| Academic Year: | 2022/23 |
| Owning Department/School: | Department of Mathematical Sciences |
| Credits: | 6 [equivalent to 12 CATS credits] |
| Notional Study Hours: | 120 |
| Level: | Certificate (FHEQ level 4) |
| Period: |
- Semester 2
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| Assessment Summary: | EX 100% |
| Assessment Detail: | |
| Supplementary Assessment: |
- Like-for-like reassessment (where allowed by programme regulations)
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| Requisites: |
Before taking this module you must take MA10209
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| Learning Outcomes:
| After taking this unit the students should be able to:
* Demonstrate understanding of basic concepts of linear algebra, e.g. bases, dimension, rank ,orthogonality, diagonalisation, and apply them in specific examples.
* Perform computations e.g. of determinants, matrix inverses, orthonormal bases, eigenvalues and eigenvectors.
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| Aims: | To provide a firm grounding in linear algebra, both via matrices and via vector spaces and linear maps, focussing on the most widely applicable aspects.
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| Skills: | Numeracy T/F A
Problem Solving T/F A
Written and Spoken Communication F (in tutorials).
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| Content: | Vector spaces (over the rational, real, and complex numbers), linear maps, subspaces, kernel and image.
Linear independence, spans, bases and dimension
Matrix of a linear map, change of basis, linear operators, similar matrices. Rank, nullity and the Rank-Nullity Theorem
Inner product spaces: orthogonality, Cauchy-Schwarz inequality and applications.
Gram-Schmidt process: orthonormal bases, orthogonal matrices and QR decomposition, orthogonal subspaces.
Determinants and adjugates: properties and computation; invertibility of matrices.
Eigenvalues, eigenvectors and eigenspaces; characteristic polynomial, algebraic and geometric multiplicities, diagonalisability.
Self-adjoint operators, symmetric/hermitian matrices and their orthogonal diagonalisation.
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| Programme availability: |
MA10210 is Compulsory on the following programmes:
Department of Computer Science
- USCM-AFB20 : BSc(Hons) Computer Science and Mathematics (Year 1)
- USCM-AAB20 : BSc(Hons) Computer Science and Mathematics with Study year abroad (Year 1)
- USCM-AKB20 : BSc(Hons) Computer Science and Mathematics with Year long work placement (Year 1)
- USCM-AFM14 : MComp(Hons) Computer Science and Mathematics (Year 1)
- USCM-AAM14 : MComp(Hons) Computer Science and Mathematics with Study year abroad (Year 1)
- USCM-AKM14 : MComp(Hons) Computer Science and Mathematics with Year long work placement (Year 1)
Department of Economics
- UHES-AFB04 : BSc(Hons) Economics and Mathematics (Year 1)
- UHES-AAB04 : BSc(Hons) Economics and Mathematics with Study year abroad (Year 1)
- UHES-AKB04 : BSc(Hons) Economics and Mathematics with Year long work placement (Year 1)
- UHES-ACB04 : BSc(Hons) Economics and Mathematics with Combined Placement and Study Abroad (Year 1)
Department of Mathematical Sciences
- USMA-AFB15 : BSc(Hons) Mathematical Sciences (Year 1)
- USMA-AAB16 : BSc(Hons) Mathematical Sciences with Study year abroad (Year 1)
- USMA-AKB16 : BSc(Hons) Mathematical Sciences with Year long work placement (Year 1)
- USMA-AFB13 : BSc(Hons) Mathematics (Year 1)
- USMA-AAB14 : BSc(Hons) Mathematics with Study year abroad (Year 1)
- USMA-AKB14 : BSc(Hons) Mathematics with Year long work placement (Year 1)
- USMA-AFB01 : BSc(Hons) Mathematics and Statistics (Year 1)
- USMA-AAB02 : BSc(Hons) Mathematics and Statistics with Study year abroad (Year 1)
- USMA-AKB02 : BSc(Hons) Mathematics and Statistics with Year long work placement (Year 1)
- USMA-AFB20 : BSc(Hons) Mathematics, Statistics, and Data Science (Year 1)
- USMA-AAB20 : BSc(Hons) Mathematics, Statistics, and Data Science with Study year abroad (Year 1)
- USMA-AKB20 : BSc(Hons) Mathematics, Statistics, and Data Science with Industrial Placement (Year 1)
- USMA-AFM14 : MMath(Hons) Mathematics (Year 1)
- USMA-AAM15 : MMath(Hons) Mathematics with Study year abroad (Year 1)
- USMA-AKM15 : MMath(Hons) Mathematics with Year long work placement (Year 1)
Department of Physics
- USXX-AFB03 : BSc(Hons) Mathematics and Physics (Year 1)
- USXX-AAB04 : BSc(Hons) Mathematics and Physics with Study year abroad (Year 1)
- USXX-AKB04 : BSc(Hons) Mathematics and Physics with Year long work placement (Year 1)
- USXX-AFM01 : MSci(Hons) Mathematics and Physics (Year 1)
- USXX-AAM01 : MSci(Hons) Mathematics and Physics with Study year abroad (Year 1)
- USXX-AKM01 : MSci(Hons) Mathematics and Physics with Year long work placement (Year 1)
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