good math books
sanand: 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.Initially, this can cause excruciating pain and frustration.  But every exercise is a little research problem and soon -- if you are the curious type who cannot rest until you have got to the bottom of a problem -- you'll find you've mastered the subject faster than you would have learnt its elements, had you taken a formal classroom course.  The most important benefit of this method is that it will train you in some modes of thinking that are crucial in research.  Think of it as callisthenics for problem solving type of research!