### MAS2223 : Linear Algebra

• Offered for Year: 2015/16
• Module Leader(s): Dr Martina Balagovic
• Owning School: Mathematics & Statistics
##### Semesters
 Semester 1 Credit Value: 10 ECTS Credits: 5.0
##### Pre Requisites
Code Title
MAS1041Mathematical Methods A
MAS1042Mathematical Methods B
MAS1241Number Systems
MAS1242The Foundations of Analysis

N/A

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#### Aims

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.

Module summary:
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.

#### Outline Of Syllabus

Sets and maps, vector spaces, span and bases, linear maps, eigenvectors and eigenvalues, inner product spaces, change of basis, diagonalisation.

#### Learning Outcomes

##### Intended Knowledge Outcomes

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.

##### Intended Skill Outcomes

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.

• Cognitive/Intellectual Skills
• Numeracy : Assessed
• Self Management
• Personal Enterprise
• Problem Solving : Assessed
• Interaction
• Communication
• Written Other : Assessed

#### Teaching Methods

##### Teaching Activities
Category Activity Number Length Student Hours Comment
Scheduled Learning And Teaching ActivitiesLecture221:0022:00Formal lectures
Scheduled Learning And Teaching ActivitiesLecture21:002:00Revision lectures
Scheduled Learning And Teaching ActivitiesLecture61:006:00Problem classes
Guided Independent StudyAssessment preparation and completion111:0011:00Revision for Unseen Exam
Guided Independent StudyAssessment preparation and completion11:301:30Unseen Exam
Scheduled Learning And Teaching ActivitiesDrop-in/surgery61:006:00Drop-ins in the lecture room
Guided Independent StudyIndependent study121:3021:30Studying, practising and gaining understanding of course material
Guided Independent StudyIndependent study55:0025:00Written assignments and CBAs
Guided Independent StudyIndependent study51:005:00Assignment review
Total100:00
##### Jointly Taught With
Code Title
MAS3223Linear Algebra
##### Teaching Rationale And Relationship

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 studentsâ€™ 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.

#### Assessment Methods

The format of resits will be determined by the Board of Examiners

##### Exams
Description Length Semester When Set Percentage Comment
Written Examination901A90unseen
##### Exam Pairings
Module Code Module Title Semester Comment
MAS3223Linear Algebra1N/A
##### Other Assessment
Description Semester When Set Percentage Comment
Prob solv exercises1M10Written assignments and computer based assessments
##### Assessment Rationale And Relationship

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.

#### General Notes

N/A

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.