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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

MT3600 FUNDAMENTALS OF PURE MATHEMATICS Aims The aims of the course are (a) to present ideas, concepts, results and methods that are part of the mathematician's general knowledge; (b) to highlight the importance of rigorous argument and proof; (c) to encourage a creative attitude towards mathematics through conjecture making, rigorous argumentation (proof) and problem solving. Objectives To acquire both working and deeper conceptual understand of fundamental mathematical concepts such as: sets, relations and mappings as the basic language of modern mathematics; algebraic and analytic properties of standard number systems; infinite sets and cardinal numbers. Syllabus The course will include topics from the following list: Review of sets, relations, functions. Construction and algebraic and order properties of number systems: - Natural Numbers: with a brief discussion of the Peano axioms. - The Integers. - The Rational Numbers: construction from integers, derivation of basic algebraic properties, Archimedean property. - The Real Numbers: construction via Dedekind cuts, basic algebraic properties, completeness, extraction of roots, decimal expansions, properties of e and pi. - The Complex Numbers: basic properties; Fundamental Theorem of Algebra. Infinite sets: countable and uncountable sets, cardinal numbers, arithmetic of cardinals, Axiom of Choice. Textbooks The Foundations of Mathematics: Ian Stewart & David Tall, Oxford Science Publications, 1997. Assessment 2 Hour Examination = 100% Prerequisites MT2002 or (MT2001 and MT1003) Availability Every year in semester 1 at 10 Lecturer Prof K J Falconer Click here for access to past examination papers for this module. Click here to see the University Course Catalogue entry. Revised: JOC (September 2010)