Real Mathematical Analysis

(1) Real Mathematical Analysis, by Charles Pugh is a wonderful introduction to pure mathematics for a mathematically inclined engineer. The back cover starts like this > Was plane geometry your favourite math course in high school? Did you like proving theorems? Are you sick of memorising integrals? (2) The Man Who Mistook His Wife for a Hat, by Oliver Sacks. I think it's impossible to read this (or a number of other works of Sacks') and not be mesmerized by the workings of the human brain. Disclaimer: I wouldn't call neuroscience my "field of study" even though I did study it.

As mentioned in another subthread, Pugh's Real Mathematical Analysis is great, and better motivated than baby Rudin. Wilf - Generatingfunctionology (CRC 3rd ed.; free 2nd ed. pdf[1]) Lovasz - Combinatorial Problems and Exercises (AMS Chelsea) The classic probability book is Feller (2 vol), but it's absurdly priced. There's also Sidney Resnick's Probability Path and Adventures in Stochastic Processes. Grinstead & Snell - Introduction to Probability Theory is free[2], and there's also Chung's A Course in Probability Theory (Academic Press/Elsevier). Dover publishes at least three good books on counterexamples and pathological cases: Counterexamples in {Analysis, Probability, Topology} [1] http://www.math.upenn.edu/~wilf/DownldGF.html [2] http://www.dartmouth.edu/~chance/teaching_aids/books_article... (http://www.dartmouth.edu/~chance/teaching_aids/books_articles/probability_book/book.html)