《数理逻辑基本原理与形式演算》是信息科学与技术基础丛书之一。全书共分十章，系统介绍数理逻辑的基本原理与形式演算。前五章涵盖了经典数理逻辑的核心内容，包括一阶语言的语法与模型，形式推理系统，可计算性与可表示性，哥德尔定理。后五章的内容是作者的研究心得。这部分阐述了形式理论的版本序列及其极限，修正演算系统，过程模式及其性质，以及归纳推理理论，提出了三个语言环境的思想以及元语言环境的基本原理，并描述了信息社会中科学研究的工作流程。

李明和Vitanyi的早期著作，描述复杂性入门的经典书。难能可贵的是，复旦大学的程岐把这本书翻译成了中文。

算法设计，ISBN：9787302143352，作者：（美）克林伯格（Kleinberg，J.），（）塔多斯（Tardos，E.） 著，张立昂，屈婉玲 译

It's been said that data is the new "dirt"—the raw material from which and on which you build the structures of the modern world. And like dirt, data can seem like a limitless, undifferentiated mass. The ability to take raw data, access it, filter it, process it, visualize it, understand it, and communicate it to others is possibly the most essential business problem for the coming decades. "Machine learning," the process of automating tasks once considered the domain of highly-trained analysts and mathematicians, is the key to efficiently extracting useful information from this sea of raw data. By implementing the core algorithms of statistical data processing, data analysis, and data visualization as reusable computer code, you can scale your capacity for data analysis well beyond the capabilities of individual knowledge workers. Machine Learning in Action is a unique book that blends the foundational theories of machine learning with the practical realities of building tools for everyday data analysis. In it, you'll use the flexible Python programming language to build programs that implement algorithms for data classification, forecasting, recommendations, and higher-level features like summarization and simplification. As you work through the numerous examples, you'll explore key topics like classification, numeric prediction, and clustering. Along the way, you'll be introduced to important established algorithms, such as Apriori, through which you identify association patterns in large datasets and Adaboost, a meta-algorithm that can increase the efficiency of many machine learning tasks.

本书由计算机理论领域的知名权威Michaael Sipser所撰写。他以独特的视角，系统地介绍了计算机理论的三个主要内容：自动机与语言、可计算性理论和计算复杂性理论。约大部分内容是基本的，同时对可计算性和计算复杂性理论中的某些高级内容进行了重点介绍。作者以清新的笔触、生动的语言给出了宽泛的数学原理，而没有拘泥于某些低层次的细节。在证明之前，均有“证明思路”，帮助读者理解数学形式下涵的概念。同样，对于算法描述，均以直观的文字而非伪代码给出，从而将注意力集中于算法本身，而不是某些模型。新版根据多年来使用本书的教师和学生的建议进行了改进，并对课堂测试题进行了全面的更新，每章末均有样例解答。 本书可作为计算机专业高年级本科生和研究生的教材，也可作为教师和研究人员的参考书。

《计算机视觉中的数学方法》由射影几何、矩阵与张量、模型估计3篇组成，它们是三维计算机视觉所涉及的基本数学理论与方法。射影几何学是三维计算机视觉的数学基础，《计算机视觉中的数学方法》着重介绍射影几何学及其在视觉中的应用，主要内容包括：平面与空间射影几何，摄像机几何，两视点几何，自标定技术和三维重构理论。矩阵与张量是描述和解决三维计算机视觉问题的必要数学工具，《计算机视觉中的数学方法》着重介绍与视觉有关的矩阵和张量理论及其应用，主要内容包括：矩阵分解，矩阵分析，张量代数，运动与结构，多视点张量。模型估计是三维计算机视觉的基本问题，通常涉及变换或某种数学量的估计，《计算机视觉中的数学方法》着重介绍与视觉估计有关的数学理论与方法，主要内容包括：迭代优化理论，参数估计理论，视觉估计的代数方法、几何方法、鲁棒方法和贝叶斯方法。

Appropriate for one- or two-semester, junior- to senior-level combinatorics courses. This trusted best-seller covers the key combinatorial ideas--including the pigeon-hole principle, counting techniques, permutations and combinations, Polya counting, binomial coefficients, inclusion-exclusion principle, generating functions and recurrence relations, combinatortial structures (matchings, designs, graphs), and flows in networks. The Fifth Edition incorporates feedback from users to the exposition throughout and adds a wealth of new exercises.

