This is a textbook for advanced undergraduate students and beginning graduate students in applied mathematics. It presents the basic mathematical foundations of stochastic analysis (probability theory and stochastic processes) as well as some important practical tools and applications (e.g., the connection with differential equations, numerical methods, path integrals, random fields, statistical physics, chemical kinetics, and rare events). The book strikes a nice balance between mathematical formalism and intuitive arguments, a style that is most suited for applied mathematicians. Readers can learn both the rigorous treatment of stochastic analysis as well as practical applications in modeling and simulation. Numerous exercises nicely supplement the main exposition.

The book systematically introduces the basic contents of data science, including data preprocessing and basic methods of data analysis, handling special problems (e.g. text analysis), deep learning, and distributed systems.In addition to systematically introducing the basic content of data science from a theoretical point of view, the book also provides a large number of data analysis practice cases.