This text, extensively class-tested over a decade at UC Berkeley and UC San Diego, explains the fundamentals of algorithms in a story line that makes the material enjoyable and easy to digest. Emphasis is placed on understanding the crisp mathematical idea behind each algorithm, in a manner that is intuitive and rigorous without being unduly formal.

This beginning graduate textbook describes both recent achievements and classical results of computational complexity theory. Requiring essentially no background apart from mathematical maturity, the book can be used as a reference for self-study for anyone interested in complexity, including physicists, mathematicians, and other scientists, as well as a textbook for a variety of courses and seminars. More than 300 exercises are included with a selected hint set.
Contents
Part I. Basic Complexity Classes: 1. The computational model - and why it doesn’t matter; 2. NP and NP completeness; 3. Diagonalization; 4. Space complexity; 5. The polynomial hierarchy and alternations; 6. Boolean circuits; 7. Randomized computation; 8. Interactive proofs; 9. Cryptography; 10. Quantum computation; 11. PCP theorem and hardness of approximation: an introduction; Part II. Lower Bounds for Concrete Computational Models: 12. Decision trees; 13. Communication complexity; 14. Circuit lower bounds; 15. Proof complexity; 16. Algebraic computation models; Part III. Advanced Topics: 17. Complexity of counting; 18. Average case complexity: Levin’s theory; 19. Hardness amplification and error correcting codes; 20. Derandomization; 21. Pseudorandom constructions: expanders and extractors; 22. Proofs of PCP theorems and the Fourier transform technique; 23. Why are circuit lower bounds so difficult?; Appendix A: mathematical background.
Reviews
Pre-Publication Review: "This text is a major achievement that brings together all of the important developments in complexity theory. Student and researchers alike will find it to be an immensely useful resource."
Michael Sipser, MIT, author of Introduction to the Theory of Computation
Pre-Publication Review: "Computational complexity theory is at the core of theoretical computer science research. This book contains essentially all of the (many) exciting developments of the last two decades, with high level intuition and detailed technical proofs. It is a must for everyone interested in this field."
Avi Wigderson, Professor, Institute for Advanced Study, Princeton
Pre-Publication Review: "This book by two leading theoretical computer scientists provides a comprehensive,insightful and mathematically precise overview of computational complexity theory, ranging from early foundational work to emerging areas such as quantum computation and hardness of approximation. It will serve the needs of a wide audience, ranging from experienced researchers to graduate students and ambitious undergraduates seeking an introduction to the mathematical foundations of computer science. I will keep it at my side as a useful reference for my own teaching and research."
Richard M. Karp, University Professor, University of California at Berkeley

The standard rules of probability can be interpreted as uniquely valid principles in logic. In this book, E. T. Jaynes dispels the imaginary distinction between 'probability theory' and 'statistical inference', leaving a logical unity and simplicity, which provides greater technical power and flexibility in applications. This book goes beyond the conventional mathematics of probability theory, viewing the subject in a wider context. New results are discussed, along with applications of probability theory to a wide variety of problems in physics, mathematics, economics, chemistry and biology. It contains many exercises and problems, and is suitable for use as a textbook on graduate level courses involving data analysis. The material is aimed at readers who are already familiar with applied mathematics at an advanced undergraduate level or higher. The book will be of interest to scientists working in any area where inference from incomplete information is necessary.

For many applications, a randomized algorithm is either the simplest or the fastest algorithm available, and sometimes both. This book introduces the basic concepts in the design and analysis of randomized algorithms. The first part of the text presents basic tools such as probability theory and probabilistic analysis that are frequently used in algorithmic applications. Algorithmic examples are also given to illustrate the use of each tool in a concrete setting. In the second part of the book, each chapter focuses on an important area to which randomized algorithms can be applied, providing a comprehensive and representative selection of the algorithms that might be used in each of these areas. Although written primarily as a text for advanced undergraduates and graduate students, this book should also prove invaluable as a reference for professionals and researchers.

