FINANCE
John Hull’s Options, Futures, and Other Derivatives. The so-called Bible of Wall Street Professionals, this book is mandatory reading for everyone entering the mathematical finance field. Somewhat dry at times, but the topics covered, presentation, and relevance to the program has no equal.
Saleh Neftci’s Principles of Financial Engineering. A great synopsis of the interaction between financial instruments and asset classes within the markets. The late Professor Neftci was truly a gifted writer.
APPLIED MATHEMATICS
Steven Shreve’s Stochastic Calculus for Finance books: namely Stochastic Calculus for Finance I: The Binomial Asset Pricing Model and Stochastic Calculus for Finance II: Continuous-Time Models. These books are standards for courses in stochastic calculus; but caution, these books can be hard to read the first time through, especially the Continuous-Time Models.
Neil Chriss’ Black Scholes and Beyond. An outdated book by some standards, but an easy-to-read account of fundamental stochastic calculus, probability, and statistics used in pricing options.
COMPUTER SCIENCE
Paul Teetor’s R Cookbook. A great, simple-to-read-and-do tutorial on the R scripting language and R framework. Many courses will rely on R or some statistical-based package. Being proficient in R will be a great time-saver as well as tool that will be useful for all time.
Yuh-Dauh Lyuu’s Financial Engineering and Computation. A great book that touches mainly on the computational aspects of mathematical finance.