Programme/Approved Electives for 2019/20
Available as a Free Standing Elective
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.
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 equivalence relations, binary operations, rings, fields and permutations: 1,2,31,2,31,2,3select and apply concepts of group theory to mathematical problems: 3state and prove theorems involving groups, rings and fields: synthesise theoretical material and concepts to solve problems:
Lectures: 36 hours Tutorials: 12 hoursPreparation for continuous assessment: 24 hoursIndependent study: 76 hoursUnseen Examination: 2 hours
1: Exercise weighted 10%
Description of Module Assessment
Take-home assignmentsTwo equally weighted take-home, written assignments. Each assignment consists of a set of questions with pre-allocated space for written solutions. The assignments are set at regular intervals across the semester. Students should expect to spend 12 hours across the semester on their assignments.¿2: Class Test weighted 20%
Two class tests.Two class tests to assess both theoretical and practical aspects of the module. The class tests are equally weighted. Each class test will last 40 minutes.3: Unseen Exam weighted 70%
2-hour unseen examinationThe examination paper will consist of no less than five and not more than eight questions all of which are compulsory.