Elementary set theory accustoms the students to mathematical abstraction, includes the standard constructions of relations, functions, and orderings, and leads to a discussion of the various orders of infinity. The material on logic covers not only the standard statement logic and first-order predicate logic but includes an introduction to formal systems, axiomatization, and model theory. The section on algebra is presented with an emphasis on lattices as well as Boolean and Heyting algebras. Background for recent research in natural language semantics includes sections on lambda-abstraction and generalized quantifiers. Chapters on automata theory and formal languages contain a discussion of languages between context-free and context-sensitive and form the background for much current work in syntactic theory and computational linguistics. The many exercises not only reinforce basic skills but offer an entry to linguistic applications of mathematical concepts. For upper-level undergraduate students and graduate students in theoretical linguistics, computer-science students with interests in computational linguistics, logic programming and artificial intelligence, mathematicians and logicians with interests in linguistics and the semantics of natural language

《频率测度论》是系统研究数列伪随机性的一门基础理论，它与概率论既有密切联系，又有明显区别。全书共分为14章，所有内容可分为两大部分：一部分是与概率论相平行的内容，包括伪随机事件，全频率公式和频率Bayes公式，频率分布，频率密度，二项分布和正态分布，边际分布和独立性，期望和方差，协方差、相关系数、条件期望、线性回归和矩，频率熵和互信息，频率大数定律和中心极限定理等；另一部分是与概率论不平行的内容，包括频率收敛性和频率振动性，数列的积分，分布混沌性，自相关数列和互相关数列，随机模拟等。《频率测度论》内容精练，语言朴实，主要内容参照了概率论的研究内容和方法，是数列伪随机性应用领域的基础理论。《频率测度论》适合具有基本的微积分、概率论和差分方程知识的本科生、研究生、理工科教师和各类科研工作者阅读。

范畴论是近十年来兴起的计算机科学前沿研究打向之一，前景广阔．本
书作者对这一领域做了很多研究工作．80年末,在美国期间收集了最新的有
关资料．在此基础上写成的本书反映了范畴论作为工具应用于计算机科学的
最新情况．
书中首先介绍代数规范的基本知识和一些泛代数的知识，然后系统地介
绍了范畴论的主要内容：范畴、函子、自然变换、积与和、极限和余极限、伴随、
笛卡儿封闭的范畴和素描等，并通过很多例子．介绍了范畴论在程序设计语
言的语义、λ演算、论域理论、演绎系统和形式规范等方面的应用．各章节岳
面附有习题．
本书可作为计算机专业的高年级本科生、研究生的教材．亦可供从事计
算机科学研究和开发的科技人员参考．

《范畴论》作者在书中使用的是现代范畴论通用的概念和术语，但是在对一些基本概念和理论的处理过程中，作者尝试使用比较简洁直接的方法，避免烦琐的论述。《范畴论》的前3章是范畴论的基础内容，适合高年级本科生和研究生的教学以及科研人员对范畴论基础知识的需要，第4章可供从事代数拓扑学尤其是同调代数研究的研究生和科研人员学习和参考，第5章既可以为从事代数几何的科研人员参考，同时也可为希望进一步学习Topos理论的读者提供层论方面的预备知识。

