This 1996 book introduces students to optimization theory and its use in economics and allied disciplines. The first of its three parts examines the existence of solutions to optimization problems in Rn, and how these solutions may be identified. The second part explores how solutions to optimization problems change with changes in the underlying parameters, and the last part provides an extensive description of the fundamental principles of finite- and infinite-horizon dynamic programming. Each chapter contains a number of detailed examples explaining both the theory and its applications for first-year master's and graduate students. 'Cookbook' procedures are accompanied by a discussion of when such methods are guaranteed to be successful, and, equally importantly, when they could fail. Each result in the main body of the text is also accompanied by a complete proof. A preliminary chapter and three appendices are designed to keep the book mathematically self-contained.

"Math, Better Explained" is a clear, intuitive guide to math topics essential for high school, college and beyond. Whether you're a student, parent, or teacher, this book is your key to unlocking the aha! moments that make math truly click -- and make learning enjoyable. The book intentionally avoids mindless definitions and focuses on building a deep, natural intuition so you can integrate the ideas into your everyday thinking. Its explanations on the natural logarithm, imaginary numbers, exponents and the Pythagorean Theorem are among the most-visited in the world. The topics in Math, Better Explained include: 1. Developing Math Intuition 2. The Pythagorean Theorem 3. Pythagorean Distance 4. Radians and Degrees 5. Imaginary Numbers 6. Complex Arithmetic 7. Exponential Functions & e 8. The Natural Logarithm (ln) 9. Interest Rates 10. Understanding Exponents 11. Euler’s Formula 12. Introduction To Calculus The book is written as the author wishes math was taught: with a friendly attitude, vivid illustrations and a focus on true understanding. Learn right, not rote! Selected testimonials: "I have several books on calculus (Calculus for Dummys, Math for the Millions, etc. etc. - never was able to read them) but your explanation is what I have needed all these years." - D. Hogg, Former Principal "This is a great explanation! I am 49 years old and have never known what e is all about. It is thanks to your article that I get it and now can explain it to my son who is 13 years old..." - C. Dhaveji "I've been following you for nearly two years...I find the intuitive approach to the subject and lucid writing unparalleled." - D. Ezell About the Author Kalid Azad graduated from Princeton University and has been writing professionally for over a decade, from chapters in the best-selling "How to Program" textbooks (from Deitel, Inc.) to technical whitepapers for Microsoft, Corp. Kalid has tutored math since high school (99% percentile for SAT/GRE/GMAT) and is enamored with finding the clearest, most intuitive insights on seemingly-complicated topics. http://www.amazon.com/Math-Better-Explained-Intuition-ebook/dp/B006J5L3VU

《数学分析》(下)为下册，内容包括数项级数和广义积分；函数项级数、幂级数、富里埃级数和富里埃变换，多元函数的极限与连续、偏导数和全微分、极值理论、隐函数存在定理与函数相关；含参变量的积分和广义积分；多变量积分学（重积分、曲线积分、曲面积分和场论初步）。 《数学分析》在复旦大学数学系陈传璋等编《数学分析》（1979年版）的基础上，由作者根据近年来的教学实践作了修订，这次修订除了文字上和内容上的刊误以及改写了不定积分与定积分的部分内容外，主要是为适应教学需要，调整了部分章节的次序，并把第一版中第十章第8节"向量值函数的导数"作为附录放在书末。

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.

《数学分析》(上)系在1979年第一版基础上的修订版，作者根据近几年来教学实践作了修订。这次修订除了文字和内容上的勘误外，主要是为了适应教学的需要，调动了部分章节的次序，并且对定积分一章作了较大修改。此外，原第一版书中第十章§8向量值函数的导数一节改为附录放在书末。《数学分析》为上册。内容有：1.极限论：包括变量与函数、数列极限、函数的极限与连续等；2.单变量微分学：包括导数与微分、微分学基本定理及其应用等；3.单变量积分学：包括不定积分、定积分及其应用等。本数可作为综合大学和师范院校数学数学系的教材。

A unique collection of competition problems from over twenty major national and international mathematical competitions for high school students. Written for trainers and participants of contests of all levels up to the highest level, this will appeal to high school teachers conducting a mathematics club who need a range of simple to complex problems and to those instructors wishing to pose a "problem of the week", thus bringing a creative atmosphere into the classrooms. Equally, this is a must-have for individuals interested in solving difficult and challenging problems. Each chapter starts with typical examples illustrating the central concepts and is followed by a number of carefully selected problems and their solutions. Most of the solutions are complete, but some merely point to the road leading to the final solution. In addition to being a valuable resource of mathematical problems and solution strategies, this is the most complete training book on the market.

