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】

Modern Mathematical Concepts for Engineers

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This textbook provides a comprehensive exploration of mathematical modeling, emphasizing the limitations of pointwise analysis and highlighting the great potential of measure theory. Measure theory not only offers better representations of phenomena, such as distributions and continuous probabilities, but also facilitates the analysis of classical partial differential equation problems. Additionally, the book introduces new classes of problems that go beyond traditional pointwise and infinitesimal analysis, integrating random and deterministic aspects into a unified framework. The narrative follows Bernard Namier, a young engineering apprentice, and Laurent Corps, a retired mathematics expert who tutors Bernard to tackle a challenging project assigned at work. Through their interwoven dialogue and the fictitious texts they study, readers are immersed in mathematical modeling as applied to engineering problems, with insights that extend to broader applications. This unique structure bridges two educational traditions: the abstract, Bourbaki-style approach common in France and the progressive, example-based learning prevalent in the Anglosphere. As a result, readers will master core concepts through rigorous proofs and applied examples and gain confidence in handling complex systems.

AP World History: Modern Premium 2026 (1版)

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【簡介】 ＂Barron’s AP World History: Modern Premium, 2026 includes in depth content review and practice. It’s the only book you’ll need to be prepared for exam day.＂--