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Programme & Unit Catalogues

## MA10209: Algebra 1A

Owning Department/School: Department of Mathematical Sciences
Credits: 6
Level: Certificate (FHEQ level 4)
Period: Semester 1
Assessment Summary: EX 100%
Assessment Detail:
• Examination (EX 100%)
Supplementary Assessment: MA10209 Mandatory extra work (where allowed by programme regulations)
Requisites: While taking this unit you must take MA10207. You must have A level Mathematics Grade A, or equivalent in order to take this unit.
Description: Aims:
To provide a firm grounding in the fundamental objects of mathematics such as sets and functions, numbers, polynomials and matrices. To give a first taste of the axiomatic method, via group theory.

Learning Outcomes:
After taking this unit the students should be able to:
* Demonstrate understanding of the elementary concepts of geometry and algebra.
* Construct correct logical proofs of theorems about these concepts, using techniques such as contradiction and induction.
* State and prove fundamental results of group theory.
* Apply abstract ideas in specific examples.

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

Content:
Sets and functions. Direct and inverse image. Equivalence relations.
Numbers (natural, integer, rational, real, complex).
Arithmetic and prime factorisation. Euclid's algorithm.
Polynomials: division with remainder. Modular arithmetic.
Groups, rings and fields (definitions and examples).
Arithmetic of matrices, 2x2 & 3x3 determinants.
Linear, affine & Euclidean transformations of R^2 & R^3, area/volume interpretation of determinants.
Geometry of the complex plane.
Axiomatic development of group theory.
Subgroups, homomorphisms, kernel and image. Isomorphism.
Order of an element and of a group; cyclic groups.
Permutations: cycle notation, sign of a permutation.
Actions, orbits, stabilizers and Cayley's theorem.
Cosets, Lagrange's theorem and applications.
Programme availability:

#### MA10209 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.