Academic Year:  2021/2 
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

Assessment Summary:  EX 100% 
Assessment Detail:  
Supplementary Assessment: 
 Likeforlike reassessment (where allowed by programme regulations)

Requisites: 
Before taking this module you must take MA10209

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.

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.

Skills:  Numeracy T/F A
Problem Solving T/F A
Written and Spoken Communication F (in tutorials).

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 RankNullity Theorem
Inner product spaces: orthogonality, CauchySchwarz inequality and applications.
GramSchmidt 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.
Selfadjoint operators, symmetric/hermitian matrices and their orthogonal diagonalisation.

Programme availability: 
MA10210 is Compulsory on the following programmes:
Department of Computer Science
 USCMAFB20 : BSc(Hons) Computer Science and Mathematics (Year 1)
 USCMAAB20 : BSc(Hons) Computer Science and Mathematics with Study year abroad (Year 1)
 USCMAKB20 : BSc(Hons) Computer Science and Mathematics with Year long work placement (Year 1)
 USCMAFM14 : MComp(Hons) Computer Science and Mathematics (Year 1)
 USCMAAM14 : MComp(Hons) Computer Science and Mathematics with Study year abroad (Year 1)
 USCMAKM14 : MComp(Hons) Computer Science and Mathematics with Year long work placement (Year 1)
Department of Economics
 UHESAFB04 : BSc(Hons) Economics and Mathematics (Year 1)
 UHESAAB04 : BSc(Hons) Economics and Mathematics with Study year abroad (Year 1)
 UHESAKB04 : BSc(Hons) Economics and Mathematics with Year long work placement (Year 1)
 UHESACB04 : BSc(Hons) Economics and Mathematics with Combined Placement and Study Abroad (Year 1)
Department of Mathematical Sciences
 USMAAFB15 : BSc(Hons) Mathematical Sciences (Year 1)
 USMAAAB16 : BSc(Hons) Mathematical Sciences with Study year abroad (Year 1)
 USMAAKB16 : BSc(Hons) Mathematical Sciences with Year long work placement (Year 1)
 USMAAFB13 : BSc(Hons) Mathematics (Year 1)
 USMAAAB14 : BSc(Hons) Mathematics with Study year abroad (Year 1)
 USMAAKB14 : BSc(Hons) Mathematics with Year long work placement (Year 1)
 USMAAFB01 : BSc(Hons) Mathematics and Statistics (Year 1)
 USMAAAB02 : BSc(Hons) Mathematics and Statistics with Study year abroad (Year 1)
 USMAAKB02 : BSc(Hons) Mathematics and Statistics with Year long work placement (Year 1)
 USMAAFB20 : BSc(Hons) Mathematics, Statistics, and Data Science (Year 1)
 USMAAAB20 : BSc(Hons) Mathematics, Statistics, and Data Science with Study year abroad (Year 1)
 USMAAKB20 : BSc(Hons) Mathematics, Statistics, and Data Science with Industrial Placement (Year 1)
 USMAAFM14 : MMath(Hons) Mathematics (Year 1)
 USMAAAM15 : MMath(Hons) Mathematics with Study year abroad (Year 1)
 USMAAKM15 : MMath(Hons) Mathematics with Year long work placement (Year 1)
Department of Physics
 USXXAFB03 : BSc(Hons) Mathematics and Physics (Year 1)
 USXXAAB04 : BSc(Hons) Mathematics and Physics with Study year abroad (Year 1)
 USXXAKB04 : BSc(Hons) Mathematics and Physics with Year long work placement (Year 1)
 USXXAFM01 : MSci(Hons) Mathematics and Physics (Year 1)
 USXXAAM01 : MSci(Hons) Mathematics and Physics with Study year abroad (Year 1)
 USXXAKM01 : MSci(Hons) Mathematics and Physics with Year long work placement (Year 1)
