A Review of A Course in Probability by Neil A. Weiss, Paul T. Holmes, and Michael Hardy
A Course in Probability is a textbook that covers the fundamentals of probability theory and its applications to various fields of mathematics, statistics, engineering, and computer science. The book is intended for readers who have a background in elementary calculus, set theory, and some linear algebra. The book aims to make the learning process smooth, efficient, and enjoyable by using pedagogical techniques such as examples, exercises, summaries, and historical notes.
The book is divided into four parts. The first part introduces the basic concepts of probability, such as events, sample spaces, axioms, counting methods, conditional probability, and independence. The second part deals with discrete random variables and their distributions, such as binomial, geometric, Poisson, hypergeometric, and negative binomial. The third part covers continuous random variables and their distributions, such as uniform, exponential, normal, gamma, beta, and chi-square. The fourth part discusses some advanced topics in probability, such as generating functions, limit theorems, Markov chains, Poisson processes, and Bayesian inference.
The book has many features that make it a valuable resource for students and instructors. The book has a clear and concise writing style that explains the concepts and proofs in a logical and rigorous manner. The book has a wealth of examples that illustrate the applications of probability to various disciplines and real-world situations. The book has over 1,500 exercises that test the understanding and skills of the readers. The book has chapter summaries that highlight the main points and formulas of each chapter. The book has historical notes that provide some background and context on the development of probability theory and its contributors.
A Course in Probability is a comprehensive and accessible introduction to probability that can be used for a first or second course in mathematical probability. The book can also serve as a reference for researchers and practitioners who need to use probability in their work. The book is available in both print and PDF formats[^1^] [^2^].
One of the strengths of the book is its emphasis on the connections between probability and other branches of mathematics, such as combinatorics, analysis, algebra, and geometry. The book shows how probability can be used to solve problems and prove results that are not obvious from other perspectives. For example, the book uses probability to derive the binomial theorem, the inclusion-exclusion principle, Stirling's formula, Euler's formula, and the central limit theorem.
Another strength of the book is its coverage of some topics that are not commonly found in other introductory probability textbooks, such as generating functions, Markov chains, Poisson processes, and Bayesian inference. These topics are important for advanced applications of probability to areas such as cryptography, coding theory, queueing theory, stochastic processes, and statistical inference. The book provides a solid foundation for readers who want to pursue further studies in these fields.
A possible limitation of the book is its level of difficulty and abstraction. The book assumes that the readers have a good grasp of calculus and linear algebra, and are comfortable with rigorous proofs and abstract concepts. The book does not shy away from presenting some challenging and sophisticated results and techniques in probability theory. The book may not be suitable for readers who are looking for a more elementary or intuitive introduction to probability. 0efd9a6b88