《应用近世代数》介绍群、环、域的基本理论与应用。近世代数(又名抽象代数)是现代数学的重要基础，在计算机科学、信息科学、近代物理与近代化学等方面有广泛的应用，是现代科学技术人员所必需的数学基础。

A state-of-the-art introduction to the powerful mathematical and statistical tools used in the field of finance The use of mathematical models and numerical techniques is a practice employed by a growing number of applied mathematicians working on applications in finance. Reflecting this development, Numerical Methods in Finance and Economics: A MATLAB?-Based Introduction, Second Edition bridges the gap between financial theory and computational practice while showing readers how to utilize MATLAB?--the powerful numerical computing environment--for financial applications. The author provides an essential foundation in finance and numerical analysis in addition to background material for students from both engineering and economics perspectives. A wide range of topics is covered, including standard numerical analysis methods, Monte Carlo methods to simulate systems affected by significant uncertainty, and optimization methods to find an optimal set of decisions. Among this book's most outstanding features is the integration of MATLAB?, which helps students and practitioners solve relevant problems in finance, such as portfolio management and derivatives pricing. This tutorial is useful in connecting theory with practice in the application of classical numerical methods and advanced methods, while illustrating underlying algorithmic concepts in concrete terms. Newly featured in the Second Edition: * In-depth treatment of Monte Carlo methods with due attention paid to variance reduction strategies * New appendix on AMPL in order to better illustrate the optimization models in Chapters 11 and 12 * New chapter on binomial and trinomial lattices * Additional treatment of partial differential equations with two space dimensions * Expanded treatment within the chapter on financial theory to provide a more thorough background for engineers not familiar with finance * New coverage of advanced optimization methods and applications later in the text Numerical Methods in Finance and Economics: A MATLAB?-Based Introduction, Second Edition presents basic treatments and more specialized literature, and it also uses algebraic languages, such as AMPL, to connect the pencil-and-paper statement of an optimization model with its solution by a software library. Offering computational practice in both financial engineering and economics fields, this book equips practitioners with the necessary techniques to measure and manage risk.

《应用随机过程》是现代应用随机过程教材，内容从入门知识到学术前沿，包括预备知识、随机过程的基本类型、Poisson过程、更新过程、Markov链、鞅、Brown运动、随机积分、随机微分方程及其应用和Levy过程等，《应用随机过程》配有大量与社会、经济、金融、生物等专业相关的例题和

Accessible but rigorous, this outstanding text encompasses all of the topics covered by a typical course in elementary abstract algebra. Its easy-to-read treatment offers an intuitive approach, featuring informal discussions followed by thematically arranged exercises. This second edition features additional exercises to improve student familiarity with applications. 1990 edition.

This book is intended as a textbook for a first course in the theory offunctions of one complex variable for students who are mathematicallymature enough to understand and execute arguments. The actual pre-requisites for reading this book are quite minimal; not much more than astiff course in basic calculus and a few facts about partial derivatives. Thetopics from advanced calculus that are used (e.g., Leibniz's rule for differ-entiating under the integral sign) are proved in detail.

The relationships （both conceptual and mathematical） between Bayesian analysis and statistical decision theory are so strong that it is somewhat unnatural to learn one without the other. Nevertheless, major portions of each have developed separately. On the Bayesian side, there is an extensively developed Bayesian theory of statistical inference （both subjective and objective versions）. This theory recognizes the importance of viewing statistical analysis conditionally （i.e., treating observed data as known rather than unknown）, even when no loss function is to be incorporated into the analysis. There is also a well-developed （frequentist） decision theory, which avoids formal utilization of prior distributions and seeks to provide a foundation for frequentist statistical theory. Although the central thread of the book will be Bayesian decision theory, both Bayesian inference and non-Bayesian decision theory will be extensively discussed. Indeed, the book is written so as to allow, say, the teaching of a course on either subject separately.

《凸分析(英文版)》内容简介：Convexity has been increasingly important in recent years in the studyof extremum problems in many areas of applied mathematics. The purposeof this book is to provide an exposition of the theory of convex sets andfunctions in which applications to extremum problems play the centralrole. Systems of inequalities, the minimum or maximum of a convex functionover a convex set, Lagrange multipliers, and minimax theorems are amongthe topics treated, as well as basic results about the structure of convexsets and the continuity and differentiability of convex functions and saddle-functions. Duality is emphasized throughout, particularly in the form ofFenchers conjugacy correspondence for convex functions.

