Financial mathematics provides a striking example of successful collaboration between academia and industry. Advanced mathematical techniques, developed in both universities and banks, have transformed the derivatives business into a multi-trillion-dollar market. This has led to demand for highly trained students and with that demand comes a need for textbooks.

This volume provides a first course in financial mathematics. The influence of Financial Calculus by Martin Baxter and Andrew Rennie will be obvious. I am extremely grateful to Martin and Andrew for their guidance and for allowing me to use some of the material from their book.

The structure of the text largely follows Financial Calculus, but the mathematics, especially the discussion of stochastic calculus, has been expanded to a level appropriate to a university mathematics course and the text is supplemented by a large number of exercises. In order to keep the course to a reasonable length, some sacrifices have been made. Most notable is that there was not space to discuss interest rate models, although many of the most popular ones do appear as examples in the exercises. As partial compensation, the necessary mathematical background for a rigorous study of interest rate models is included in Chapter 7, where we briefly discuss some of the topics that one might hope to include in a second course in financial mathematics. The exercises should be regarded as an integral part of the course.