Programme/Approved Electives for 2021/22
Available as a Free Standing Elective
MAT-20025: Abstract Algebra
This module builds on the Group Theory introduced in MAT - 20025 to develop some of the mathematics underlying the classification of finite groups. This culminates in a proof of Sylow's First Theorem which offers a partial converse to Lagrange's Theorem proved in MAT - 20025. The module also develops some applications of Group Theory, the natural setting for which is that of group actions. Several examples of applying group theoretic ideas to counting combinatorial configurations are presented.
The aim of this module is to develop some of the mathematics underlying the classification of finite groups and to develop some applications of Group Theory.
Intended Learning Outcomes
demonstrate knowledge of basic concepts such as abelian groups, normal subgroups, quotient groups and group actions: 1,2derive Burnside┐s Lemma and use it in counting configurations: 1,2demonstrate knowledge of group homomorphisms and the role of homomorphism as a unifying principle in Group Theory: 2derive and apply the First Isomorphism Theorem: 2demonstrate knowledge of conjugates, centralisers, the Class Equation and Sylow┐s theorems: 2derive and apply Sylow┐s First Theorem: 2
Learning/teaching comprises 30 hours video lectures, 5 hours flipped examples classes, and 2 hours final exam.Independent study comprises 30 hours examples class preparation, 10 hours for completion of assignment, 20 hours preparation for examination, and 53 hours consolidation of lecture material.
1: Assignment weighted 20%
Description of Module Assessment
Online, take-home assignmentOne take-home, written assignments to be completed on-line. The assignment consists of a set of questions with pre-allocated space for written solutions which will be uploaded to the KLE. Students should expect to spend 10 hours on the assessment.2: Open Book Examination weighted 80%
2 HOUR OPEN BOOK EXAMThe examination paper will consist of no less than five and not more than eight questions all of which are compulsory. The examination will be online and open book.