Modern Discrete Probability: An Essential Toolkit (Cambridge Series in Statistical and Probabilistic Mathematics) (1版)

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【簡介】 Providing a graduate-level introduction to discrete probability and its applications, this book develops a toolkit of essential techniques for analysing stochastic processes on graphs, other random discrete structures, and algorithms. Topics covered include 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 showing them in action on simple examples and more substantial classical results. The focus is predominantly on non-asymptotic methods and results. All chapters provide a detailed background review section, plus exercises and signposts to the wider literature. Readers are assumed to have undergraduate-level linear algebra and basic real analysis, while prior exposure to graduate-level probability is recommended. This much-needed broad overview of discrete probability could serve as a textbook or as a reference for researchers in mathematics, statistics, data science, computer science and engineering. 【目錄】

Statistical and Thermal Physics (2版)

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【簡介】 Description This revised and expanded edition of Statistical and Thermal Physics introduces students to the essential ideas and techniques used in many areas of contemporary physics. Ready-to-run programs help make the many abstract concepts concrete. The text requires only a background in introductory mechanics and some basic ideas of quantum theory, discussing material typically found in undergraduate texts as well as topics such as fluids, critical phenomena, and computational techniques, which serve as a natural bridge to graduate study. Completely revised to be more accessible to students Encourages active reading with guided problems tied to the text Updated open source programs available in Java, Python, and JavaScript Integrates Monte Carlo and molecular dynamics simulations and other numerical techniques Self-contained introductions to thermodynamics and probability, including Bayes’ theorem A fuller discussion of magnetism and the Ising model than other undergraduate texts Treats ideal classical and quantum gases within a uniform framework Features a new chapter on transport coefficients and linear response theory Draws on findings from contemporary research Solutions manual (available only to instructors) 【目錄】 Table of Contents 1 From Microscopic to Macroscopic Behavior 2 Thermodynamic Concepts and Processes 3 Concepts of Probability 4 Methodology of Statistical Mechanics 5 Magnetic Systems 6 Many-Particle Systems 7 The Chemical Potential and Phase Equilibria 8 Classical Gases and Liquids 9 Critical Phenomena: Landau Theory and the Renormalization Group Method 10 It Is About Time: Time-Dependent Phenomena Appendix: Physical Constants and Mathematical Relations Index