《概率、随机变量与随机过程》是美国著名学者A·帕普里斯教授所著的一本经典教材。自1965年第1版问世以来至今已第4版，一直被美国多所大学用作相关专业的研究生教材。它的特点是将高深的理论恰当地应用于工程实际，因而深受工程界专业人士的青睐。本书（第4版）在保持前三版风格和精华的基础上作了大量的修订：更新了约三分之一的章节内容，包括几个新的专题和新增的第15、16章，增加了大量的新例子，进一步澄清了一些复杂的概念，使读者能更容易地理解它们。
本书可供无线电通信系统、信号处理、控制理论、优化、滤波等专业的研究生和本科高年级学生使用，也可供相关领域的科开人员和工程技术人员参考。

Written by acclaimed author and mathematician George Simmons, this revision is designed for the calculus course offered in two and four year colleges and universities. It takes an intuitive approach to calculus and focuses on the application of methods to real-world problems. Throughout the text, calculus is treated as a problem solving science of immense capability.

"Interesting and useful as all this will be for anyone interested in knowing more about Bayes, this is just part of the riches contained in this book ...Beyond doubt this book is a work of the highest quality in terms of the scholarship it displays, and should be regarded as a must for every mathematical library." --MAA ONLINE

This book is an introduction to the field of asymptotic statistics. The treatment is both practical and mathematically rigorous. In addition to most of the standard topics of an asymptotics course, including likelihood inference, M-estimation, the theory of asymptotic efficiency, U-statistics, and rank procedures, the book also presents recent research topics such as semiparametric models, the bootstrap, and empirical processes and their applications. The topics are organized from the central idea of approximation by limit experiments, which gives the book one of its unifying themes. This entails mainly the local approximation of the classical i.i.d. set up with smooth parameters by location experiments involving a single, normally distributed observation. Thus, even the standard subjects of asymptotic statistics are presented in a novel way. Suitable as a graduate or Master's level statistics text, this book will also give researchers an overview of research in asymptotic statistics.

The study of networks, including computer networks, social networks, and biological networks, has attracted enormous interest in the last few years. The rise of the Internet and the wide availability of inexpensive computers have made it possible to gather and analyze network data on an unprecedented scale, and the development of new theoretical tools has allowed us to extract knowledge from networks of many different kinds. The study of networks is broadly interdisciplinary and central developments have occurred in many fields, including mathematics, physics, computer and information sciences, biology, and the social sciences. This book brings together the most important breakthroughs in each of these fields and presents them in a coherent fashion, highlighting the strong interconnections between work in different areas.
Topics covered include the measurement of networks; methods for analyzing network data, including methods developed in physics, statistics, and sociology; fundamentals of graph theory; computer algorithms; mathematical models of networks, including random graph models and generative models; and theories of dynamical processes taking place on networks.

概率图模型将概率论与图论相结合，是当前非常热门的一个机器学习研究方向。本书详细论述了有向图模型（又称贝叶斯网）和无向图模型（又称马尔可夫网）的表示、推理和学习问题，全面总结了人工智能这一前沿研究领域的最新进展。为了便于读者理解，书中包含了大量的定义、定理、证明、算法及其伪代码，穿插了大量的辅助材料，如示例（examples）、技巧专栏（skill boxes）、实例专栏（case study boxes）、概念专栏（concept boxes）等。另外，在第 2章介绍了概率论和图论的核心知识，在附录中介绍了信息论、算法复杂性、组合优化等补充材料，为学习和运用概率图模型提供了完备的基础。
本书可作为高等学校和科研单位从事人工智能、机器学习、模式识别、信号处理等方向的学生、教师和研究人员的教材和参考书。
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很高兴能够看到我们所著的《概率图模型》一书被翻译为中文出版。我们了解到这本书涵盖的课题已在中国引起了巨大的兴趣。已有众多中国读者写信向我们解释这本书对于他们的学习的重要性，并希望获得更易理解的版本。随着众多来自中国研究机构或国外研究机构的中国学者署名或共同署名的文章的发表，中国研究者已在概率图领域中扮演了非常重要的角色。这些文章对于概率图模型领域的发展起到了非常重要的作用。我们相信《概率图模型》中文版的出版将帮助许多中国读者学习并掌握这一重要课题的基础。同时，这也将进一步提高中国学者应用概率图模型思想的能力，并为这一领域的发展做出贡献。
本书的翻译工作由王飞跃研究员主导，并得到了王珏研究员及其众多助手和合作者的支持。这是一份历时 5年、具有里程碑意义的努力，我深深地感谢该团队所有为本书翻译做出贡献的人员。我尤其希望借此机会感谢王珏研究员——一位中国机器学习领域的开拓者。王珏研究员是此项翻译工作的十分重要的推动者。没有他的支持，没有他的众多杰出的机器学习领域的学生的帮助，可能这项工作到现在还没有结果。很遗憾王珏研究员于 2014年 12月死于癌症，终年 66岁，已不能看到他努力的结果。然而，他的思想活在他的学生们的工作中，与本书的出版同在。
Daphne Koller
（复杂系统管理与控制国家重点实验室王晓翻译）

