Programme/Approved Electives for 2022/23
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: 1,3derive Burnside┐s Lemma and use it in counting configurations: 1,3demonstrate knowledge of group homomorphisms and the role of homomorphism as a unifying principle in Group Theory: 2,3derive and apply the First Isomorphism Theorem: 2,3demonstrate knowledge of conjugates, centralisers, the Class Equation and Sylow┐s theorems: 2,3derive and apply Sylow┐s First Theorem: 2,3
Learning/teaching comprises 30 hours video lectures, and 5 hours flipped examples classes. Independent study comprises 30 hours examples class preparation, 10 hours for completion of assignment, 20 hours preparation for examination, 53 hours consolidation of lecture material, and 2 hours final exam.
1: Assignment weighted 15%
Description of Module Assessment
Take-home assignmentWritten assignment. The 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 CourseworkWritten 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%
2 HOUR CLOSED 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 closed book.