《小波与傅里叶分析基础(第2版)》的目的主要是向读者展示傅里叶分析和小波的许多基础知识以及在信号分析方面的应用。全书分为8章和3个附录，第0章是学习第1章至第7章的准备知识，即内积空间；第1章讲解傅里叶级数的基础知识；第2章讲解傅里叶变换；第3章介绍离散傅里叶变换及快速傅里叶变换；第4章至第7章讨论小波，重点在于正交小波的构建；附录部分则介绍稍微复杂的一些技术主题、部分习题解答及演示概念或产生图形的MATLAB代码。小波分析的应用领域十分广泛，它包括：数学领域的许多学科；信号分析、图像处理；量子力学、理论物理；军事电子对抗与武器的智能化；计算机分类与识别；音乐与语言的人工合成：医学成像与诊断：地质勘探数据处理；大型机械的故障诊断等方面。 《小波与傅里叶分析基础(第2版)》适用于高校相关院系信号处理专业的研究生和本科生，也可供相关的工程技术人员参考。 点击链接进入英文版： A First Course in Wavelets with Fourier Analysis

Discrete Mathematics and its Applications is a focused introduction to the primary themes in a discrete mathematics course, as introduced through extensive applications, expansive discussion, and detailed exercise sets. These themes include mathematical reasoning, combinatorial analysis, discrete structures, algorithmic thinking, and enhanced problem-solving skills through modeling. Its intent is to demonstrate the relevance and practicality of discrete mathematics to all students. The Fifth Edition includes a more thorough and linear presentation of logic, proof types and proof writing, and mathematical reasoning. This enhanced coverage will provide students with a solid understanding of the material as it relates to their immediate field of study and other relevant subjects. The inclusion of applications and examples to key topics has been significantly addressed to add clarity to every subject. True to the Fourth Edition, the text-specific web site supplements the subject matter in meaningful ways, offering additional material for students and instructors. Discrete math is an active subject with new discoveries made every year. The continual growth and updates to the web site reflect the active nature of the topics being discussed. The book is appropriate for a one- or two-term introductory discrete mathematics course to be taken by students in a wide variety of majors, including computer science, mathematics, and engineering. College Algebra is the only explicit prerequisite.

《计算几何:算法与应用》(第2版)的前4章对几何算法进行了讨论，包括几何求交、三角剖分、线性规划等，其中涉及的随机算法也是《计算几何:算法与应用》(第2版)的一个鲜明特点。第5章至第10章介绍了多种几何结构，包括几何查找、kd树、区域树、梯形图、Voronoi图、排列、Delaunay三角剖分、区间树、优先查找树以及线段树等。第11章至第16章结合实际问题，继续讨论了若干几何算法及其数据结构，包括高维凸包、空间二分及BSP树、运动规划、网格生成及四叉树、最短路径查找及可见性图、单纯性区域查找及划分树和切分树等，这些也是对前十章内容的进一步深化。

国内首部复杂网络专著 【图书目录】 第1章 引论 1．1 引言 1．2 复杂网络研究简史 1．3 基本概念 1．4 本书内容简介 参考文献 第2章 网络拓扑基本模型及其性质 2．1 引言 2．2 规则网络 2．3 随机图 2．4 小世界网络模型 2．5 无标度网络模型 2．6 局域世界演化网络模型 2．7 模块性与等级网络 2．8 复杂网络的自相似性 参考文献 第3章 Internet拓扑特性及建模 3．1 引言 3．2 Internet的拓扑特性 3．3 随机图产生器 3．4 结构产生器 3．5 基于连接度的产生器 3．6 多局域世界模型 3．7 各类模型的定性比较 参考文献 第4章 复杂网络上的传播机理与动力学分析 4．1 引言 4．2 复杂网络的传播临界值理论 4．3 复杂网络的免疫策略 4．4 复杂网络的传播动力学 4．5 计算机病毒在Internet上的传播 4．6 复杂网络中的其他传播现象 参考文献 第5章 复杂网络上的相继故障 5．1 引言 5．2 复杂网络相继故障的动态模型分析 5．3 基于耦合映象格子的相继故障模型 参考文献 第6章 复杂网络中的搜索 6．1 引言 6．2 社会网络搜索 6．3 几种复杂网络搜索策略分析 6．4 P2P网络中的搜索 6．5 复杂网络中的搜索和拥塞 参考文献 第7章 复杂网络中的社团结构 7．1 引言 7．2 Kernighan—Lin算法 7．3 谱平分法 7．4 分裂方法 7．5 凝聚算法 7．6 派系过滤算法 参考文献 第8章 复杂网络中的同步 8．1 引言 8．2 复杂网络的完全同步判据 8．3 复杂动力网络的完全同步 8．4 连续时间时变耦合网络完全同步 8．5 其他网络完全同步判据 8．6 复杂网络中各个因子与完全同步的关系 8．7 改进复杂网络同步的方法 8．8 复杂网络的相位同步 参考文献 第9章 复杂动态网络的控制 9．1 引言 9．2 规则网络时空混沌的牵制控制 9．3 无标度动态网络的牵制控制：鲁棒性与脆弱性 9．4 一般复杂动态网络的牵制控制 9．5 随机驱动下动态网络的有序性与动力学 参考文献 附录名词对照