《数论1:Fermat的梦想和类域论》起点低，但内容丰富，包括了现代数论的基本知识，如：椭圆曲线、p进数、代数数域、局部-整体方法等。该书的主要目标是证明数论的顶峰之一：类域论。在以往的数论书籍中，代数数论、椭圆曲线、类域论是分开的三《数论1:Fermat的梦想和类域论》，但《数论1:Fermat的梦想和类域论》在有限的篇幅内，将三者巧妙地融为一体，使读者能很快地达到数论的一个顶峰。开篇通过介绍Fermat的工作，给出了现代数论的一些定理的背景和意义。对于初学者难以掌握的类域论，专门有一章介绍类域论的背景和主要定理的意义。类域论的主要定理通过应用函数计算Brauer群而得到证明。《数论1:Fermat的梦想和类域论》的另一特点是先承认一些结论，然后推导出一些进一步的结果，而将它们的证明放在一起一个一个地进行。
《数论1:Fermat的梦想和类域论》的第零章通过介绍Fermat的工作和结果，从而窥见丰富的、深奥的数的世界。第一章以Fermat的工作为起点，介绍椭圆曲线的基本知识。第二章介绍p进数及二次曲线的Hasse原理。第三章介绍了涵数在整点的特殊值。这几章适合于仅知道群、环、域概念的低年级本科生。后面几章关于代数数论和类域论的内容适合于高年级本科生和研究生学习。

The P-NP problem is the most important open problem in computer science, if not all of mathematics. The Golden Ticket provides a nontechnical introduction to P-NP, its rich history, and its algorithmic implications for everything we do with computers and beyond. In this informative and entertaining book, Lance Fortnow traces how the problem arose during the Cold War on both sides of the Iron Curtain, and gives examples of the problem from a variety of disciplines, including economics, physics, and biology. He explores problems that capture the full difficulty of the P-NP dilemma, from discovering the shortest route through all the rides at Disney World to finding large groups of friends on Facebook. But difficulty also has its advantages. Hard problems allow us to safely conduct electronic commerce and maintain privacy in our online lives. The Golden Ticket explores what we truly can and cannot achieve computationally, describing the benefits and unexpected challenges of the P-NP problem.

