A comprehensive, self-contained treatment presenting general results of the theory. Establishes a geometric intuition and a working facility with specific geometric practices. Emphasizes applications through the study of interesting examples and the development of computational tools. Coverage ranges from analytic to geometric. Treats basic techniques and results of complex manifold theory, focusing on results applicable to projective varieties, and includes discussion of the theory of Riemann surfaces and algebraic curves, algebraic surfaces and the quadric line complex as well as special topics in complex manifolds.

Modelling with the Ito integral or stochastic differential equations has become increasingly important in various applied fields, including physics, biology, chemistry and finance. However, stochastic calculus is based on a deep mathematical theory. This text should be suitable for the reader without a deep mathematical background. It seeks to provide an elementary introduction to that area of probability theory, without burdening the reader with a great deal of measure theory. Applications are taken from stochastic finance. In particular, the Black-Scholes option pricing formula is derived.

"Simulation," writes Gary Flake in his preface, "becomes a form of experimentation in a universe of theories. The primary purpose of this book is to celebrate this fact."In this book, Gary William Flake develops in depth the simple idea that recurrent rules can produce rich and complicated behaviors. Distinguishing "agents" (e.g., molecules, cells, animals, and species) from their interactions (e.g., chemical reactions, immune system responses, sexual reproduction, and evolution), Flake argues that it is the computational properties of interactions that account for much of what we think of as "beautiful" and "interesting." From this basic thesis, Flake explores what he considers to be today's four most interesting computational topics: fractals, chaos, complex systems, and adaptation.Each of the book's parts can be read independently, enabling even the casual reader to understand and work with the basic equations and programs. Yet the parts are bound together by the theme of the computer as a laboratory and a metaphor for understanding the universe. The inspired reader will experiment further with the ideas presented to create fractal landscapes, chaotic systems, artificial life forms, genetic algorithms, and artificial neural networks.

In this renowned volume, Hermann Weyl discusses the symmetric, full linear, orthogonal, and symplectic groups and determines their different invariants and representations. Using basic concepts from algebra, he examines the various properties of the groups. Analysis and topology are used wherever appropriate. This book also covers topics such as matrix algebras, semigroups, commutators, and spinors, which are of great importance in understanding the group-theoretic structure of quantum mechanics. Hermann Weyl was among the greatest mathematicians of the twentieth century. He made fundamental contributions to most branches of mathematics, but he is best remembered as one of the major developers of group theory, a powerful formal method for analyzing abstract and physical systems in which symmetry is present.In "The Classical Groups", his most important book, Weyl provided a detailed introduction to the development of group theory, and he did it in a way that motivated and entertained his readers. Departing from most theoretical mathematics books of the time, he introduced historical events and people as well as theorems and proofs. One learned not only about the theory of invariants but also when and where they were originated, and by whom. He once said of his writing, 'My work always tried to unite the truth with the beautiful, but when I had to choose one or the other, I usually chose the beautiful'. Weyl believed in the overall unity of mathematics and that it should be integrated into other fields. He had serious interest in modern physics, especially quantum mechanics, a field to which "The Classical Groups" has proved important, as it has to quantum chemistry and other fields.Among the five books Weyl published with Princeton, "Algebraic Theory of Numbers" inaugurated the "Annals of Mathematics Studies" book series, a crucial and enduring foundation of Princeton's mathematics list and the most distinguished book series in mathematics.

《线性代数(第2版)》内容包括行列式、矩阵、n维向量与线性方程组、线性空间、矩阵的对角化、实二次型和线性变换等线性代数的基本知识以及基本线性代数问题的计算机实现，通过将线性代数的基本知识与计算机相结合使学生能利用数学软件解决一些简单的线性代数的实际问题，书末还给出了有关的 Mathematica软件的使用说明。 《线性代数(第2版)》可作为高等工科院校理工科、经济学、管理学等各专业“线性代数”课程的教材，也可供教师和学生作参考之用。

《近世代数基础》是教育部“高等教育面向21世纪教学内容和课程体系改革计划”的研究成果，是面向21世纪课程教材和普通高等教育“九五”国家级重点教材。《近世代数基础》作者在介绍近世代数课程的传统内容时，在以下各方面进行了有益的探索；强调代数系统的出现是刻画物理量和几何量的需要；较深入地介绍一些具体的群、环、域以及介绍代数的应用；注意讲授近世代数中的数学思想等。全书共四章及一个附录。第一章由刻画“对称”而引入群的概念；第二章介绍群论基础；第三章介绍环、域和模；第四章介绍有限域和Calois理论；附录介绍了计算代数几何的基石——Grobner基和Buchberser算法。 《近世代数基础》可作为高等学校数学专业的教科书，也可供相关专业师生和有关科研人员参考。

The rewards and dangers of speculating in the modern financial markets have come to the fore in recent times with the collapse of banks and bankruptcies of public corporations as a direct result of ill-judged investment. At the same time, individuals are paid huge sums to use their mathematical skills to make well-judged investment decisions. Here now is the first rigorous and accessible account of the mathematics behind the pricing, construction and hedging of derivative securities. Key concepts such as martingales, change of measure, and the Heath-Jarrow-Morton model are described with mathematical precision in a style tailored for market practitioners. Starting from discrete-time hedging on binary trees, continuous-time stock models (including Black-Scholes) are developed. Practicalities are stressed, including examples from stock, currency and interest rate markets, all accompanied by graphical illustrations with realistic data. A full glossary of probabilistic and financial terms is provided. This unique, modern and up-to-date book will be an essential purchase for market practitioners, quantitative analysts, and derivatives traders, whether existing or trainees, in investment banks in the major financial centres throughout the world.