he present book is based on lectures given by the author at the University of Tokyo during the past ten years. It is intended as a textbook to be studied by students on their own or to be used in a course on Functional Analysis, i.e., the general theory of linear operators infunction spaces together with salient features of its application to diverse fields of modem and classical analysis. Necessary prerequisites for the reading of this book are summarized,with or without proof, in Chapter 0 under titles: Set Theory, Topological Spaces, Measure Spaces and Linear Spaces. Then, starting with the chapter on Semi-norms, a general theory of Banach and Hilbert spaces is presented in connection with the theory of generalized functions of S. L. SOBOLEV and L. SCHWARTZ. While the book is primarily addressed to graduate students, it is hoped it might prove useful to research mathematicians, both pure and applied. The reader may pass, e.g., fromChapter IX (Analytical Theory. of Semi-groups) directly to Chapter XIII (Ergodic Theory and Diffusion Theory) and to Chapter XIV (Integration of the Equation of Evolution). Such materials as "Weak Topologies and Duality in Locally Convex Spaces" and "Nuclear Spaces" are presented in the form of the appendices to Chapter V and Chapter X,respectively. These might be skipped for the first reading by those who are interested rather in the application of linear operators.

本书作者现任美国西北大学教授，多种国际权威杂志的主编、副主编。作者根据在教学、研究和咨询中的经验，写了这本适合学生和实际工作者的书。本书提供连续优化中大多数有效方法的全面的最新的论述。每一章从基本概念开始，逐步阐述当前可用的最佳技术。　　本书强调实用方法，包含大量图例和练习，适合广大读者阅读，可作为工程、运筹学、数学、计算机科学以及商务方面的研究生教材，也可作为该领域的科研人员和实际工作人员的手册。　　总之，作者力求本书阅读性强，内容丰富，论述严谨，能揭示数值最优化的美妙本质和实用价值。

My main purpose in this book is to present a unified treatment of that part of measure theory which in recent years has shown itself to be most useful for its applications in modern analysis. If I have accomplished my purpose, then the book should be found usable both as a text for students and as a source of reference for the more advanced mathematician. I have tried to keep to a minimum the amount of new and unusual terminology and notation. In the few places where my nomenclature differs from that in the existing literature of measure theory, I was motivated by an attempt to harmonize with the usage of other parts of mathematics. There are, for instance, sound algebraic reasons for using the terms "lattice" and "ring" for certain classes of sets--reasons which are more cogent than the similarities that caused Hausdorff to use "ring" and "field."

本书系统地论述了微分几何的基本知识。作者用前3章，以及第6章共计4章的篇幅介绍了流形、多重线性函数、向量场、外微分、李群和活动标架等基本知识和工具。基于上述基础知识，论述了微分几何的核心问题，即联络、黎曼几何、以及曲面论。第7章是当前十分活跃的研究领域——复流形。陈省身先生是此研究领域的大家，此章包含有作者独到、深刻的见解和简捷、有效的方法。第8章的Finsler几何是本书第2版新增加的一章，它是陈省身先生近年来一直倡导的研究课题，其中Chern联络具有突出的性质，它使得黎曼几何成为Finsler几何的特殊情形。最后两个附录，介绍了大范围曲线论和曲面论，以及微分几何与理论物理关系的论述，为这两个活跃的前沿领域提出了不少进一步的研究课题。 此书可作为高校数学与理论物理专业高年级本科生和研究生教材，也可供从事物理和数学等相关学科研究人员参考。如果从双语教学角度来考虑，它无疑也是理想的候选者。

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.

Do you want easy access to the latest methods in scientific computing? This greatly expanded third edition of Numerical Recipes has it, with wider coverage than ever before, many new, expanded and updated sections, and two completely new chapters. The executable C++ code, now printed in colour for easy reading, adopts an object-oriented style particularly suited to scientific applications. Co-authored by four leading scientists from academia and industry, Numerical Recipes starts with basic mathematics and computer science and proceeds to complete, working routines. The whole book is presented in the informal, easy-to-read style that made earlier editions so popular. Highlights of the new material include: a new chapter on classification and inference, Gaussian mixture models, HMMs, hierarchical clustering, and SVMs; a new chapter on computational geometry, covering KD trees, quad- and octrees, Delaunay triangulation, and algorithms for lines, polygons, triangles, and spheres; interior point methods for linear programming; MCMC; an expanded treatment of ODEs with completely new routines; and many new statistical distributions. For support, or to subscribe to an online version, please visit www.nr.com. • Most comprehensive book available on scientific computing, now updated • New routines for classification and inference HMMs and SVMs, computational geometry, ODEs, interior point methods for linear programming, and MCMC • Over 600,000 Numerical Recipes products in print Contents 1. Preliminaries; 2. Solution of linear algebraic equations; 3. Interpolation and extrapolation; 4. Integration of functions; 5. Evaluation of functions; 6. Special functions; 7. Random numbers; 8. Sorting and selection; 9. Root finding and nonlinear sets of equations; 10. Minimization or maximization of functions; 11. Eigensystems; 12. Fast Fourier transform; 13. Fourier and spectral applications; 14. Statistical description of data; 15. Modeling of data; 16. Classification and inference; 17. Integration of ordinary differential equations; 18. Two point boundary value problems; 19. Integral equations and inverse theory; 20. Partial differential equations; 21. Computational geometry; 22. Less-numerical algorithms; References.