数学译林——国际数学进展
国内唯一的综合性数学译刊。精选国际各类数学刊物中有关数学发展趋势与现状、数学教学、数学争鸣、数学史及人物传记的重要文章。
《数学译林》自1980年创刊以来，得到数学界各方面人士及广大读者的支持与帮助，我们仅向爱护和鼓励本刊的各界人士致意！
《数学译林》是综合性学术刊物，介绍国外数学最新进展、现代数学知识、各种数学观点、数学史及人物传记资料，以促进我国数学事业的发展，加速数学人
才的培养。
《数学译林》翻译英。日、法、德、俄等多种文字的资料，选题广泛，内容丰富。数学研究工作者、大学教师、中学教师、研究生、大学生、数学爱好者都能从本刊找到感兴趣和具有保存价值的文献资料。己开设的主要栏目是。
综合报告 世界著名数学家在各种会议、讨论班及杂志上发表的对某一学科或专题的综述性文章，从中可窥见世界数学研究的潮流
学科与专题介绍 涉及数学中古老分支与新兴交叉学科或专题的现代研究内容及方法。为您了解当代数学面貌，选择研究方向提供信息。
进展简介 尽快反映数学家近期获得的重要研究成果。您能从中感知当今世界数学发展的脉搏
数 学 史 介绍重要数学分支和概念的萌发、形成与发展，对数学发展产生重大影响的事件，以及数学家集体的活动。它将使您更全面地了解和认识数学家成长发展之路。
人物与传记 杰出数学家的奋斗之路、研究方法、治学态度及生平轶事，将向您提供启迪思路的精神营养。
数学争鸣 选登数学家对数学本质、数学发展前景，数学教育改革等各种问题的见解与争论。读后能开阔眼界、活跃思想、耳目一新。
数学教育 各国各级数学教育的过去及现在、数学教育改革问题、外国数学博士资格试题等。
数学小品 为您展现数学宝库中那些晶莹的小宝石。对数学感兴趣的人，都能亲自领略它们的光彩。
本刊还不定期地开设数学哲学、数学奖与数学竞赛、书评、研究生课程设置、数学问题等栏目。
自2000年始,本刊将陆续增加国内数学信息的内容,如招考研究生,学术会议及数学出版物等方面的信息。

本书运用优美的语言和精致的图片描绘了世界著名版画艺术家埃舍尔的生平、创作以及他对版画艺术的理解。埃舍尔的许多版画都源于悖论、幻觉和双重意义。自相缠绕的怪圈是他作品中经常出现的一个主题。他努力追求图景的完备而不顾它们的不一致性，或者说让那些不可能同时在场者同时出场。借此他创造了一个颇具魅力的“不可能世界”。埃舍尔对“不可能世界”的营造极其成功，使他在世界各地拥有众多的崇拜者，其中包括很多知名科学家，比如诺贝尔奖得主李政道就非常欣赏埃舍尔的艺术作品。

数学的危机——今天数学无处不在，已经高度拜物教化的交往方式完全建立在二进制语言、新代数、素数编码等基础上，但大量的用户对此一无所知。公众对数学的看法一分为二，一边是对精英主义的礼貌地尊重——相信数学会在物理学或者技术上大有用处，认可数学作为精英选拔的标准；另一边自认“我没有数学天分”而在生活中或通过考试后与数学隔绝。
数学的美德——它纯粹、明确，不与事物状态和杂乱意见妥协，不会遮遮掩掩或含糊其辞，没有双重意义，不容欺瞒和瞎糊弄。数学的这些特性为人们提供理性训练，引导人们思考与生存，做出复杂的决定，走向“真实生活”。
拯救数学——用鲜明活泼的方式讲述数学史，大力宣扬数学的乐趣；修复数学和哲学之间的裂缝，在学前教育中同时向孩子们教授哲学和数学：5岁的孩子肯定能很好地应用无限的形而上学和集合论！

Game theory has revolutionized economics research and teaching during the past two decades. There are few undergraduate or graduate courses in which it does not form a core component. Game theory is the study of multi-decision problems and such problems occur frequently in economics. Industrial organization provides many examples where firms must consider the reactions of others. But there are many other areas in which it is applicable - from individual workers vying for promotion to countries competing or colluding to choose trade policies. Bob Gibbons provides an introduction to the branches of game theory that have been widely applied in economics. He emphasizes the applications as much as the pure theory. This not only helps to teach the theory, but also illustrates the process of model building - the process of translating an informal description of a multi-person decision situation into a formal, game theoretic problem to be analyzed. The approach aims to serve as both an introduction to those who will go on to specialize as pure game-theorists. It also introduces game theory to those who will later construct (or at least use) game-theoretic models in applied fields of economics.

