This is the first volume in a two volume sequence providing the foundational material on Stochastic calculus models in finance. This first volume is suitable for discrete-time finance. The only pre-requisite is standard calculus; may aspects such as martingales and change of measure are treated in detailed depth. Probability is covered in detail using the binomial model.

The book will be suitable for advanced undergraduate courses and beginning masters-level students in mathematical finance and financial engineering. There are exercises and examples throughout and summaries at the end of each chapter.