## MA1LA-Linear Algebra

Module Provider: Mathematics and Statistics
Number of credits: 20 [10 ECTS credits]
Level:4
Terms in which taught: Autumn / Spring / Summer module
Pre-requisites:
Non-modular pre-requisites: Pre-req: A level Mathematics grade B or higher
Co-requisites: MA1CA Calculus
Modules excluded:
Current from: 2021/2

Module Convenor: Prof Paul Glaister

Type of module:

Summary module description:

This module introduces the mathematics of linearity needed for other modules, and includes various topics in linear algebra.

Aims:

To introduce the mathematics of linearity needed for other modules; taking as our starting point the need to be able to solve systems of linear equations we develop the algebra of matrices which we use as a stepping stone to the more general theory of linear and inner-product spaces.

Assessable learning outcomes:

By the end of the module the students are expected to be able to solve systems of linear equations, manipulate matrices and solve the eigenvalue problem in low dimensionality. The student will be able to use the concepts of linear space, linear independence, dimension and linear mapping, and inner product spaces to carry out appropriate calculations in a variety of contexts. Appropriate communication of mathematics.

Outline content:

Matrices feature in many areas of mathematics, particularly in applicable and numerical mathematics. The theory of matrices, their properties and application also play a key role in the sciences, engineering, social sciences, and computing. This module comprises both an introduction to matrix theory and its applications, and an introduction to the basic theory of vector spaces and linear transformations in a more abstract framework, which leads to simple, more transp arent proofs of many results and provides further tools to treat problems in mathematics, engineering and physics. Also, the abstract view of vector spaces is indispensable for infinite-dimensional spaces, which appear in other branches of mathematics (such as functional analysis and operator theory) and applications (such as the theory of differential equations and quantum physics).

Brief description of teaching and learning methods:

Lectures supported by problem sheets, practicals and tutorials.

Contact hours:
 Autumn Spring Summer Lectures 20 20 4 Tutorials 9 9 Guided independent study: 69 69 Total hours by term 98 98 4 Total hours for module 200

Summative Assessment Methods:
 Method Percentage Written exam 70 Set exercise 30

Summative assessment- Examinations:

3 hours.

Summative assessment- Coursework and in-class tests:

One examination and a number of assignments.

Formative assessment methods:

Problem sheets.

Penalties for late submission:

The Support Centres will apply the following penalties for work submitted late:

• where the piece of work is submitted after the original deadline (or any formally agreed extension to the deadline): 10% of the total marks available for that piece of work will be deducted from the mark for each working day (or part thereof) following the deadline up to a total of five working days;
• where the piece of work is submitted more than five working days after the original deadline (or any formally agreed extension to the deadline): a mark of zero will be recorded.
The University policy statement on penalties for late submission can be found at: http://www.reading.ac.uk/web/FILES/qualitysupport/penaltiesforlatesubmission.pdf
You are strongly advised to ensure that coursework is submitted by the relevant deadline. You should note that it is advisable to submit work in an unfinished state rather than to fail to submit any work.

Assessment requirements for a pass:

A mark of 40% overall.

Reassessment arrangements:

One examination paper of 3 hours duration in August/September - the resit module mark will be the higher of the exam mark (100% exam) and the exam mark plus previous coursework marks (70% exam, 30% coursework).