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2014/5 |
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Department of Mathematical Sciences |
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6 |
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Certificate (FHEQ level 4) |
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Semester 1 |
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EX 100% |
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MA10209 Mandatory extra work (where allowed by programme regulations) |
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While taking this unit you must take MA10207. You must have A level Mathematics Grade A, or equivalent in order to take this unit. |
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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. |
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MA10209 is Compulsory on the following programmes:Department of Computer Science
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