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Session: 2022/23
Last modified: 10/01/2023 11:04:47
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Title of Module: Linear Algebra |
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Code: MATH08007 |
SCQF Level: 8
(Scottish Credit and Qualifications Framework) |
Credit Points: 20 |
ECTS: 10
(European Credit Transfer Scheme) |
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| School: | School of Computing, Engineering and Physical Sciences |
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| Module Co-ordinator: | Wan
Mekwi |
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| Summary of Module |
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This module extends the material on matrices and vectors covered in Mathematics of Space & Change and Mathematics of Space & Change 2.
Properties of square matrices of higher order than 2x2 are covered in detail. This includes a treatment of determinants and their properties, and of their inverses, including a discussion on such topics as adjoint matrices and Cramer’s rule. The concepts of eigenvalues and eigenvectors are consolidated in this higher order setting, and extended to a wider range of problems including diagonalisation.
The concept of a vector space is introduced, and then developed to include discussion of subspaces, spanning sets, linear independence and basis and dimension.
Linear transformations are discussed, including matrix representation of these and problems involving a change of basis. Fundamental ideas such as kernel, image rank and nullity of these transformations are discussed, as is the Dimension Theorem.
The concept of an inner product space is introduced, and then developed to extend the familiar notion of perpendicular vectors to the more general orthogonality. Such processes as Gram-Schmidt orthogonalisation are discussed.
The Graduate Attributes relevant to this module are given below:
- Academic: Critical thinker; Analytical; Inquiring; Knowledgeable; Problem-solver; Autonomous.
- Personal: Motivated; Resilient
- Professional: Ambitious; Driven.
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| Module Delivery Method |
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| Face-To-Face | Blended | Fully Online | HybridC | HybridO | Work-based Learning |
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Face-To-Face
Term used to describe the traditional classroom environment where the students and the lecturer meet synchronously in the same room for the whole provision.
Blended
A mode of delivery of a module or a programme that involves online and face-to-face delivery of learning, teaching and assessment activities, student support and feedback. A programme may be considered “blended” if it includes a combination of face-to-face, online and blended modules. If an online programme has any compulsory face-to-face and campus elements it must be described as blended with clearly articulated delivery information to manage student expectations
Fully Online
Instruction that is solely delivered by web-based or internet-based technologies. This term is used to describe the previously used terms distance learning and e learning.
HybridC
Online with mandatory face-to-face learning on Campus
HybridO
Online with optional face-to-face learning on Campus
Work-based Learning
Learning activities where the main location for the learning experience is in the workplace.
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| Term(s) for Module Delivery |
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(Provided viable student numbers permit).
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| Term 1 | | Term 2 | | Term 3 | |
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| Learning Outcomes: (maximum of 5 statements) |
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On successful completion of this module the student will be able to:
L1.
Determine key features of square matrices of higher order than 2x2, and use them in the solution of a range of problems.
L2.
Use a range of standard techniques in problems involving vector spaces and their applications.
L3.
Apply a range of standard techniques in problems involving inner product spaces and Gram-Schmidt orthogonalisation.
L4.
Solve a range of problems that require the use of linear transformations and their associated properties. |
| Employability Skills and Personal Development Planning (PDP) Skills |
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| SCQF Headings |
During completion of this module, there will be an opportunity to achieve
core skills in:
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| Knowledge and Understanding (K and U) |
SCQF Level 8.
Demonstrating a knowledge and understanding of a range of important mathematical constructs in linear algebra. |
| Practice: Applied Knowledge and Understanding |
SCQF Level 8.
Using a range of standard techniques to solve problems, in a range of contexts. |
| Generic Cognitive skills |
SCQF Level 8.
Conceptualising and analysing problems with the aid of appropriate concepts. |
| Communication, ICT and Numeracy Skills |
SCQF Level 8.
Making formal written presentation(s) based on the output from an investigative problem. |
| Autonomy, Accountability and Working with others |
SCQF Level 8.
Exercising independence and initiative in carrying out a range of activities.
Identifying learning needs through reflection based on self, tutor and peer evaluation of work.
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| Pre-requisites: |
Before undertaking this module the student should have
undertaken the following:
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Module Code:
MATH07009
| Module Title:
Mathematics of Space & Change 2
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| Other: | or equivalent |
| Co-requisites | Module Code:
| Module Title:
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* Indicates that module descriptor is not published.
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| Learning and Teaching |
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Learning Activities
During completion of this module, the learning activities undertaken to
achieve the module learning outcomes are stated below:
| Student Learning Hours
(Normally totalling 200 hours):
(Note: Learning hours include both contact hours and hours spent on other learning activities) |
| Lecture/Core Content Delivery | 36 |
| Independent Study | 164 |
| 200
Hours Total
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**Indicative Resources: (eg. Core text, journals, internet
access)
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The following materials form essential underpinning for the module content
and ultimately for the learning outcomes:
“Linear Algebra” class notes as published on the University VLE.
"Linear Algebra: A Modern Introduction", D Poole.
"Linear Algebra and Geometry", D Smart.
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(**N.B. Although reading lists should include current publications,
students are advised (particularly for material marked with an asterisk*) to
wait until the start of session for confirmation of the most up-to-date
material)
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| Engagement Requirements |
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In line with the Academic Engagement Procedure, Students are defined as academically engaged if they are regularly engaged with timetabled teaching sessions, course-related learning resources including those in the Library and on the relevant learning platform, and complete assessments and submit these on time. Please refer to the Academic Engagement Procedure at the following link: Academic engagement procedure |
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Supplemental Information
| Programme Board | Physical Sciences |
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| Assessment Results (Pass/Fail) |
No
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| Subject Panel | Physical Sciences |
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| Moderator | Laura Stewart |
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| External Examiner | P Wilson |
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| Accreditation Details | |
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| Version Number | 1.07 |
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| Assessment: (also refer to Assessment Outcomes Grids below) |
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| A series of coursework assignments; 50% of the final mark |
| A final, closed book examination, 50% of the final mark |
(N.B. (i) Assessment Outcomes Grids for the module
(one for each component) can be found below which clearly demonstrate how the learning outcomes of the module
will be assessed.
(ii) An indicative schedule listing approximate times
within the academic calendar when assessment is likely to feature will be
provided within the Student Handbook.)
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Assessment Outcome Grids (Footnote A.)
Footnotes
A. Referred to within Assessment Section above
B. Identified in the Learning Outcome Section above
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Note(s):
- More than one assessment method can be used to assess individual learning outcomes.
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Schools are responsible for determining student contact hours. Please refer to University Policy on contact hours (extract contained within section 10 of the Module Descriptor guidance note).
This will normally be variable across Schools, dependent on Programmes &/or Professional requirements.
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| Equality and Diversity |
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The module is suitable for any student satisfying the pre-requisites.
UWS Equality and Diversity Policy |
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(N.B. Every effort
will be made by the University to accommodate any equality and diversity issues
brought to the attention of the School)
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