MA10209: Algebra 1A
[Page last updated: 10 August 2020]
Academic Year:  2020/1 
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 1

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

Requisites: 
While taking this module 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
 USCMAFB20 : BSc(Hons) Computer Science and Mathematics (Year 1)
 USCMAAB20 : BSc(Hons) Computer Science and Mathematics with Study year abroad (Year 1)
 USCMAKB20 : BSc(Hons) Computer Science and Mathematics with Year long work placement (Year 1)
 USCMAFM14 : MComp(Hons) Computer Science and Mathematics (Year 1)
 USCMAAM14 : MComp(Hons) Computer Science and Mathematics with Study year abroad (Year 1)
 USCMAKM14 : MComp(Hons) Computer Science and Mathematics with Year long work placement (Year 1)
Department of Economics
 UHESAFB04 : BSc(Hons) Economics and Mathematics (Year 1)
 UHESAAB04 : BSc(Hons) Economics and Mathematics with Study year abroad (Year 1)
 UHESAKB04 : BSc(Hons) Economics and Mathematics with Year long work placement (Year 1)
 UHESACB04 : BSc(Hons) Economics and Mathematics with Combined Placement and Study Abroad (Year 1)
Department of Mathematical Sciences
 USMAAFB15 : BSc(Hons) Mathematical Sciences (Year 1)
 USMAAAB16 : BSc(Hons) Mathematical Sciences with Study year abroad (Year 1)
 USMAAKB16 : BSc(Hons) Mathematical Sciences with Year long work placement (Year 1)
 USMAAFB13 : BSc(Hons) Mathematics (Year 1)
 USMAAAB14 : BSc(Hons) Mathematics with Study year abroad (Year 1)
 USMAAKB14 : BSc(Hons) Mathematics with Year long work placement (Year 1)
 USMAAFB01 : BSc(Hons) Mathematics and Statistics (Year 1)
 USMAAAB02 : BSc(Hons) Mathematics and Statistics with Study year abroad (Year 1)
 USMAAKB02 : BSc(Hons) Mathematics and Statistics with Year long work placement (Year 1)
 USMAAFB05 : BSc(Hons) Statistics (Year 1)
 USMAAAB06 : BSc(Hons) Statistics with Study year abroad (Year 1)
 USMAAKB06 : BSc(Hons) Statistics with Year long work placement (Year 1)
 USMAAFM14 : MMath(Hons) Mathematics (Year 1)
 USMAAAM15 : MMath(Hons) Mathematics with Study year abroad (Year 1)
 USMAAKM15 : MMath(Hons) Mathematics with Year long work placement (Year 1)
Department of Physics
 USXXAFB03 : BSc(Hons) Mathematics and Physics (Year 1)
 USXXAAB04 : BSc(Hons) Mathematics and Physics with Study year abroad (Year 1)
 USXXAKB04 : BSc(Hons) Mathematics and Physics with Year long work placement (Year 1)
 USXXAFM01 : MSci(Hons) Mathematics and Physics (Year 1)
 USXXAAM01 : MSci(Hons) Mathematics and Physics with Study year abroad (Year 1)
 USXXAKM01 : MSci(Hons) Mathematics and Physics with Year long work placement (Year 1)