《离散数学教程》共分五编。第一编为集合论，其中包括集合的基本概念、二元关系、函数、自然数、基数、序数。第二编为图论，其中包括图的基本概念、图的连通性、欧拉图与哈密顿图、树、平面图、图的着色、图的矩阵表示、覆盖集、独立集、匹配、带权图及其实用。第三编为代数结构，其中包括代数系统的基本概念、几个重要的代数系统：半群、群、环、域、格与布尔代数。第四编为组合灵敏学，其中包括组合存在性、组合计数、级合设计与编码以及组合最优化。第五编为数理逻辑，其中包括命题逻辑、一阶谓词逻辑、Her-brand定理和直觉逻辑。

Clearly written graduate-level text considers the Soviet ellipsoid algorithm for linear programming; efficient algorithms for network flow, matching, spanning trees, and matroids; the theory of NP-complete problems; approximation algorithms, local search heuristics for NP-complete problems, more. "Mathematicians wishing a self-contained introduction need look no further." -- "American Mathematical Monthly." 1982 edition..

From the Back Cover Nearly 30 years ago, John Horton Conway introduced a new way to construct numbers. Donald E. Knuth, in appreciation of this revolutionary system, took a week off from work on The Art of Computer Programming to write an introduction to Conway's method. Never content with the ordinary, Knuth wrote this introduction as a work of fiction--a novelette. If not a steamy romance, the book nonetheless shows how a young couple turned on to pure mathematics and found total happiness. The book's primary aim, Knuth explains in a postscript, is not so much to teach Conway's theory as "to teach how one might go about developing such a theory." He continues: "Therefore, as the two characters in this book gradually explore and build up Conway's number system, I have recorded their false starts and frustrations as well as their good ideas. I wanted to give a reasonably faithful portrayal of the important principles, techniques, joys, passions, and philosophy of mathematics, so I wrote the story as I was actually doing the research myself."... It is an astonishing feat of legerdemain. An empty hat rests on a table made of a few axioms of standard set theory. Conway waves two simple rules in the air, then reaches into almost nothing and pulls out an infinitely rich tapestry of numbers that form a real and closed field. Every real number is surrounded by a host of new numbers that lie closer to it than any other "real" value does. The system is truly "surreal." quoted from Martin Gardner, Mathematical Magic Show, pp. 16--19 Surreal Numbers, now in its 13th printing, will appeal to anyone who might enjoy an engaging dialogue on abstract mathematical ideas, and who might wish to experience how new mathematics is created.

The latest edition of this classic is updated with new problem sets and material The Second Edition of this fundamental textbook maintains the book's tradition of clear, thought-provoking instruction. Readers are provided once again with an instructive mix of mathematics, physics, statistics, and information theory. All the essential topics in information theory are covered in detail, including entropy, data compression, channel capacity, rate distortion, network information theory, and hypothesis testing. The authors provide readers with a solid understanding of the underlying theory and applications. Problem sets and a telegraphic summary at the end of each chapter further assist readers. The historical notes that follow each chapter recap the main points. The Second Edition features: * Chapters reorganized to improve teaching * 200 new problems * New material on source coding, portfolio theory, and feedback capacity * Updated references Now current and enhanced, the Second Edition of Elements of Information Theory remains the ideal textbook for upper-level undergraduate and graduate courses in electrical engineering, statistics, and telecommunications. An Instructor's Manual presenting detailed solutions to all the problems in the book is available from the Wiley editorial department.

