Course Information

Course Description

This course reviews the basic theory of metric spaces and their topology including continuity, completeness, compactness, and connectedness. An introduction to abstract measure theory follows, with topics including measurability, measures, integration, the construction of Lebesgue measure and the Lebesque integral, as well as additional topics as time allows.

PREREQUISITES: MATH 63 Links to an external site. or MATH 35 Links to an external site. and the permission of the instructor.

 

Textbooks

We do not have a prescribed textbook. The following books are recommendations, but not required:

Real Analysis, Modern techniques and their applications (Second edition) by G.B. Folland

Real Analysis (fourth edition) by H.L. Royden and P.M. Fitzpatrick

Linear Functional Analysis, by B.P. Rynne and M.A. Youngson (Chapter 1)