This text offers an accessible yet rigorous development of many of the fields of mathematics necessary for success in investment and quantitative finance, covering topics applicable to portfolio theory, investment banking, option pricing, investment, and insurance risk management. The approach emphasizes the mathematical framework provided by each mathematical discipline, and the application of each framework to the solution of finance problems. It emphasizes the thought process and mathematical approach taken to develop each result instead of the memorization of formulas to be applied (or misapplied) automatically. The objective is to provide a deep level of understanding of the relevant mathematical theory and tools that can then be effectively used in practice, to teach students how to "think in mathematics" rather than simply to do mathematics by rote. Each chapter covers an area of mathematics such as mathematical logic, Euclidean and other spaces, set theory and topology, sequences and series, probability theory, and calculus, in each case presenting only material that is most important and relevant for quantitative finance. Each chapter includes finance applications that demonstrate the relevance of the material presented. Problem sets are offered on both the mathematical theory and the finance applications sections of each chapter. The logical organization of the book and the judicious selection of topics make the text customizable for a number of courses. The development is self-contained and carefully explained to support disciplined independent study as well. A solutions manual for students provides solutions to the book's Practice Exercises; an instructor's manual offers solutions to the Assignment Exercises as well as other materials.

罗伯特·R.雷伊塔诺，美国布兰迪斯大学应用金融学教授，麻省理工大学数学博士学位，曾任John Hancock／Manulife公司的执行副总裁及首席投资顾问，在金融及数学方面具有深厚的学术背景并且有多年的理论实践经验。 马博，中国社会科学院研究生院数量经济学博士研究生，硕士毕业于中国人民大学经济学院。主要研究领域是行为与实验经济学、微观计量等。 隆云滔，就职于中国科学院数学与系统科学研究院。中国社会科学院研究生院数量经济学博士，圣菲研究所、密歇根大学安娜堡分校、芝加哥大学等访问学者。主要研究方向为行为金融与计算实验、演化博弈、复杂适应社会系统等。 刘洁，中国社会科学院研究生院数量经济学博士研究生，逢甲大学访问学者。主要研究方向为经济模型与经济预测。