Linear Algebra

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 vector 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 vector space, linear independence, dimension and linear mapping, and inner product spaces to carry out appropriate calculations.

Additional outcomes:
The student will gain familiarity with various mathematical software packages, such as Maple and MatLab.

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 and the student will be given the opportuniy to utilise appropriate software to illustrate key aspects of the theory. The module will begin with a discussion of matrix algebra before introducing the concept of a vector space which is used to place previous results within the context of the broader theory and show applications in other areas. The focus of the module will be on the consequences of the vector 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 and tutorials.

Summative Assessment Methods:
Written exam 70%
Set exercise 30%

Other information on summative assessment:
Three pieces of assessed work and one examination

Formative assessment methods:
Problem sheets

Penalties for late submission:
The Module Convener 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