One of the most cited books in mathematics, John Milnor's exposition of Morse theory has been the most important book on the subject for more than forty years. Morse theory was developed in the 1920s by mathematician Marston Morse. (Morse was on the faculty of the Institute for Advanced Study, and Princeton published his "Topological Methods in the Theory of Functions of a Complex Variable" in the "Annals of Mathematics Studies" series in 1947.) One classical application of Morse theory includes the attempt to understand, with only limited information, the large-scale structure of an object. This kind of problem occurs in mathematical physics, dynamic systems, and mechanical engineering. Morse theory has received much attention in the last two decades as a result of a famous paper in which theoretical physicist Edward Witten relates Morse theory to quantum field theory. Milnor was awarded the Fields Medal (the mathematical equivalent of a Nobel Prize) in 1962 for his work in differential topology. He has since received the National Medal of Science (1967) and the Steele Prize from the American Mathematical Society twice (1982 and 2004) in recognition of his explanations of mathematical concepts across a wide range of scientific.c disciplines. The citation reads, "The phrase sublime elegance is rarely associated with mathematical exposition, but it applies to all of Milnor's writings. Reading his books, one is struck with the ease with which the subject is unfolding and it only becomes apparent after re.ection that this ease is the mark of a master." Milnor has published five books with Princeton University Press.

Information theory and inference, taught together in this exciting textbook, lie at the heart of many important areas of modern technology - communication, signal processing, data mining, machine learning, pattern recognition, computational neuroscience, bioinformatics and cryptography. The book introduces theory in tandem with applications. Information theory is taught alongside practical communication systems such as arithmetic coding for data compression and sparse-graph codes for error-correction. Inference techniques, including message-passing algorithms, Monte Carlo methods and variational approximations, are developed alongside applications to clustering, convolutional codes, independent component analysis, and neural networks. Uniquely, the book covers state-of-the-art error-correcting codes, including low-density-parity-check codes, turbo codes, and digital fountain codes - the twenty-first-century standards for satellite communications, disk drives, and data broadcast. Richly illustrated, filled with worked examples and over 400 exercises, some with detailed solutions, the book is ideal for self-learning, and for undergraduate or graduate courses. It also provides an unparalleled entry point for professionals in areas as diverse as computational biology, financial engineering and machine learning.

Book Description "Lang's Algebra changed the way graduate algebra is taught, retaining classical topics but introducing language and ways of thinking from category theory and homological algebra. It has affected all subsequent graduate-level algebra books." NOTICES OF THE AMS "The author has an impressive knack for presenting the important and interesting ideas of algebra in just the right way, and he never gets bogged down in the dry formalism which pervades some parts of algebra." MATHEMATICAL REVIEWS This book is intended as a basic text for a one-year course in algebra at the graduate level, or as a useful reference for mathematicians and professionals who use higher-level algebra. It successfully addresses the basic concepts of algebra. For the revised third edition, the author has added exercises and made numerous corrections to the text. (From amazon.com)

《解析几何》是学习几何学的入门教材。书中既讲解了空间解析几何的基本内容和方法（向量代数，仿射坐标系，空间的直线和平面，常见曲面等），等讲解了仿射几何学中的基本内容和思想（仿射坐标变换，二次曲线的仿射理论，仿射变换和保距变换等），还介绍了射影几何学中的基本知识，较好地反映了几何学课程的全貌。全书共分五章，每章内都附有一定数量的习题，书末附有习题答案和提示，便于读者深入学习或自学。

图论导引，ISBN：9787115161536，作者：（美）沙特朗、张萍

《经济理论中的最优化方法》(第2版)为了全面地、系统地反映当代经济学的全貌及其进程，总结与挖掘当代经济学已有的和潜在的成果，展示当代经济学新的发展方向，特此编写了《当代经济学系列丛书》，《经济理论中的最优化方法》(第2版)是其中之一。

