|Semester 1 Credit Value:||10|
|MAS1041||Mathematical Methods A|
|MAS1042||Mathematical Methods B|
|MAS1242||The Foundations of Analysis|
The module aims to provide students with an introduction to modern abstract linear algebra. Building on their existing knowledge of matrix methods, students will experience the benefits of an abstract and rigorous mathematical theory for the deeper understanding of a mathematical subject.
Linear algebra is a fundamental subject that pervades many areas of modern mathematics. On the one hand it is often convenient to replace a complicated problem by a linear approximation which is easier to solve. On the other hand, linear algebra has beautiful applications in coding theory, projective geometry, and many other areas of mathematics and statistics.
Initially linear algebra aims to solve systems of linear equations. In the first year courses this led naturally to matrix algebra. In MAS2223/3223 abstraction and generalisation are pushed one level further with the formal introduction of vector spaces and linear maps as a replacement for real n-dimensional space and matrices, respectively. This allows us to consider analogous problems in different settings simultaneously and eventually makes explanations easier and faster. We will need to introduce notions of dimension and basis in this general setting. A guiding question is how to transform matrices (or linear maps) to a simple form in which essential properties can be immediately read off.
Sets and maps, vector spaces, span and bases, linear maps, eigenvectors and eigenvalues, inner product spaces, change of basis, diagonalisation.
Upon successful completion of MAS2223 students will be able to demonstrate a reasonable understanding of abstract linear algebra. They will be able to reproduce definitions of elementary notions of linear algebra such as vector space, linear map, basis, dimension, inner product space.
Upon successful completion of MAS2223 students should have a reasonable grasp of the following skills:
i) Perform elementary mathematical arguments with the above notions (see knowledge outcomes).
ii) Calculate the dimension and find a basis for various vector spaces.
iii) Write down matrices representing linear maps.
iv) Identify kernel and image of linear maps.
v) Perform Gram-Schmidt orthonormalisation in explicit examples.
vi) Diagonalise matrices.
|Graduate Skills Framework Applicable:||Yes|
|Guided Independent Study||Assessment preparation and completion||1||1:30||1:30||Unseen Exam|
|Scheduled Learning And Teaching Activities||Lecture||22||1:00||22:00||Formal lectures|
|Scheduled Learning And Teaching Activities||Lecture||2||1:00||2:00||Revision lectures|
|Scheduled Learning And Teaching Activities||Lecture||6||1:00||6:00||Problem classes|
|Guided Independent Study||Assessment preparation and completion||1||11:00||11:00||Revision for Unseen Exam|
|Scheduled Learning And Teaching Activities||Drop-in/surgery||6||1:00||6:00||Drop-ins in the lecture room|
|Guided Independent Study||Independent study||1||21:30||21:30||Studying, practising and gaining understanding of course material|
|Guided Independent Study||Independent study||5||5:00||25:00||Written assignments and CBAs|
|Guided Independent Study||Independent study||5||1:00||5:00||Assignment review|
Lectures are used for the delivery of theory and explanation of methods, illustrated with examples, and for giving general feedback on marked work. Problem Classes are used to help develop the students’ abilities at applying the theory to solving problems. Drop-ins are used to identify and resolve specific queries raised by students and to allow students to receive individual feedback on marked work. Office hours provide an opportunity for more direct contact between individual students and the lecturer.
The format of resits will be determined by the Board of Examiners
|Module Code||Module Title||Semester||Comment|
|Prob solv exercises||1||M||10||Written assignments and computer based assessments|
A substantial formal unseen examination is appropriate for the assessment of the material in this module. Coursework assignments (approximately 5 assignments of approximately equal weight) allow the students to develop their problem solving techniques, to practise the methods learnt in the module, to assess their progress and to receive feedback; this is thus formative as well as summative assessment. The coursework assignments may be written assignments, computer based assessments or a combination of the two, and in the case of combined assessments the deadlines for the two parts will not necessarily be the same.
Note: The Module Catalogue now reflects module information relating to academic year 15/16. Please contact your School Office if you require module information for a previous academic year.
Disclaimer: The University will use all reasonable endeavours to deliver modules in accordance with the descriptions set out in this catalogue. Every effort has been made to ensure the accuracy of the information, however, the University reserves the right to introduce changes to the information given including the addition, withdrawal or restructuring of modules if it considers such action to be necessary.