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Developed from the esteemed author's advanced undergraduate and graduate courses at the University of Cambridge, this text provides a hands-on, sound introduction to mathematical finance. Assuming no prior knowledge of stochastic calculus or measure-theoretic probability, the author includes the relevant mathematical background as well as many exercises with solutions. He first presents the classical topics of utility and the mean-variance approach to portfolio choice. Focusing on derivative pricing, the text then covers the binomial model, the general discrete-time model, Brownian motion, the Black-Scholes model, and various interest-rate models.