【编辑推荐】 由在IBM工作50余年的资深计算机专家撰写，Amazon全五星评价，算法领域最有影响力的著作之一 Google公司首席架构师、Jolt大奖得主Hoshua Bloch和Emacs合作创始人、C语言畅销书作者Guy Steele倾情推荐 算法的艺术和数学的智慧在本书中得到了完美体现，书中总结了大量高效、优雅和奇妙的算法，并从数学角度剖析了其背后的原理 【读者评价】 “这是第一本宣称能讲解计算机算法隐晦细节的书，而且讲得还真不错。我知道的每一条技巧书里都提到了，而且还讲了好多好多我不知道的。不论是在开发程序库或编译器，还是在极力搜求优雅算法，此书都可谓天赐良册，应放在高德纳所著《计算机程序设计艺术》那套书旁边。本书第一版刊印后的10年间，它对我在Sun和Google的工作大有裨益，而第二版所添加新内容亦令我惊羡不已。” —— Joshua Bloch “初看本书书名时，我想，这是教人怎么入侵计算机系统的书吗？不太可能吧。嗯，那就肯定是一本编程小技巧的集锦。看了之后发现，没错，这就是一本编程秘籍，然而却是一本包罗万象的秘籍。第二版新增了两个大主题，并用数十个小技巧丰富了本书内容，其中有个小绝招是如何在不溢出的情况下求两数均值，我写二分查找算法时直接就把这条拿来用了。这真是本令算法爱好者开怀畅读的书啊！” —— Guy Steele 【内容简介】 在本书中，作者给我们带来了一大批极为诱人的知识，其中包括各种节省程序运行时间的技巧、算法与窍门。学习了这些技术，程序员就可写出优雅高效的软件，同时还能洞悉其中原理。这些技术极为实用，而且其问题本身又非常有趣，有时甚至像猜谜解谜一般，需要奇思妙想才行。简而言之，软件开发者看到这些改进程序效率的妙计之后，定然大喜。 本书较第1版增补了大量内容 新增了循环冗余校验（CRC）一章，其中讲解了常用的CRC-32校验码 新增了纠错码（ECC）一章，其中讲解了汉明码 详解了除数为常数的整数除法，增补了仅含移位操作和加法操作的算法 不计算商而直接求余数 扩充了与种群计数和前导0计数有关的知识 数组种群计数 执行压缩与扩展操作的新算法 LRU算法 浮点数与整数互化 估算浮点数的平方根倒数 一系列离散函数图像 各章均配有习题与参考答案

本书介绍组合数学中的基础理论和实际应用，讲述的内容非常广泛，讨论的问题涵盖组合数学所涉及的绝大部分领域。本书不仅包含了通常组合数学教科书中的经典内容，而且收集了若干新的内容，如Lovász筛法、范德瓦尔登积和式猜想、结合区组设计、码和设计等。 本书阐述深入浅出，简明易懂，适合作为高等院校高年级本科生与低年级研究生的组合数学课程教材，也适合作为数学和其他学科的研究人员的参考书。

Numerical Optimization presents a comprehensive and up-to-date description of the most effective methods in continuous optimization. It responds to the growing interest in optimization in engineering, science, and business by focusing on the methods that are best suited to practical problems.Drawing on their experiences in teaching, research, and consulting, the authors have produced a textbook that will be of interest to students and practitioners alike. Each chapter begins with the basic concepts and builds up gradually to the best techniques currently available.Because of the emphasis on practical methods, as well as the extensive illustrations and exercises, the book is accessible to a wide audience. It can be used as a graduate text in engineering, operations research, mathematics, computer science, and business. It also serves as a handbook for researchers and practitioners in the field.Above all, the authors have strived to produce a text that is pleasant to read, informative, and rigorous - one that reveals both the beautiful nature of the discipline and its practical side.MMOR Mathematical Methods of Operations Research, 2001: "The book looks very suitable to be used in an graduate-level course in optimization for students in mathematics, operations research, engineering, and others. Moreover, it seems to be very helpful to do some self-studies in optimization, to complete own knowledge and can be a source of new ideas.... I recommend this excellent book to everyone who is interested in optimization problems."

This course is offered to undergraduates and is an elementary discrete mathematics course oriented towards applications in computer science and engineering. Topics covered include: formal logic notation, induction, sets and relations, permutations and combinations, counting principles, and discrete probability.