Real Analysis

This course provides a rigorous treatment of real analysis. The emphasis will be on theory and understanding of concepts, though applications such as fixed-point theorems and the evaluation of series, integrals and products, will certainly be included. All students should have completed an introductory analysis course, such as MATH3210.03. Students contemplating graduate work in mathematics are strongly advised to take this course, since it would be almost impossible to embark on advanced courses in functional analysis or probability theory without such material.

Specific topics include: point set topology of the real line and of metric spaces; limits, continuity, differentiability; functions of bounded variation; Riemann-Stieltjes integration; infinite products; sequences and series of functions; Lebesgue measure and integration; and possibly some Fourier series.

The text is W. Rudin, Principles of Mathematical Analysis, 3rd ed. (McGraw-Hill).

The final grade may be based on assignments (20%), two class tests (40%) and a final examination (40%).