This advanced text introduces the principles of noncooperative game theory - including strategic form games, Nash equilibria, subgame perfection, repeated games, and games of incomplete information - in a direct and uncomplicated style that will acquaint students with the broad spectrum of the field while highlighting and explaining what they need to know at any given point. The analytic material is accompanied by many applications, examples, and exercises.The theory of noncooperative games studies the behavior of agents in any situation where each agent's optimal choice may depend on a forecast of the opponents' choices. "Noncooperative" refers to choices that are based on the participant's perceived selfinterest. Although game theory has been applied to many fields, Fudenberg and Tirole focus on the kinds of game theory that have been most useful in the study of economic problems. They also include some applications to political science. The fourteen chapters are grouped in parts that cover static games of complete information, dynamic games of complete information, static games of incomplete information, dynamic games of incomplete information, and advanced topics.Drew Fudenberg and Jean Tirole are Professors of Economics at MIT.

向量既是一种图形，也是一种数学表达式，因而向量法的特点是数形结合，且运算有法可循，带有综
合法的技巧，呈现或蕴含坐标法的规则，是一种“价廉物美”的数学工具。沈文选、杨清桃著,王梓坤主编的《从Stewart定理的表示谈起--向量理论漫谈(精)/现代数学中的著名定理纵横谈丛书》介绍了向量的概念及运算，研究并举例说明了一些特殊数学关系的向量表示，给出了一些著名平面几何定理的向量法证
明。本书运用大篇幅介绍了如何运用向量知识处理中学代数问题、平面几何问题、立体几何问题，还介绍了向量与复数相互配合运用问题。全书中以大量的高考试题、数学竞赛试题为实例，运用向量法来求解。
本书可供初等数学、竞赛数学、教育数学研究工作者及广大数学爱好者参考，适用于广大中学数学教师、师范院校数学专业教师与学生以及高中学有余力的学生学习。

"Extremely readable recollections of the author... A rare testimony of a period of the history of 20th century mathematics. Includes very interesting recollections on the author's participation in the formation of the Bourbaki Group, tells of his meetings and conversations with leading mathematicians, reflects his views on mathematics. The book describes an extraordinary career of an exceptional man and mathematicians. Strongly recommended to specialists as well as to the general public." EMS Newsletter (1992) "This excellent book is the English edition of the author's autobiography. This very enjoyable reading is recommended to all mathematicians."Acta Scientiarum Mathematicarum (1992)

计算机程序设计艺术：英文版（第2卷 半数值算法），ISBN：9787302058151，作者：（美）Donald E. Knuth著

第1卷首先介绍编程的基本概念和技术，然后详细讲解信息结构方面的内容，包括信息在计算机内部的表示方法、数据元素之间的结构关系，以及有效的信息处理方法。此外，书中还描述了编程在模拟、数值方法、符号计算、软件与系统设计等方面的初级应用。此第3版增加了数十项简单但重要的算法和技术，并根据当前研究发展趋势在数学预备知识方面做了大量修改。

《组合预测方法有效性理论及其应用》研究预测方法的有效性理论及其应用，建立了基于不同准则的组合预测模型，在模型的构造方面，建立了基于预测有效度准则的最优组合预测模型、基于多种诱导有序加权平均算子的最优化组合预测模型、基于相关性指标的最优组合预测模型、基于非线性加权夹针的最优组合预测模型等；在模型的有效性理论的探讨方面，针对多种准则下最优组合预测提出了优性组合预测、预测方法优超和冗余等概念，给出了非劣性组合预测、优性组合预测、冗余预测方法的存在性以及冗余预测信息的判定；在模型的应用方面，探讨了组合预测技术在证券组合投资、剩余劳动力优化配置、组合赋权决策等领域的应用。