MA20216: Algebra 2A
[Page last updated: 03 August 2022]
Academic Year:  2022/23 
Owning Department/School:  Department of Mathematical Sciences 
Credits:  6 [equivalent to 12 CATS credits] 
Notional Study Hours:  120 
Level:  Intermediate (FHEQ level 5) 
Period: 
 Semester 1

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

Requisites: 
Before taking this module you must take MA10209 AND take MA10210

Learning Outcomes:
 After taking this unit, students should be able to:
* Demonstrate understanding of vector spaces and abstract linear algebra, including quotient spaces, dual spaces and bilinear forms.
* Classify linear operators in theory and practice.
* Compute the Jordan Normal Form of matrices
* Classify quadratic forms in theory and practice.

Aims:  Deepen understanding of linear algebra. Classify linear operators on finitedimensional complex vector spaces. Introduce multilinear algebra, with emphasis on bilinear forms.

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

Content:  Vector subspaces, sums and intersections, complementary subspaces, quotients. Dual spaces and bases, transpose of a linear map, annihilators.
Linear operators: review of eigenvalues and eigenvectors; eigenspaces, invariant subspaces. Minimal polynomials, CayleyHamilton theorem. Generalised eigenspaces, Jordan normal form theorem and applications.
Bilinear maps and forms. Symmetric bilinear forms: radical and rank. Quadratic forms: polarisation, diagonalisation, rank and signature.

Programme availability: 
MA20216 is Compulsory on the following programmes:
Department of Computer Science
 USCMAFB20 : BSc(Hons) Computer Science and Mathematics (Year 2)
 USCMAAB20 : BSc(Hons) Computer Science and Mathematics with Study year abroad (Year 2)
 USCMAKB20 : BSc(Hons) Computer Science and Mathematics with Year long work placement (Year 2)
 USCMAFM14 : MComp(Hons) Computer Science and Mathematics (Year 2)
 USCMAAM14 : MComp(Hons) Computer Science and Mathematics with Study year abroad (Year 2)
 USCMAKM14 : MComp(Hons) Computer Science and Mathematics with Year long work placement (Year 2)
Department of Mathematical Sciences
 USMAAFB13 : BSc(Hons) Mathematics (Year 2)
 USMAAAB14 : BSc(Hons) Mathematics with Study year abroad (Year 2)
 USMAAKB14 : BSc(Hons) Mathematics with Year long work placement (Year 2)
 USMAAFM14 : MMath(Hons) Mathematics (Year 2)
 USMAAAM15 : MMath(Hons) Mathematics with Study year abroad (Year 2)
 USMAAKM15 : MMath(Hons) Mathematics with Year long work placement (Year 2)
Department of Physics
 USXXAFB03 : BSc(Hons) Mathematics and Physics (Year 2)
 USXXAAB04 : BSc(Hons) Mathematics and Physics with Study year abroad (Year 2)
 USXXAKB04 : BSc(Hons) Mathematics and Physics with Year long work placement (Year 2)
 USXXAFM01 : MSci(Hons) Mathematics and Physics (Year 2)
 USXXAAM01 : MSci(Hons) Mathematics and Physics with Study year abroad (Year 2)
 USXXAKM01 : MSci(Hons) Mathematics and Physics with Year long work placement (Year 2)
MA20216 is Optional on the following programmes:
Department of Economics
 UHESAFB04 : BSc(Hons) Economics and Mathematics (Year 2)
 UHESAFB04 : BSc(Hons) Economics and Mathematics (Year 3)
 UHESAAB04 : BSc(Hons) Economics and Mathematics with Study year abroad (Year 2)
 UHESAAB04 : BSc(Hons) Economics and Mathematics with Study year abroad (Year 4)
 UHESAKB04 : BSc(Hons) Economics and Mathematics with Year long work placement (Year 2)
 UHESAKB04 : BSc(Hons) Economics and Mathematics with Year long work placement (Year 4)
 UHESACB04 : BSc(Hons) Economics and Mathematics with Combined Placement and Study Abroad (Year 2)
 UHESACB04 : BSc(Hons) Economics and Mathematics with Combined Placement and Study Abroad (Year 4)
Department of Mathematical Sciences
 USMAAFB15 : BSc(Hons) Mathematical Sciences (Year 2)
 USMAAAB16 : BSc(Hons) Mathematical Sciences with Study year abroad (Year 2)
 USMAAKB16 : BSc(Hons) Mathematical Sciences with Year long work placement (Year 2)
 USMAAFB01 : BSc(Hons) Mathematics and Statistics (Year 2)
 USMAAAB02 : BSc(Hons) Mathematics and Statistics with Study year abroad (Year 2)
 USMAAKB02 : BSc(Hons) Mathematics and Statistics with Year long work placement (Year 2)
 USMAAFB20 : BSc(Hons) Mathematics, Statistics, and Data Science (Year 2)
 USMAAAB20 : BSc(Hons) Mathematics, Statistics, and Data Science with Study year abroad (Year 2)
 USMAAKB20 : BSc(Hons) Mathematics, Statistics, and Data Science with Industrial Placement (Year 2)

Notes:  This unit catalogue is applicable for the 2022/23 academic year only. Students continuing their studies into 2023/24 and beyond should not assume that this unit will be available in future years in the format displayed here for 2022/23.
 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 prerequisite rules.
 Find out more about these and other important University terms and conditions here.
