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Programme & Unit Catalogues

## MA10210: Algebra 1B

Owning Department/School: Department of Mathematical Sciences
Credits: 6
Level: Certificate (FHEQ level 4)
Period: Semester 2
Assessment Summary: EX 100%
Assessment Detail:
• Examination (EX 100%)
Supplementary Assessment: MA10210 Mandatory extra work (where allowed by programme regulations)
Requisites: Before taking this unit you must take MA10209 and while taking this unit you must take MA10207
Description: Aims:
To provide a firm grounding in linear algebra, both practically via matrices and abstractly via vector spaces and linear maps.

Learning Outcomes:
After taking this unit the students should be able to:
* Demonstrate understanding of abstract concepts of elementary linear algebra, (e.g. linear independence, dimension) and apply abstract ideas in specific examples.
* Solve systems of linear equations.
* Compute determinants, matrix inverses, eigenvalues and eigenvectors.

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

Content:
Systems of linear equations: matrix representation, row echelon form. Linear algebra and geometry in R2 and R3. Matrices as linear maps. Axiomatic development of vector spaces. Linear maps and subspaces, kernel and image. Linear independence and bases.
Linear maps as matrices, change of basis, similar matrices.
Dimension, rank, nullity. Rank-Nullity theorem.
Determinants: definition, properties and computation. Adjugate and inverse formula. Invertibility of matrices. Cramer's rule.
Eigenvalues, eigenvectors and eigenspaces. Characteristic polynomial.
Algebraic and geometric multiplicities. Diagonalisation.
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 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-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)
• 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-AFB05 : BSc(Hons) Statistics (Year 1)
• USMA-AAB06 : BSc(Hons) Statistics with Study year abroad (Year 1)
• USMA-AKB06 : BSc(Hons) Statistics 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 2014/15 academic year only. Students continuing their studies into 2015/16 and beyond should not assume that this unit will be available in future years in the format displayed here for 2014/15.
* Programmes and units are subject to change at any time, 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.