《教育部高等教育司推荐•国外优秀信息科学与技术系列教学用书:数值分析(第7版)(影印版)》是在对我国高校信息科学和技术专业的课程与美国高校的进行对比分析的基础上展开的；所影印出版的教材均由我国主要高校的信息科学和技术专家组成的专家组，从国外近两年出版的大量最新教材中精心筛选评审通过的内容新、有影响的优秀教材。

本书主要讨论紧黎曼曲面，中心是Riemann-Roch定理的证明及其应用，因为黎曼曲面是近代数学不少分支的最简单的模型．本书在讨论中采用一些必要的近代数学的概念与方法作为工具，以期使本书能成为近代数学很多方面的入门书．本书可供数学专业高年级学生、研究生、数学教师及其它数学工作者参今

Knots are familiar objects. We use them to moor our boats, to wrap our packages, to tie our shoes. Yet the mathematical theory of knots quickly leads to deep results in topology and geometry. "The Knot Book" is an introduction to this rich theory, starting with our familiar understanding of knots and a bit of college algebra and finishing with exciting topics of current research. "The Knot Book" is also about the excitement of doing mathematics. Colin Adams engages the reader with fascinating examples, superb figures, and thought-provoking ideas. He also presents the remarkable applications of knot theory to modern chemistry, biology, and physics. This is a compelling book that will comfortably escort you into the marvelous world of knot theory. Whether you are a mathematics student, someone working in a related field, or an amateur mathematician, you will find much of interest in "The Knot Book".Colin Adams received the Mathematical Association of America (MAA) Award for Distinguished Teaching and has been an MAA Polya Lecturer and a Sigma Xi Distinguished Lecturer. Other key books of interest available from the "AMS" are "Knots and Links" and "The Shoelace Book: A Mathematical Guide to the Best (and Worst) Ways to Lace your Shoes".

This comprehensive history traces the development of mathematical ideas and the careers of the mathematicians responsible for them. Volume 1 looks at the discipline's origins in Babylon and Egypt, the creation of geometry and trigonometry by the Greeks, and the role of mathematics in the medieval and early modern periods. Volume 2 focuses on calculus, the rise of analysis in the 19th century, and the number theories of Dedekind and Dirichlet. The concluding volume covers the revival of projective geometry, the emergence of abstract algebra, the beginnings of topology, and the influence of Godel on recent mathematical study.

本书实例丰富，涉及多学科各种概率模型。主要内容有随机变量、条件概率及条件期望、离散及连续马尔科夫链、指数分布、泊松过程、布朗运动及平稳过程、更新理论及排队论等，最后介绍了随机模拟。本书写得极其生动和直观，并附有大量的不同领域的习题和实用的例子。　　本书可作为概率论与统计，计算机科学、保险学、物理学和社会科学、生命科学、管理科学与工程学专业随机过程基础课教材。

