Math 360: Advanced Calculus

This course is over. Please see Prof. Shatz if you have questions about your grade or anything else.

"Real mathematics must be justified as art if it can be justified at all," wrote the British mathematician G. H. Hardy. In this class we will learn the art of real analysis - the study of functions of one real variable.

We will challenge and improve our mathematical intuition while learning to write beautiful proofs. By the end, we should be able to answer questions like: does the Cantor set contain any irrational numbers? Can the set of points where a function is discontinuous be arbitrary? Are derivatives always continuous? Are derivatives always integrable? Are "the majority" of continuous functions differentiable?

You should plan to attend all the lectures (even if Professor Shatz calls them "optional"), as well as the weekly laboratory. Real analysis is a difficult subject, and even the best of you might find yourselves stuck at some point. Please make use of the laboratory and my office hours!