Dr Konrad Swanepoel

This course is compulsory on the BSc in Mathematics and Economics and BSc in Mathematics with Economics. This course is available on the BSc in Business Mathematics and Statistics, BSc in Econometrics and Mathematical Economics and BSc in Statistics with Finance. This course is available as an outside option to students on other programmes where regulations permit. This course is available with permission to General Course students.

Introduction to Abstract Mathematics (MA103), or some equivalent giving experience with formal proofs, convergence of sequences and continuity of functions.

This is a course in real analysis for those who have already met the basic concepts of sequences and continuity in R. Here we generalize these concepts to Rn and to more general normed spaces and metric spaces.  These more general spaces are introduced at the start and are emphasized throughout the course.
Topics covered are: metric and normed spaces, open and closed sets, sequences in metric spaces, pointwise and uniform convergence of sequences of functions, series in R and in normed spaces, continuous functions between metric spaces, compactness, uniform continuity, the mean value theorem, differentiation of functions between Rn and Rm, partial derivatives, the Riemann integral.

20 hours of lectures and 9 hours of classes in the MT. 1 hour of classes in the LT. 2 hours of lectures in the ST.

Written answers to set problems will be expected on a weekly basis.

Lecture notes will be provided. The following may prove useful: Robert G Bartle & Donald R Sherbert, Introduction to Real Analysis; K G Binmore, Mathematical Analysis: a straightforward approach; Victor Bryant, Yet Another Introduction to Analysis; W A Sutherland, Introduction to Metric and Topological Spaces.

Exam (100%, duration: 2 hours) in the main exam period.