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MAT-30045 - Module Specification
School of Computing and Mathematics
Faculty of Natural Sciences

For academic year: 2021/22 Last Updated: 16 February 2022

MAT-30045 - Linear Algebra and Rings
Coordinator: Raymond N Turner Room: MAC2.27 Tel: +44 1782 7 33739
Lecture Time: See Timetable...
Level: Level 6
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-20025 Abstract Algebra

Barred Combinations

None

Description for 2021/22

The module builds on the knowledge of vector spaces and rings gained from second year Abstract Algebra and Exploring Algebra and Analysis. Concepts such as linear independence, span basis are generalised from Euclidean space to other vector spaces, such as function spaces, in such a way that seemingly disparate results from different branches of mathematics are sometimes just different specialisations of the same general concept. The module also studies some of the properties of an algebraic object called a ring, again concentrating on generalisations and structure as in the case of vector spaces.

Aims
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: 1,3
recall the definitions of eigenvalue and eigenvector of a linear transformation and apply these concepts to, inter alia, the diagonalisation of square matrices: 1,3
2,3
2,3
define different types of ring, and state and prove associated results: 2,3
recognise and define ideals and Euclidean domains, prove associated results and/or solve associated problems: define polynomial rings and solve associated problems:

Study hours

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.

School Rules

None

Description of Module Assessment

1: Assignment weighted 15%
Linear Algebra assignment
Take-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 Coursework
Take-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 examination
The 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.

Please note that for the 2021/22 Academic Year all programmes will be adapted to operate in accordance with a flexible, digital approach. This means that there will be some changes made to how modules are delivered and assessed. The latest information will be provided to you by your School in module handbooks. We endeavour to give you as much notice as possible of any changes and details about the circumstance in which changes are made to programmes can be found in the Student Agreement, available at: https://www.keele.ac.uk/student-terms-and-conditions/

Last Updated: 16 February 2022