悖论一词是“Paradox”的意译，也可叫“逆论”，或“反论”，包括逻辑学、概率论、数论、几何学、统计学和时间等六个方面的数学悖论。“悖论”这个词的意义比较丰富，它包括一切与人 的直觉和日常经验相矛盾的数学结论，那些结论会使我们惊异无比。悖论有三种主要形式。 1．一种论断看起来好像肯定是对的，但实际上却错了（似是而非型，也叫假语悖论）。 2．一种论断看起来好像肯定错了，但实际上却是对的（真言悖论或佯谬）。 3．一系列推理看起来好像无懈可击，可是却导致逻辑上自相矛盾（二难推理或叫二律相反）。

《数学科学文化理念传播丛书·经典译丛：数学经验（学习版）》第一版吸引读者去欣赏数学，深入思考数学，介入关于数学的讨论。但那里不包含问题。如果一位教师选用它，就需要补充书中缺少的东西。而学习版对教师和学生都更为方便。这里的目标是建立做题与思维之间的平衡。其中有丰富的问题，主要是由马奇绍特欧（E.A.Marchisotto）教授创设的，他还提供了大量的讨论指南、作文题目和参考文献。我们也介绍了“启发学生构思课程”，提出一系列由易到难相互联系的问题。它们提供了问题解决的额外乐趣，表明了数学的本质特征。我们用十几页的篇幅写了关于微积分运算的一节，还有一节涉及复数的有趣题目，它们无论从数学角度还是哲学角度看都是很吸引人的。

《高等数学(上册)(第4版)》第四版是在全国高校工科数学课程教学指导委员会指导下，遵照国家教委“对质量较高，基础较好，使用面较广的教材要进行锤炼”的精神，并结合修订的《高等数学课程教学基本要求》在第三版的基础上修改成的。这次修改广泛吸取了全国同行的意见，从教学角度出发进行仔细推敲，改写了一些重要概念的论述，调整了习题的配置，每章增加总习题，使内容和系统更加完整，也便于教学。 《高等数学(上册)(第4版)》分上、下两册出版。上册内容为函数与极限、导数与微分、中值定理与导数的应用、不定积分、定积分、定积分的应用、空间解析几何与向量代数等七章，书末还附有二、三阶行列式简介、几种常用的曲线、积分表、习题答案与提示。 《高等数学(上册)(第4版)》仍保持了第三版结构严谨、逻辑清晰、叙述详细、通俗浅显、例题较多、便于自学等优点，又在保证教学基本要求的前提下，扩大了适应面，增强了伸缩性，供高等工科院校不同专业的学生使用。

本书是黎曼几何的一本入门教材。本书从黎曼度量及联络出发，介绍了黎曼流形研究中的各种基本概念和技巧。以测地线的研究为重点讨论了各种形式的比较定理和Morse指数定理，同时还介绍了子流形几何学。书中也勾画了近代微分几何中的一些重大成果，如球面定理、正质量猜想以及几乎平坦流形等，最后还列举了当今微分几何研究中的一些尚待解决的问题。 本书可供大学、师范院校数学系高年级选修课教材以及研究生教材，也可供数学工作者参考。

本书最为难能可贵的是始终贯穿着强烈的应用意识，即把数学理论紧密地与政治、经济、体育、艺术、医学、生物、科技、环境等实际问题相结合，这在国内外数学教科书中是不多见的。本书内容包括集合论、数理逻辑、图论、运筹、统计、概率、排列组合、代数、几何和矩阵等。书中每一章的开始提出实际问题，然后发展必要的数学工具，解决问题，从而在应用中进一步加强对数学的理解。讨论的问题涉及日常生活，如信用卡购物、年利率计算、运动队成绩的评价等；也有著名的数学问题，如四色问题等；还有数学在高新技术中的应用。众多的应用问题使本书变得趣味横生。 　　本书主要可作为非理工类专业师生的教科书，也可作为理工类师生、工程技术人员、管理人员的参考书。

现代几何学：方法与应用（第1卷几何曲面变换群与场第5版），ISBN：9787040189469，作者：（俄）Б.А.杜布洛文、С.П.诺维可夫、А.Т.福明柯