The present volume is the first of three that will be published under the general title Lectures in lbstract fllgebra. These vol-umes are based on lectures which the author has given during the past ten years at the University of North Carolina, at The Johns Hopkins University, and at Yale University. The general plan of the work is as follows.The present first volume gives an introduction to abstract algebra and gives an account of most of the important algebraic concepts. In a treatment of this type it is impossible to give a comprehensive account of the topics which are introduced. Nevertheless we have tried to go beyond ?the foundations and elementary properties of the algebraic sys-tems. This has necessitated a certain amount of selection and omission. We feel that even at the present stage a deeper under-standing of a few topics is to be preferred to a superficial under-standing of many. 　　此书为英文版！

《让数据告诉你》用一种比较通俗的方式向大学生介绍数据分析的基础知识和基本方法，以帮助他们全面理解和正确把握数据、培养定量化的思维方式。在五彩缤纷的现实世界中，到处充斥着数字。这些数字有时会让人看得眼花缭乱，使人心绪不宁。因此，数据的收集、处理、分析尤为重要。掌握正确的数据收集、数据处理、数据分析的方法，由表及里、去伪存真，是人们在学习、生活、工作中必不可少的。 《让数据告诉你》具有以下特点：叙述浅显，书中假设《让数据告诉你》读者没有学过《高等数学》课程，所以全书没有包含任何数学公式的推导，而采用叙述的方式引入重要的概念，同时把计算公式压缩到最低的限度；案例丰富，书中大量采用案例引入主题；内容完整，《让数据告诉你》除介绍数据采集和数据分析外，还介绍了概率和数据决策方面的内容。

Optimization is an important tool used in decision science and for the analysis of physical systems used in engineering. One can trace its roots to the Calculus of Variations and the work of Euler and Lagrange. This natural and reasonable approach to mathematical programming covers numerical methods for finite-dimensional optimization problems. It begins with very simple ideas progressing through more complicated concepts, concentrating on methods for both unconstrained and constrained optimization.

《数学翻译丛书:高等微积分(修订版)》是哈佛大学的高等微积分教材，内容涵盖了从基本的向量空间概念到经典力学基本定理。包括多元微积分、外微分、微分形式的积分等。《数学翻译丛书:高等微积分(修订版)》的特点是作者从拓扑一几何的观点来写微积分。用更现代的方式讲线性代数，把线性代数与微积分紧密地结合起来，这顺应了当代数学“拓扑几何与分析结合”的发展潮流。

《高等数学》(上)是上册，本套教材是综合性大学、高等师范院校及其他理工科大学中的非教学类各专业（尤其是物理类专业）学生的高等数学教材，全书共上、下两册，上册内容是一元函数的微积分，向量代数与空间解析几何，多元函数微分学；下册内容是多元函数积分学、级数与常微分方程。 本套教材的前身《高等数学简明教程》（全三册，北京大学出版社，1998）曾荣获教育部2002年全国普通高等学校优秀教材一等奖，《高等数学》是在原书的基础上修订而成，修订内容请参看《高等数学》“序言”。 《高等数学》是作者在北京大学进行数学试点的成果，它对传统的高等数学课的内容体系作了适当的整合，力求突出数学概念与理论的实质，避免过分形式化，使读者对所讲内容感到朴实自然，《高等数学》强调数学理论与其他学科的联系，书中附有历史的注记，简要叙述相关概念和理论的发展演变过程，以及重要数学家的贡献，《高等数学》语言流畅，叙述简捷，学入浅出，有较多的例题，便于读者自学，每小节有适量习题，每章配置综合练习题，习题给出答案或提示供读者参考

本书是一本随机过程的优秀教材，不仅以浅显易懂的语言阐述基本概念和方法，而且通过一些非常基础的应用实例，让读者了解如何应用随机过程理论解决实际问题。主要内容包括有限马尔可夫链、可数马尔可夫链、连续时间马尔可夫链、最优停时、鞅、可逆马尔可夫链、布朗运动和随机积分等. 本书侧重数学思想的分析而不是具体细节的理论证明，所需的数学基础只是本科程度的概率论和一些线性代数知识，而不需要读者有测度论的基础，适合作为高等院校数学及相关专业高年级本科生和研究生教材，也适合作为相关领域研究人员的参考书.

