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Courses in Mathematics and Statistics Level 1 Modules Level 2 Modules Level 3 Modules Level 4 Modules Level 5 Modules Honours timetable 2011/2012 Sem. 1 2011/2012 Sem. 2 2012/2013 Sem. 1 & Sem. 2 2013/2014 Sem. 1 & Sem. 2

MT4516 FINITE MATHEMATICS Aims - To introduce the student to finite mathematical structures such as codes, Latin squares, finite geometries and designs. - To demonstrate relationships between different structures. - To illustrate applications of more classical mathematical disciplines (such as fields and vector spaces) - To investigation of finite structures, as well as the application of finite structures to other branches of mathematics and science. Objectives By the end of the course students are expected to - know the basic definitions and facts about codes, Latin squares, finite geometries and designs. - understand basic existential, constructive and counting proofs, and to be able to reproduce them. - apply the above knowledge to problem solving. - understand history and applications of the considered concepts. Syllabus - Codes: linear codes, decoding with coset leaders and syndromes, perfect codes; - Latin squares: existence, counting, orthogonality; - Finite geometries: affine and projective planes, connections with Latin squares. - Designs: necessary conditions for existence, Steiner triple systems, connections with codes. Textbooks Combinatorics : Topics, Techniques, Algorithms, P J Cameron, Cambridge University Press, 1994; A Course in Combinatorics: J H van Lint and R M Wilson, Cambridge University Press, 1992; Combinatorial Theory, an Introduction: A P Street and W D Wallis, CBRC, Manitoba, 1977. Assessment 2 Hour Examination = 100% Co-requisites one of MT3501, MT3503, MT3504, MT3606 Availability Academic year 2011/12 in semester 1 at 11 Lecturer Dr C Roney-Dougal Click here for access to past examination papers for this module. Click here to see the University Course Catalogue entry. Revised: PMH (September 2011)