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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: 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 (Full-time) - Year 1
• USCM-AKB20 : BSc (hons) Computer Science and Mathematics (Full-time with Thick Sandwich Placement) - Year 1
• USCM-AAB20 : BSc (hons) Computer Science and Mathematics with Study Year Abroad (Full-time with Study Year Abroad) - Year 1
• USCM-AFM14 : MComp (hons) Computer Science and Mathematics (Full-time) - Year 1
• USCM-AKM14 : MComp (hons) Computer Science and Mathematics with Industrial Placement (Full-time with Thick Sandwich Placement) - Year 1
• USCM-AAM14 : MComp (hons) Computer Science and Mathematics with Study Year Abroad (Full-time with Study Year Abroad) - Year 1
Department of Mathematical Sciences
• USMA-AFB15 : BSc (hons) Mathematical Sciences (Full-time) - Year 1
• USMA-AKB16 : BSc (hons) Mathematical Sciences (Full-time with Thick Sandwich Placement) - Year 1
• USMA-AAB16 : BSc (hons) Mathematical Sciences with Study Year Abroad (Full-time with Study Year Abroad) - Year 1
• USMA-AFB13 : BSc (hons) Mathematics (Full-time) - Year 1
• USMA-AKB14 : BSc (hons) Mathematics (Full-time with Thick Sandwich Placement) - Year 1
• USMA-AFB01 : BSc (hons) Mathematics and Statistics (Full-time) - Year 1
• USMA-AKB02 : BSc (hons) Mathematics and Statistics (Full-time with Thick Sandwich Placement) - Year 1
• USMA-AAB02 : BSc (hons) Mathematics and Statistics with Study Year Abroad (Full-time with Study Year Abroad) - Year 1
• USMA-AAB14 : BSc (hons) Mathematics with Study Year Abroad (Full-time with Study Year Abroad) - Year 1
• USMA-AFB05 : BSc (hons) Statistics (Full-time) - Year 1
• USMA-AKB06 : BSc (hons) Statistics (Full-time with Thick Sandwich Placement) - Year 1
• USMA-AAB06 : BSc (hons) Statistics with Study Year Abroad (Full-time with Study Year Abroad) - Year 1
• USMA-AFM14 : MMath Mathematics (Full-time) - Year 1
• USMA-AAM15 : MMath Mathematics with Study Year Abroad (Full-time with Study Year Abroad) - Year 1
Department of Physics
• USXX-AFB03 : BSc (hons) Mathematics and Physics (Full-time) - Year 1
• USXX-AKB04 : BSc (hons) Mathematics and Physics with Placement (Full-time with Thick Sandwich Placement) - Year 1
• USXX-AAB04 : BSc (hons) Mathematics and Physics with Study Year Abroad (Full-time with Study Year Abroad) - Year 1
• USXX-AFM01 : MSci (hons) Mathematics and Physics (Full-time) - Year 1

Notes:
* This unit catalogue is applicable for the 2012/13 academic year only. Students continuing their studies into 2013/14 and beyond should not assume that this unit will be available in future years in the format displayed here for 2012/13.
* 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.