Stochastic Tools in Mathematics and Science is an introductory book on probability-based modeling. It covers basic stochastic tools used in physics, chemistry, engineering and the life sciences. The topics covered include conditional expectations, stochastic processes, Brownian motion and its relation to partial differential equations, Langevin equations, the Liouville and Fokker-Planck equations, as well as Markov chain Monte Carlo algorithms, renormalization and dimensional reduction, and basic equilibrium and non-equilibrium statistical mechanics. The applications include data assimilation, prediction from partial data, spectral analysis, and turbulence. A noteworthy feature of the book is the systematic analysis of memory effects. The presentation is mathematically attractive, and should form a useful bridge between the theoretical treatments familiar to mathematical specialists and the more practical questions raised by specific applications. The book is based on lecture notes from a class that has attracted graduate and advanced undergraduate students from mathematics and from many other science departments at the University of California, Berkeley. Each chapter is followed by exercises. The book will be useful for scientists and engineers working in a wide range of fields and applications.

Stochastic Tools in Mathematics and Science is an introductory book on probability based modeling in mathematics and physics, in particular Brownian motion, Langevin Equations, Liouville equations, stastitical projections, renormalization, maximum likelihood estimation, expectation maximization, with applications to statistical mechanics, fluid mechanics, and neural computation. The book covers the basic stochastic tools needed for modeling in physics, chemistry, engineering and the life sciences. Exercises are included at the end of each chapter.This book is based on lecture notes for a class that has attracted graduate students from mathematics and many other science departments at the University of California, Berkeley, where both authors are distinguished professors and are experts in their field. It should be useful to graduate students and advanced undergraduates in a wide range of study.

Preliminaries.- Introduction to Probability.- Brownian Motion and Its Applications.- Stationary Stochastic.-Processes.- Statistical Mechanics.- Time-Dependent Statistical Mechanics.