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 Academic Year: | 2016/7 |
| Owning Department/School: | Department of Mathematical Sciences |
| Credits: | 6 [equivalent to 12 CATS credits] |
| Notional Study Hours: | 120 |
| Level: | Certificate (FHEQ level 4) |
| Period: |
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| Assessment Summary: | EX 100% |
| Assessment Detail: |
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| Supplementary Assessment: |
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| 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
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Notes:
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