Mathematics and Tools for Financial Engineering

Based on a master's program course at the University of Southern California, the main goal of Mathematics and Tools for Financial Engineering is to train students to use mathematical and engineering tools to understand and solve financial problems. The book contains numerous examples and problems and is divided into two parts: Part I covers mathematical preliminaries (set theory, linear algebra, sequences and series, real functions and analysis, numerical approximations and computations, basic optimization theory, and stochastic processes). Part II addresses financial topics, ranging from low- to high-risk investments. Mathematics and Tools for Financial Engineering is intended for senior undergraduate or graduate students in finance or financial engineering. It is appropriate for the following courses: Advanced Numerical Analysis, Special Topics on Numerical Analysis, Topics on Data Science, Topics on Numerical Optimization, and Topics on Approximation Theory. Readers with no prior knowledge in finance can use the book to learn about various mathematical theories and tools.