Programme/Approved Electives for 2022/23
Available as a Free Standing Elective
MAT-20025 Abstract Algebra
This module will introduce students to more advanced ideas in vector spaces and rings, building on the introduction to these mathematical structures at level 5. The module aims to broaden the scope of these ideas and to prepare students for more advanced study of these topics at Level 7.
Intended Learning Outcomes
recall the definition of a linear transformation and be able to prove and apply associated results, including the use of linear transformations to change between bases in a vector space: 1,3recall the definitions of eigenvalue and eigenvector of a linear transformation and apply these concepts to, inter alia, the diagonalisation of square matrices: 1,32,32,3define different types of ring, and state and prove associated results: 2,3recognise and define ideals and Euclidean domains, prove associated results and/or solve associated problems: define polynomial rings and solve associated problems:
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
Linear Algebra assignmentTake-home, written assignment. This 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%
Ring Theory CourseworkTake-home written coursework covering the Ring Theory part of the module. Students should expect to spend 5 hours on the assessment.3: Exam weighted 70%
Closed-book examinationThe 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.