Description: This classroom-tested textbook is an introduction to probability theory, with the right balance between mathematical precision, probabilistic intuition, and concrete applications. Introduction to Probability covers the material precisely, while avoiding excessive technical details. After introducing the basic vocabulary of randomness, including events, probabilities, and random variables, the text offers the reader a first glimpse of the major theorems of the subject: the law of large numbers and the central limit theorem. The important probability distributions are introduced organically as they arise from applications. The discrete and continuous sides of probability are treated together to emphasize their similarities. Intended for students with a calculus background, the text teaches not only the nuts and bolts of probability theory and how to solve specific problems, but also why the methods of solution work.
Brief description: Benedek Valkó is a Professor of Mathematics at the University of Wisconsin, Madison. His research focuses on probability theory, in particular in the study of random matrices and interacting stochastic systems. He has published over thirty research papers. He has won a National Science Foundation (NSF) CAREER award and he was a 2017-18 Simons Fellow.
Review Quotes: 'The authors have carefully chosen a set of core topics, resisting the temptation to overload the reader. They tie it all together with a coherent philosophy. Knowing the authors' work, I would expect nothing less. I predict that this text will become the standard for beginning probability courses.' Carl Mueller, University of Rochester, New York