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:
Module version for: 2017/8

Module Convenor: Dr Calvin Smith

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 the space of vector, matrices and function.  Appropriate communication of mathematics.

Outline content:

Linear algebra is the study of vector spaces and linear mappings. Our approach will be to blend both the practical examples of the subject with the abstract theory (where the general structure is more easily illustrated). Examples will be drawn from a variety of applications. The module will introduce the concept of a linear space and show how this structure provides a framework for studying vectors, matrices and functions. The focus of the module will be on the consequences of the linear space structure; this is an elegant approach which influences many other branches of mathematics. Elementary properties of inner product spaces will be introduced and discussed.

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 10 Guided independent study 69 68 Total hours by term 98.00 98.00 4.00 Total hours for module 200.00

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

Other information on summative assessment:
A number of assignments and one examination.

Formative assessment methods:

Problem sheets.

Penalties for late submission:
The Module Convenor will apply the following penalties for work submitted late, in accordance with the University policy.

• where the piece of work is submitted up to one calendar week after the original deadline (or any formally agreed extension to the deadline): 10% of the total marks available for the 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.

Length of examination:

3 hours.

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).