We are in the wake of chaos - trying to make sense of the news that the universe is a far more unpredictable place than anyone ever imagined. What began with the discovery of randomness in simple physical systems - a curl of smoke, a tumble of water - has exploded into a fascination with "chaotic" models of everything from brainwaves to business cycles. Why has chaos captured so much attention? What does it do to our basic beliefs about knowledge, meaning, and our place in a suddenly turbulent world? In this provocative book, Stephen Kellert takes the first sustained look at the broad intellectual implications of chaos. Like quantum mechanics and relativity before it, chaos has an irresistible appeal as a radical new vision of reality. But how solid are its claims? Has chaos been oversold? How far can the science of chaos take us? These are just some of the intriguing questions Kellert sets out to answer. Kellert describes the challenge of chaos to traditional science - from its power to thwart the search for universal laws to its unsettling effect on such essential concepts as fact and event, cause and control. And he paints a suggestive portrait of what knowledge - with science as its source - might have to be in order to account for the profoundly counterintuitive findings of chaos. This is also the story of the coming of age of a new science. Chaotic phenomena have been observed for ages, but only recently have scientists begun to study chaos systematically. Kellert points to the deep biases for order and control that have kept the study of chaos in the background. In today's culture, however, chaos flourishes as a powerful organizing principle for those seeking to expand theboundaries of the knowable and redefine what we mean by legitimate knowledge itself. Revealing glimpses of beauty and diversity in the most routine phenomena, of order within apparent disorder, chaos is neither the new toy of media-savvy scientists and their followers nor the mystical

Manfred D. Laubichler, Science
[A] brilliant biography, one can hardly imagine a better summary of Karl Pearson's fascinating life and complicated persona. --This text refers to the Hardcover edition.
Review
John Aldrich American Scientist : Exceeds all expectations in recreating the intellectual worlds in which Pearson tried to find a home.
Manfred D. Laubichler Science : [A] brilliant biography, one can hardly imagine a better summary of Karl Pearson's fascinating life and complicated persona.
Peter J. Bowler Nature : Highlights the complex route by which [Pearson's] quest for emotional and intellectual satisfaction led him towards . . . modern statistics.
Jenny Marie Journal of the History of Biology : This book is a remarkable achievement.
Richard J. Cleary The American Statistician : Very effectively conveys . . . that . . . [statistics allows students] to see the world in a new and beautiful way.
Ramachandran Bharath MAA Reviews : Theodore Porter's Karl Pearson explores the fullness and richness of Pearson's intellectual and emotional life.

A classic series in the field of quantitative measurement, Volume I introduces the distinct mathematical results that serve to formulate numerical representations of qualitative structures. Volume II extends the subject in the direction of geometrical, threshold, and probabilistic representations, and Volume III examines representation as expressed in axiomatization and invariance. 1971 edition.

An introductory text in nonlinear dynamics and chaos, emphasizing applications in several areas of science, which include vibrations, biological rhythms, insect outbreaks, and genetic control systems. Contains a rich selection of illustrations, with many exercises and examples. Softcover.

The autobiography of mathematician Stanislaw Ulam, one of the great scientific minds of the twentieth century, tells a story rich with amazingly prophetic speculations and peppered with lively anecdotes. As a member of the Los Alamos National Laboratory from 1944 on, Ulam helped to precipitate some of the most dramatic changes of the postwar world. He was among the first to use and advocate computers for scientific research, originated ideas for the nuclear propulsion of space vehicles, and made fundamental contributions to many of today's most challenging mathematical projects. With his wide-ranging interests, Ulam never emphasized the importance of his contributions to the research that resulted in the hydrogen bomb. Now Daniel Hirsch and William Mathews reveal the true story of Ulam's pivotal role in the making of the "Super," in their historical introduction to this behind-the- scenes look at the minds and ideas that ushered in the nuclear age. An epilogue by Franoise Ulam and Jan Mycielski sheds new light on Ulam's character and mathematical originality.

In most mathematics departments at major universities one of the three or four basic first-year graduate courses is in the subject of algebraic topology. This introductory textbook in algebraic topology is suitable for use in a course or for self-study, featuring broad coverage of the subject and a readable exposition, with many examples and exercises. The four main chapters present the basic material of the subject: fundamental group and covering spaces, homology and cohomology, higher homotopy groups, and homotopy theory generally. The author emphasizes the geometric aspects of the subject, which helps students gain intuition. A unique feature of the book is the inclusion of many optional topics which are not usually part of a first course due to time constraints, and for which elementary expositions are sometimes hard to find. Among these are: Bockstein and transfer homomorphisms, direct and inverse limits, H-spaces and Hopf algebras, the Brown representability theorem, the James reduced product, the Dold-Thom theorem, and a full exposition of Steenrod squares and powers. Researchers will also welcome this aspect of the book.

