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This textbook provides an introduction to financial mathematics and financial engineering for undergraduate students who have completed a three or four semester sequence of calculus courses. It introduces the theory of interest, random variables and probability, stochastic processes, arbitrage, option pricing, hedging, and portfolio optimization. The student progresses from knowing only elementary calculus to understanding the derivation and solution of the Black?Scholes partial differential equation and its solutions. This is one of the few books on the subject of financial mathematics which is accessible to undergraduates having only a thorough grounding in elementary calculus. It explains the subject matter without ?hand waving? arguments and includes numerous examples. Every chapter concludes with a set of exercises which test the chapter's concepts and fill in details of derivations.