Authorised by Academic Registrar, April 1996
Objectives The objectives for this subject are for students to learn the discipline of axiomatic proof, and understand the meta-mathematical properties of axiom systems; understand the Dedekind cut model for the real numbers, and its status in relation to an axiomatic specification for the real numbers; build an understanding of analytic proof, sufficient to be able to apply this to new tasks; use the concept of uniform convergence to justify mathematical methods of calculus involving sequences and series of functions, and apply this to examples; understand the basis for the Riemann integral, and prove the existence of functions which are Riemann integrable and of functions which are not.
Synopsis This subject provides an introduction to classical real analysis, a formal treatment of the methods of calculus. Introduction to proof in axiomatic systems; an axiom system for the real numbers; convergence of sequences and series, decimal representation, power series; limits of functions, continuity, differentiability, the mean value theorem and its consequences; uniform convergence, continuity of the limit function, differentiation and integration of infinite series term by term, application to power series; the Riemann integral; improper and infinite integrals, Cauchy principal value. For distance students, four two-hour expository and discussion classes are held over the semester to supplement the textbook, class notes and exercises.
Assessment Assignments: 40% + Examination: 60%