This book evolved from the first ten years of the Carnegie Mellon professional Master's program in Computational Finance. The contents of the book have been used successfully with students whose mathematics background consists of calculus and calculus-based probability. The author does not assume familiarity with advanced mathematical concepts from measure-theoretic probability, but rather develops the necessary tools from this subject informally within the text. Many classroom-tested examples, exercises, and intuitive arguments are presented throughout the book.