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MA10210: Algebra 1B

[Page last updated: 20 April 2021]

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%
Supplementary Assessment:
Like-for-like 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 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.

Programme availability:
NB. Postgraduate programme information will be added when the postgraduate catalogues are published in August 2021

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)

Notes:

  • This unit catalogue is applicable for the 2021/22 academic year only. Students continuing their studies into 2022/23 and beyond should not assume that this unit will be available in future years in the format displayed here for 2021/22.
  • Programmes and units are subject to change in accordance with normal University procedures.
  • Availability of units will be subject to constraints such as staff availability, minimum and maximum group sizes, and timetabling factors as well as a student's ability to meet any pre-requisite rules.
  • Find out more about these and other important University terms and conditions here.