MAT-20025 - Abstract Algebra
Coordinator: Raymond N Turner Room: MAC2.27 Tel: +44 1782 7 33739
Lecture Time: See Timetable...
Level: Level 5
Credits: 15
Study Hours: 150
School Office: 01782 733075

Programme/Approved Electives for 2021/22

None

Available as a Free Standing Elective

No

Co-requisites

None

Prerequisites

MAT-10047 Algebra

Barred Combinations

None

Description for 2021/22

This module introduces and studies the abstract algebraic structure known as a group. Starting with the axiomatic and theoretical foundations, the module progresses, through a study of subgroups, to the proof of one of the most important theorems in Group Theory, Lagrange's Theorem. The module also examines applications of group theory, and the often beautiful way in which it interacts with geometry and number theory. It concludes with a preliminary exploration of other, closely related algebraic structures, namely rings and fields.
This module provides develops material required for a large number of Level 6 options.

Aims
The module aims to provide students with their first rigorous treatment of group theory as an axiomatic system, as well as exploring applications to geometry and number theory. It also aims to expose students, at an introductory level, to other algebraic structures such as rings and fields.

Intended Learning Outcomes

define and identify abstract algebraic structures and concepts including, binary operations, groups, rings, fields and permutations: 1,3
1,2,3
2,3
select and apply concepts of group theory to mathematical problems: 2,3
state and prove theorems involving groups, rings and fields: synthesise theoretical material and concepts to solve problems:

Study hours

Learning and teaching comprise video lectures at 30 hours, and flipped examples classes at 5 hours.
Independent study hours comprise preparation for examples classes at 20 hours, preparation for and completion of the continuous assessment at 15 hours, consolidation of lecture material at 58 hours, examination preparation at 20 hours, and final examination at 2 hours.

School Rules

None

Description of Module Assessment

1: Assignment weighted 15%
Take-home assignment
One take-home, written assignment. This assignment consists of a set of questions with pre-allocated space for written solutions. Students should expect to spend 5 hours on the assessment.

2: Coursework weighted 15%
Take-home coursework
One take-home, written coursework. This consists of a set of questions with pre-allocated space for written solutions. Students should expect to spend 5 hours on the assessment.

3: Exam weighted 70%
Closed book 2 hour examination
The examination paper will consist of no less than five and not more than eight questions all of which are compulsory.