We know, down to the tiniest details, the molecular structure of the human immunodeficiency virus (HIV). Yet despite this tremendous accomplishment, and despite other remarkable advances in our understanding of individual viruses and cells of the immune system, we still have no agreed understanding of the ultimate course and variability of the pathogenesis of AIDS. Gaps in our understanding like these impede our efforts towards developing effective therapies and preventive vaccines. Martin Nowak and Robert M May describe the emerging field of theoretical immunology in this accessible and well- written text. Using mathematical modelling techniques, the authors set out their ideas about how populations of viruses and populations of immune system cells may interact in various circumstances, and how infectious diseases spread within patients. They explain how this approach to understanding infectious diseases can reveal insights into the dynamics of viral and other infections, and the interactions between infectious agents and immune responses. The book is structured around the examples of HIV/AIDS and Hepatitis B virus, although the approaches described will be more widely applicable. The authors use mathematical tools to uncover the detailed dynamics of the infection and the effects of antiviral therapy. Models are developed to describe the emergence of drug resistance, and the dynamics of immune responses, viral evolution, and mutation. The practical implications of this work for optimisation of the design of therapy and vaccines are discussed. The book concludes with a glance towards the future of this fascinating, and potentially highly useful, field of study.

This famous book was the first treatise on Lie groups in which a modern point of view was adopted systematically, namely, that a continuous group can be regarded as a global object. To develop this idea to its fullest extent, Chevalley incorporated a broad range of topics, such as the covering spaces of topological spaces, analytic manifolds, integration of complete systems of differential equations on a manifold, and the calculus of exterior differential forms.
The book opens with a short description of the classical groups: unitary groups, orthogonal groups, symplectic groups, etc. These special groups are then used to illustrate the general properties of Lie groups, which are considered later. The general notion of a Lie group is defined and correlated with the algebraic notion of a Lie algebra; the subgroups, factor groups, and homomorphisms of Lie groups are studied by making use of the Lie algebra. The last chapter is concerned with the theory of compact groups, culminating in Peter-Weyl's theorem on the existence of representations. Given a compact group, it is shown how one can construct algebraically the corresponding Lie group with complex parameters which appears in the form of a certain algebraic variety (associated algebraic group). This construction is intimately related to the proof of the generalization given by Tannaka of Pontrjagin's duality theorem for Abelian groups.
The continued importance of Lie groups in mathematics and theoretical physics make this an indispensable volume for researchers in both fields.
Table of Contents:
INTRODUCTION vii
I. THE CLASSICAL LINEAR GROUPS 1
II. TOPOLOGICAL GROUPS 25
III. MANIFOLDS 68
IV. ANALYTIC GROUPS. LIE GROUPS 99
V. THE DIFFERENTIAL CALCULUS 0F CARTAN 139
VI. COMPACT LIE GROUPS AND THEIR REPRESENTATIONS 171
INDEX 215

《数学与数学人》是一套国际化的科学普及丛书，我们将邀请当代一流的中外科学家谈他们的数学人生——研究经历和成功经验。活跃在研究前沿的数学家们将会用轻松的文笔，通俗地介绍数学各领域激动人心的最新进展、某些数学专题精彩曲折的发展历史以及数学在现代科学技术中的广泛应用。

From Ancient Greek times, music has been seen as a mathematical art, and the relationship between mathematics and music has fascinated generations. This collection of wide ranging, comprehensive and fully-illustrated papers, authored by leading scholars, presents the link between these two subjects in a lucid manner that is suitable for students of both subjects, as well as the general reader with an interest in music. Physical, theoretical, physiological, acoustic, compositional, and analytical relationships between mathematics and music are unfolded and explored with focus on tuning and temperament, the mathematics of sound, bell-ringing and modern compositional techniques.