in a group theoretic setting. Give examples which illustrate concepts from the course. Use the methods from the course to solve problems. State definitions and theorems covered in the course.

Learning Outcomes

Teaching & Learning methods

Assessment

	Autumn Supplementals/Resits
	Are supplemental/resit registrations permitted? Yes Continuous assessment mark is carried forward to the Autumn. University scheduled written examination (Autumn): 120 minutes, On-campus

	Pre-Requisites
	MT212A/MT216C and MT311S or equivalent.

Timetable

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GROUPS

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