I will list and review the books that allowed me to become a Quant. I will start in Chronological order the study I undertook. Before I started my formal studies at Rugters Mathematical Finance Program, I realized early on that to be successful, I needed to do lots of exercises. Books that do not provides adequate questions and answers are not useful in remembering the mathematics of the material.
I will labels the material as below. 1. Foundations begins with 'F' 2. Stochastic Calculus begins with 'SC' 3. Computation Finance begins with 'C' 4. Statistics begins with 'S' 5. Portfolia begins with 'P' 6. Numerical Analysis begins with 'N'
F-2: How to Ace Calculus: The Streetwise Guide This is a very good introduction book to calculus. It helps explain how to use and understand the role of elementary calculus to the layman. It's drawback is that there is not enough exercises.
F-10: Measure, Integral and Probability Not an easy book to read. Unless someone has a better suggestion, this is the best I found. Don't get bogged down with the proofs. Just get a feel for what measure theory is all about.
SC-3: Stochastic Calculus for Finance II: Continuous-Time Models (Springer Finance) I have a love hate relationship with this book. I love the book for its logical description of difficult topics. I hate this book because it is more like a set of notes than a learning text. Nevertheless if you can master this book your efforts will have paid off. Core chapters are 1 - 6. The rest is optional.