An Introduction to Probability Theory and Its Applications

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)

My recommendations: Hardy, A Course of Pure Mathematics. Knuth, Graham and Patashnik, Concrete Mathematics. Hoffman and Kunze, Linear Algebra (there are several free online books on Linear Algebra and Vector Spaces, Strang, Axler, Lang Halmos and Shilov are also recommended). Feller, An Introduction to Probability Theory and Its Applications. If you're not studying for exams and you have plenty of time on your hands, try the following algorithm: 1. Dive into some random chapter in the book and attempt the first exercise in that chapter. 2. Understand the problem by referring back and learning everything that might potentially have relevance to the exercise. 3. Attempt to solve exercise. 4. If unsuccessful, go to step 2. 5. If there are more exercises in the chapter, pick the next exercise and go to step 2. 6. If there are still unsolved exercises in the book, go to step 1.…