MA1LA: Linear Algebra

Module code: MA1LA

Module provider: Mathematics and Statistics; School of Mathematical, Physical and Computational Sciences

Credits: 20

Level: Level 1 (Certificate)

When you'll be taught: Semester 2

Module convenor: Professor Paul Glaister, email: p.glaister@reading.ac.uk

Module co-convenor: Dr Peter Chamberlain, email: p.g.chamberlain@reading.ac.uk

Pre-requisite module(s): Before taking this module, you must have at least a grade B in A-Level Mathematics grade B, or equivalent. (Open)

Co-requisite module(s):

Pre-requisite or Co-requisite module(s):

Module(s) excluded:

Placement information: NA

Academic year: 2024/5

Available to visiting students: Yes

Talis reading list: Yes

Last updated: 21 May 2024

Overview

Module aims and purpose

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 and determine eigenvalues and eigenvectors we develop the algebra of matrices which we use as a stepping stone to the more general theory of linear spaces. 

Module learning outcomes

By the end of the module, it is expected that students will be able to: 

1. Perform operations in matrix algebra. 
2. Prove statements in matrix algebra. 
3. Determine inverses, determinants, the solution of linear equations, eigenvalues and eigenvectors. 
4. Use the concepts of linear space, linear independence, dimension and linear mapping, to carry out appropriate calculations in a variety of contexts. 

Module 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 transparent proofs of many results and provides further tools to treat problems in mathematics, engineering and physics. 

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). 

Structure

Teaching and learning methods

Lectures supported by problem sheets, and tutorials. 

Study hours

At least 54 hours of scheduled teaching and learning activities will be delivered in person, with the remaining hours for scheduled and self-scheduled teaching and learning activities delivered either in person or online. You will receive further details about how these hours will be delivered before the start of the module.

Please note the independent study hours above are notional numbers of hours; each student will approach studying in different ways. We would advise you to reflect on your learning and the number of hours you are allocating to these tasks.

Semester 1 The hours in this column may include hours during the Christmas holiday period.

Semester 2 The hours in this column may include hours during the Easter holiday period.

Summer The hours in this column will take place during the summer holidays and may be at the start and/or end of the module.

Assessment

Requirements for a pass

Students need to achieve an overall module mark of 40% to pass this module.

Summative assessment

Penalties for late submission of summative assessment

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

Assessments with numerical marks

• 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 three working days;
• the mark awarded due to the imposition of the penalty shall not fall below the threshold pass mark, namely 40% in the case of modules at Levels 4-6 (i.e. undergraduate modules for Parts 1-3) and 50% in the case of Level 7 modules offered as part of an Integrated Masters or taught postgraduate degree programme;
• where the piece of work is awarded a mark below the threshold pass mark prior to any penalty being imposed, and is submitted up to three working days after the original deadline (or any formally agreed extension to the deadline), no penalty shall be imposed;
• where the piece of work is submitted more than three working days after the original deadline (or any formally agreed extension to the deadline): a mark of zero will be recorded.

Assessments marked Pass/Fail

• where the piece of work is submitted within three working days of the deadline (or any formally agreed extension of the deadline): no penalty will be applied;
• where the piece of work is submitted more than three working days after the original deadline (or any formally agreed extension of the deadline): a grade of Fail will be awarded.

The University policy statement on penalties for late submission can be found at: https://www.reading.ac.uk/cqsd/-/media/project/functions/cqsd/documents/qap/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.

Formative assessment

Formative assessment is any task or activity which creates feedback (or feedforward) for you about your learning, but which does not contribute towards your overall module mark.

Reassessment

Additional costs