
Academic Year:  2012/3 
Owning Department/School:  Department of Mathematical Sciences 
Credits:  6 
Level:  Certificate (FHEQ level 4) 
Period: 
Semester 1 
Assessment:  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