《金融建模与投资管理中的数学》涵盖了金融和数学的广泛的技术选题——力图使投资管理实践者、研究人员和学生全面了解金融决策过程及其经济学基础。这一丰富的资源将向你介绍关键的数学技术:矩阵代数、微积分、常微分方程、概率论、随机分析、时间序列分析、优化——同肘向你展现这些技术如何在现代金融领域得到成功的使用。对那些能够帮助我们更深入地理解金融计量学和金融经济学的新的数学工具更是给予了特别的关注。对于金融计量学的最近的进展,如估计和表示分布尾部的工具、相关现象的分析、通过因素分析和协整降维等,进行了深入的讨论。 借助大量的实例,福卡尔迪和法博齐同时向我们展示了数学技术和这些技术所应用的金融领域,包括广泛的有用的金融应用,如: 套利定价 利率建模 衍生品定价 信用风险管理 股票和债券投资组合管理 风险管理及其他 《金融建模与投资管理中韵数学》、以深入的视角和专业的见解将金融理论和数学技术紧密地联系起来。

《复分析:可视化方法(英文版)》是复分析领域近年来较有影响的一本著作。作者用丰富的图例展示各种概念、定理和证明思路，十分便于读者理解，充分揭示了复分析的数学之美。书中讲述的内容有几何、复变函数变换、默比乌斯变换、微分、非欧几何、复积分、柯西公式、向量场、复积分、调和函数等。

《概率论基础》主要内容包括有：第一章：事件与概率；第二章：条件概率与统计独立性；第三章：随机变量与分布函数；第四章：数字特征与特征函数；第五章：极限定理等。

在线阅读本书 Since the publication of the first edition of this classic textbook over thirty years ago, tens of thousands of students have used A Course in Probability Theory . New in this edition is an introduction to measure theory that expands the market, as this treatment is more consistent with current courses. While there are several books on probability, Chung's book is considered a classic, original work in probability theory due to its elite level of sophistication.

《特殊函数概论》较系统地讲述了一些主要的特殊函数，如超几何函数、勒让德函数、合流超几何函数、贝塞耳函数、椭圆函数、椭球谐函数、马丢(Mathieu)函数等。同时也阐明一些在讨论特殊函数时常用的概念和理论，如关于函数的级数展开和无穷乘积展开，渐进展开，线性常微分方程的级数解法和积分解法等，在各章之末还附有习题，习题中包含了一些有用的公式作为《特殊函数概论》正文的补充。

《奇妙的数王国》一场莫名其妙的战争：“打仗啦！打仗啦！”弟弟小华一溜烟似地跑进了屋。哥哥小强正在专心做题，小华这一喊，把他吓了一跳。“哪里打仗啦？”小强问。“山那边。”小华抹了一把头上的汗，上气不接下气的说，“山那边来了两支军队，真刀真枪地打得可凶啦！哥哥，你听，这隆隆的炮声有多清楚！”小强侧耳细听，隐约的真有枪炮声。“奶奶一直不叫咱们到山那边去玩。”小强假装生气了。小华用手挠挠头，一副可怜相：“可是，能看看打仗该多有意思呀！” 本书内容：小强和小华虽说是亲兄弟，可是长相却有很大差别。哥哥小强长得又高又瘦，但是脑袋挺大，给人以“细脖大脑壳”的感觉，念初中一年级，功课学得很棒，数学曾在区里、市里的比赛中得过奖；弟弟小华却长得又矮又胖，像一个小肉球。他比哥哥小两岁，读小学五年级，好说好动，功课倒也说得过去。“哈哈，我逗你玩哪！走，咱们到山顶上看看去。”小强说完，拿起望远镜，拉着华就往山上跑。到了山顶，小强举起望远镜向山那边看。嘿，两支军队打得还挺热闹。

《数学证明之美》呈现了一些最著名的数学证明，无论对数学专家、数学迷还是非数学专家，《数学证明之美》都具有同样的吸引力。首先它让读者瞬间领会了勾股定理为什么一定是正确的；接着讲述了古代中国人对角锥体公式的证明：并学习了阿基米德求解圆面积和球体积的方法；然后探索并研究了推倒数学多米诺骨牌的微妙艺术性；探寻了如何通过对圆锥体的切分拯救一个城市，进而将人类送上月球。通过对熟知定理和公式正确性的论证。并将它们形象地展示出来，以期带领读者进入数学思想的深层次领域。