LINEAR ALGEBRA - 2022/3

Module code: MAT1034

Module Overview

This module is an introduction to the theory and methods of Linear Algebra.

Module provider

Mathematics

WOLF Martin (Maths)

Number of Credits: 15

ECTS Credits: 7.5

Framework: FHEQ Level 4

JACs code: G130

Module cap (Maximum number of students): N/A

Independent Learning Hours: 95

Seminar Hours: 11

Guided Learning: 11

Captured Content: 33

Module Availability

Semester 2

Prerequisites / Co-requisites

MAT1031 Algebra

Module content

The module is divided into four main parts:

• Systems of linear equations: rank and nullity of matrices, elementary row operations and row-echelon form, Gaussian elimination, solubility of linear equations;

• Vector spaces: axiomatic development of vector spaces, linear independence of vectors, basis representations of vectors, change of basis, dimension, vector subspaces;

• Linear maps: basic properties of linear maps, rank-nullity theorem, matrix representation, Cayley-Hamilton theorem, eigenvalues and eigenvectors, eigenspaces, algebraic and geometric multiplicities, diagonalisation;

• Inner product spaces: inner products, norms, Cauchy-Schwarz inequality, orthogonality, orthogonal complement, Gram-Schmidt process, orthogonal and unitary changes of basis, isometries, self-adjoint operators.

Assessment pattern

Assessment type Unit of assessment Weighting
Online Scheduled Summative Class Test ONLINE TEST 25
Examination Online ONLINE EXAM 75

Alternative Assessment

None.

Assessment Strategy

The assessment strategy is designed to provide students with the opportunity to demonstrate:

That they have learnt the basic material in the field, and are able to apply it to examples and problems.

The summative assessment for this module consists of:

·         In-Semester Test that constitutes 25% of the final mark;

·         Final Examination that constitutes 75% of the final mark.

Formative assessment and feedback:

Students receive written feedback via a number of marked coursework assignments over an 11 week period. Additional verbal feedback will be provided by the lecturer or a tutor at fortnightly seminars.

Module aims

• The aim of this module is to extend students' knowledge of matrices, vectors and systems of linear equations and to introduce the abstract concepts of vector spaces, linear maps and inner products.

Learning outcomes

Attributes Developed
001 Students should develop an understanding of the concepts of linear algebra, and master the basic tools needed for the qualitative and quantitative description. In particular, at the end of the module the student should be able to demonstrate a proper understanding of KCT
002 Whether systems of linear equations are soluble and be able to solve such systems by means of the Gaussian elimination; KC
003 The concepts of vector spaces and vector subspaces; KC
004 Linear (in-)dependence of vectors, basis representations of vectors, and changes of basis; KC
005 The concepts of linear maps, their matrix representations, eigenvalues and eigenvectors, and carry out matrix diagonalisation; KC
006 The concepts of inner products, norms, and orthogonality and be able to orthogonalise vectors by means of the Gram-Schmidt procedure; KC
007 The concept of orthogonal and unitary changes of basis; KC
008 The concept of self-adjoint operators; KC
009 Simple proofs similar to those covered in the module. KCT

Attributes Developed

C - Cognitive/analytical

K - Subject knowledge

T - Transferable skills

P - Professional/Practical skills

Methods of Teaching / Learning

The learning and teaching strategy is designed to provide:

• A detailed introduction to linear algebra and its application in other areas

• Experience (through demonstration) of the methods used to interpret, understand and solve problems in linear algebra

The learning and teaching methods include:

• 4 x 1 hour lectures per week x 11 weeks, with lecture notes provided;

• (every second week) 1 x 1 hour seminar for guided discussion of solutions to problem sheets provided to and worked on by students in advance.

Indicated Lecture Hours (which may also include seminars, tutorials, workshops and other contact time) are approximate and may include in-class tests where one or more of these are an assessment on the module. In-class tests are scheduled/organised separately to taught content and will be published on to student personal timetables, where they apply to taken modules, as soon as they are finalised by central administration. This will usually be after the initial publication of the teaching timetable for the relevant semester.

Upon accessing the reading list, please search for the module using the module code: MAT1034

Programmes this module appears in

Programme Semester Classification Qualifying conditions
Mathematics MMath 2 Compulsory A weighted aggregate mark of 40% is required to pass the module
Mathematics with Statistics MMath 2 Compulsory A weighted aggregate mark of 40% is required to pass the module
Mathematics with Statistics BSc (Hons) 2 Compulsory A weighted aggregate mark of 40% is required to pass the module
Mathematics BSc (Hons) 2 Compulsory A weighted aggregate mark of 40% is required to pass the module
Financial Mathematics BSc (Hons) 2 Compulsory A weighted aggregate mark of 40% is required to pass the module
Mathematics with Music BSc (Hons) 2 Compulsory A weighted aggregate mark of 40% is required to pass the module
Mathematics and Physics BSc (Hons) 2 Compulsory A weighted aggregate mark of 40% is required to pass the module
Mathematics and Physics MPhys 2 Compulsory A weighted aggregate mark of 40% is required to pass the module
Mathematics and Physics MMath 2 Compulsory A weighted aggregate mark of 40% is required to pass the module
Economics and Mathematics BSc (Hons) 2 Compulsory A weighted aggregate of 40% overall and a pass on the pass/fail unit of assessment is required to pass the module

Please note that the information detailed within this record is accurate at the time of publishing and may be subject to change. This record contains information for the most up to date version of the programme / module for the 2022/3 academic year.