MA1008: Linear Algebra I
| School | Cardiff School of Mathematics |
| Department Code | MATHS |
| Module Code | MA1008 |
| External Subject Code | 100405 |
| Number of Credits | 10 |
| Level | L4 |
| Language of Delivery | English |
| Module Leader | Professor Roger Behrend |
| Semester | Autumn Semester |
| Academic Year | 2020/1 |
Outline Description of Module
Linear algebra is a foundation stone of modern mathematics. This module will introduce and study many of the fundamental structures of linear algebra, including vector spaces, subspaces, linear transformations, linear combinations, spanning sets, linearly independent sets and dimensionality. All of these concepts will be illustrated by numerous specific examples, thereby establishing a firm link between the abstract and the concrete. The module will end with the definition of a basis of a finite-dimensional vector space, and a proof of the result that every finite-dimensional vector space can be identified with a set of finite-tuples of scalars.
On completion of the module a student should be able to
- State and apply the vector space axioms.
- Define and understand the basic structures of linear algebra, including vector spaces, subspaces, linear transformations, linear combinations, spanning sets, linearly independent sets, dimensionality and bases.
- Understand and work with specific examples of vector spaces, including geometric vectors, tuples of scalars, matrices and functions.
How the module will be delivered
Modules will be delivered through blended learning. You will be guided through learning activities appropriate to your module, which may include:
- On-line resources that you work through at your own pace (e.g. videos, web resources, e-books, quizzes),
- On-line interactive sessions to work with other students and staff (e.g. discussions, live streaming of presentations, live-coding, group meetings)
- Face to face small group sessions (e.g. tutorials, exercise classes, feedback sessions)
Skills that will be practised and developed
Appreciation of the general prevalence and significance of linear algebra in mathematics. Ability to understand and apply the fundamental concepts of vector spaces.
Transferable Skills
Recognition of the power of mathematical abstraction and the importance of mathematical rigour. Critical thinking and problem solving skills. Ability to present work in a scholarly manner
Assessment Breakdown
| Type | % | Title | Duration(hrs) |
|---|---|---|---|
| Exam - Autumn Semester | 100 | Linear Algebra I | 2 |
Syllabus content
- Vectors in three dimensional space.
- Axioms of vector spaces (over the real numbers).
- Examples of vector spaces, including geometric vectors, tuples of real numbers, real matrices and real functions.
- General properties of vector spaces.
- Definition, properties and examples of subspaces.
- Definition, properties and examples of linear transformations.
- Definitions, properties and examples of the kernel and image of a linear transformation, and of isomorphisms.
- Definitions, properties and examples of linear combinations and spanning sets.
- Definitions, properties and examples of linearly dependent and linearly independent sets.
- Definitions, properties and examples of dimensionality and of bases of finite-dimensional vector spaces.
Essential Reading and Resource List
An interactive version of this list is now available via our new reading list software: https://whelf-cardiff.alma.exlibrisgroup.com/leganto/public/44WHELF_CAR/lists/6034754790002420?auth=SAML