Modern Discrete Probability: An Essential Toolkit

This book provides a comprehensive introduction to discrete probability, covering techniques such as first and second moment methods, concentration inequalities, coupling and stochastic domination, martingales and potential theory, spectral methods, and branching processes. It focuses on non-asymptotic methods and results and is suitable for researchers in mathematics, statistics, data science, computer science, and engineering.

Format: Hardback
Length: 452 pages
Publication date: 18 January 2024
Publisher: Cambridge University Press

This comprehensive textbook offers a thorough introduction to discrete probability, covering a wide range of topics and applications. It begins by developing a toolkit of essential techniques for analyzing stochastic processes on graphs, other random discrete structures, and algorithms. The book delves into various concepts, including the first and second moment methods, concentration inequalities, coupling and stochastic domination, martingales and potential theory, spectral methods, and branching processes. Each chapter expands on a fundamental technique, outlining common uses and demonstrating them through simple examples and significant classical results. The emphasis is primarily on non-asymptotic methods and findings, making the content accessible to readers with a solid background in undergraduate linear algebra and basic real analysis. Additionally, the book includes a detailed background review section, exercises, and signposts to the broader literature, making it an invaluable resource for researchers in mathematics, statistics, data science, computer science, and engineering.

Discrete Probability: An Introduction

This textbook provides a comprehensive and in-depth exploration of discrete probability, covering a wide range of topics and applications. It begins by introducing the fundamental concepts and principles of probability theory, including random variables, probability distributions, and conditional probability. The book then delves into various topics related to discrete probability, such as Markov chains, random walks, and stochastic processes. Each chapter focuses on a specific topic and provides a detailed explanation, accompanied by examples and exercises to help readers understand and apply the concepts. The book also includes a comprehensive review section that covers important theorems and results in discrete probability, as well as pointers to further readings and research opportunities. Whether you are a student studying mathematics, statistics, or computer science, or a professional seeking to advance your knowledge in this field, this textbook is an essential resource for understanding and applying discrete probability concepts.

Discrete Probability: An Introduction

This textbook offers a comprehensive and accessible introduction to discrete probability, covering a wide range of topics and applications. It begins by providing a solid foundation in probability theory, including random variables, probability distributions, and conditional probability. The book then delves into various discrete probability concepts, such as Markov chains, random walks, and stochastic processes. Each chapter is well-organized and includes clear explanations, examples, and exercises to help readers understand and apply the concepts. The book also includes a comprehensive review section that covers important theorems and results in discrete probability, as well as pointers to further readings and research opportunities. Whether you are a student studying mathematics, statistics, or computer science, or a professional seeking to expand your knowledge in this field, this textbook is an invaluable resource for understanding and applying discrete probability concepts.

Weight: 1098g
Dimension: 262 x 187 x 30 (mm)
ISBN-13: 9781009305112