科学与方法，ISBN：9787100048385，作者：（法）昂利·彭加勒

纵观数学发展史，这类重要的、有价值的数学问题可谓不胜枚举。而我们《好的数学:“下金蛋”的数学问题》所要介绍的正是从代数、几何、图论、数论中采撷出的6个这类经典数学问题。在第一章中，我们介绍多项式方程根式解问题。这一问题涉及的是代数的中心问题——解方程。而通过对这一问题的介绍，我们将看到代数学是如何随着这一问题的研究一步一步发展起来的。而我们还将看到正是问题最终的解决，又将代数学引向了新的方向。 在第二章中，我们介绍几何三大问题，即用尺规三等分角、倍立方、化圆为方。这一问题属于平面几何。而问题的解决却要以解析几何作为工具之一。因此，我们在这一章也会简单介绍一下解析几何。 在第三章中，我们介绍欧几里得第五公设问题。这一问题同样来自欧氏平面几何，但对它的2000多年探讨的最终结果却导致了非欧几何的创立。我们还将看到，非欧几何的产生对数学的重要意义及其在相对论中的应用。 在第四章中，我们介绍四色问题。这一问题属于拓扑学或更确切说属于图论。我们将看到，诞生于数学游戏的拓扑学与图论是如何随着四色问题的研究而得到进一步发展的。而最终四色定理的计算机证明，又引发了人们对数学证明等问题的深入探讨。 在第五章中，我们介绍费马问题。这一问题属于数论。我们的介绍亦将从数论的起源开始，并简单介绍在数论早期发展中做出重要贡献的几位数学家及其工作。而最终，我们将以英国数学家怀尔斯的圆梦之旅作为这出精彩数学戏剧的尾声。我们还将从中看到，早期的数论伴随着这一问题的研究而得以扩展向新的数学分支——代数数论。 在第六章，我们介绍素数问题。这一同样属于数论的问题曾被列入“希尔伯特问题”，也可称为“希尔伯特第8问题”。自然，这是一个涵盖面非常广的问题。而我们将主要介绍数学之圣杯——黎曼猜想。这一问题与《好的数学:“下金蛋”的数学问题》前五章介绍的问题有一个重要差别，前者都是已经获解的问题，而只有黎曼猜想这一被许多数学家认为是最重要的数学问题至今仍是有待攀登的数学珠穆朗玛峰。

《21世纪普通高等教育新教材:初等数学解题方法教学研究》按照从简单到复杂，从低级到高级的顺序把数学方法分为直接方法、一般方法、数学思想方法三类，且对每种方法的特点、应用、注意事项进行了条理有序的说明，实现了数学知识和解题方法的有机结合，使得教材结构严谨、叙述简明、易教易学，并具有较强的科学性、实用性和可操作性。

《数学那玩意:自主招生秘籍》按如下模式编写：基础知识+例题+练习。在基础知识中，我先介绍一些基本的公式、定理、方法，并适当配以例题。有些时候，我会一个方法配一道题目，有时候我会先一口气将方法全说完，再举一堆例题。这是因为有些题目方法比较单一，可以专门作为某个方法的例题，但有些题目有多种方法，或者需要综合运用多种方法，这就很难将它放在某个方法下去做例子了。 例题中，我按照“分析”+“解”+“小结”的模式论述。目前市面上的大部分教辅书，都是冷冰冰的题目和答案，这固然可以激发读者思考，但有时也会让读者难以理解，不知道是怎么想到的。我也是过来人，深知读这种书的痛苦。所以，在“分析”中，我会介绍这道题的想法——应该往什么方向考虑，为什么要往这个方向考虑，有时对一些新的知识与方法先做介绍。在“解”中，展示完整的过程。在“小结”中进行一些总结。

离散数学及其应用：英文本，ISBN：9787040162301，作者：（ ）Susanna S.Epp著

最优化导论（英文版），ISBN：9787115176073，作者：（美国）（Sundaram、R、K）桑达拉姆

《高等代数(下册):大学高等代数课程创新教材》作为大学“高等代数”课程的创新教材，是国家级优秀教学团队（北京大学基础数学教学团队）课程建设的组成部分，是国家级教学名师多年来进行高等代数课程建设和教学改革的成果。 本套书以讲述线性空间和多项式环的结构及其态射为主线，遵循高等代数知识的内在规律和学生的认知规律安排内容体系，按照数学思维方式编写，着重培养数学思维能力。上册内容包括：线性方程组，行列式，n维向量空间K，矩阵的运算，欧几里得空间R，矩阵的相抵、相似，以及矩阵的合同与二次型。下册内容包括：多项式环，线性空间，线性映射，具有度量的线性空间（欧几里得空间、酉空间、正交空间和辛空间），环、域和群的概念及重要例子，以及多重线性代数。 书中每节均包括内容精华、典型例题、习题，章末有补充题（除第11章外），还特别设置了“应用小天地”板块。《高等代数(下册):大学高等代数课程创新教材》内容丰富、全面、深刻，阐述清晰、详尽、严谨，可以帮助读者在高等代数理论上和科学思维能力上都达到相当的高度。《高等代数(下册):大学高等代数课程创新教材》适合用作综合大学、高等师范院校和理工科大学的“高等代数”课程的教材，还可作为“高等代数”或“线性代数”课程的教学参考书，也是数学教师和科研工作者高质量的参考书。