《应用数值线性代数》共分7章,包括引论、线性方程组求解、线性最小二乘问题、非对称特征值问题、对称特征问题和奇异值分解、线性方程组迭代方法及特征值问题迭代方法，《应用数值线性代数》不仅给出了数值线性代数的常用算法，而且也介绍了多重网格法和区域分解法等新算法，并指导读者如何编写数值软件以及从何处找到适用的优秀数值软件。 《应用数值线性代数》可作为计算数学和相关理工科专业一年级研究生的教材,也可作为从事科学计算的广大科技工作者的参考书。

本书由国内著名高校长期从事运筹学教学的教师集体编写而成，其内容紧密结合经济管理专业的特点。本书自1998年正式出版以来，第1、2版的累计印数达224000册，说明其使用面之广，并深受读者欢迎。本书系统地讲述了线性规划、目标规划、整数规划、动态规划、图与网络分析、排队论、存贮论、对策论、决策论的基本概念、理论、方法和模型，以及数据包络分析、运筹学问题的启发式算法等。各章后均附有习题，以帮助复习基本知识和检查学习效果。 本书可作为高等院校经济管理类和理工类其他专业本科生、研究生的教材，也可作为工程技术人员和经济管理干部的自学参考书。 绪论 第一节　运筹学释义与发展简史 第二节　运筹学研究的基本特征与基本方法 第三节　运筹学主要分支简介 第四节　运筹学与管理科学 第一章 线性规划及单纯形法 第一节　线性规划问题及其数学模型 第二节　图解法 第三节　单纯形法原理 第四节　单纯形法计算步骤 第五节　单纯形法的进一步讨论 第六节　数据包络分析 第七节　其他应用例子 习题 第二章 线性规划的对偶理论与灵敏度分析 第一节　线性规划的对偶问题 第二节　对偶问题的基本性质 第三节　影子价格 第四节　对偶单纯形法 第五节　灵敏度分析 第六节　参数线性规划 习题 第三章　运输问题 第一节　运输问题及其数学模型 第二节　用表上作业法求解运输问题 第三节　运输问题的进一步讨论 第四节　应用问题举例 习题 第四章 目标规划 第一节　目标规划问题及其数学模型 第二节　目标规划的图解法 第三节　解目标规划的单纯形法 第四节　目标规划的灵敏度分析 第五节　目标规划应用举例 习题 第五章　整数规划 第一节　整数规划的数学模型及解的特点 第二节　解纯整数规划的割平面法 第三节　分支定界法 第四节　O—1型整数规划 第五节　指派问题 习题 第六章 非线性规划 第一节　基本概念 第二节　一维搜索 第三节　无约束极值问题 第四节　约束极值问题 习题 第七章　动态规划 第一节　多阶段决策过程的最优化 第二节　动态规划的基本概念和基本原理 第三节　动态规划模型的建立与求解 第四节　动态规划在经济管理中的应用 第五节　马氏决策规划简介 习题 第八章　图与网络分析 第一节　图与网络的基本知识 第二节　树 第三节　最短路问题 第四节　最大流问题最小费用流问题 第五节　最小费用流问题 习题 第九章　网络计划 第十章　排队论 第十一章　存贮论 第十二章　对策论 第十三章　决策分析 第十四章　运筹学中的启发式方法 参考文献

《多少只袜子是一双:生活中最鲜活的数学谜题》是一本引人入胜且令人耳目一新的数学书，包含许许多多你希望自行验证的数学理论，适合于每一个人。如果你本来就喜欢数学，你会发现大量新的惊奇；而如果你天生就讨厌数学，《多少只袜子是一双:生活中最鲜活的数学谜题》将彻底改变你对这一学科的看法。 在一个有50人参加的小型婚礼上，要找出同一天过生日的两个人，概率有多大？ 足球场的边线长100米，而球场管理员买了101长的彩带。他将彩带系紧在两端的角旗上，如果把彩带从中间举起来，高度足够让球员们入场吗？ 看似公平的“硬币抛投游戏”实际上可以让你胜率大增，你相信吗？ 多少只袜子配成一对？答案不一定总是2，你同意吗？这些问题背后的数学原理。令人既觉得惊奇，又觉得有趣；甚至还能感受到数学的美。

常微分方程基础（英文版·原书第五版），ISBN：9787111178484，作者：（美）爱德华兹、（美）彭尼

English translation of standard mathematical work on theory of numbers, first published in Latin in 1801. "Among the greatest mathematical treatises of all fields and periods."--Asger Aaboe.

数据之美（影印版），ISBN：9787564122720，作者：（美）西格兰，（美）哈梅巴赫 著

《吉米多维奇数学分析习题集题解》：数学分析是大学数学系的必修课，也是理工科高等数学的主要组成部分，更是研究生考试的必考内容。关于数学分析，最富盛名习题，莫过于前苏联数学家，鲍里斯帕夫罗维奇 吉米多维奇编写的《数学分析习题集》。但是在相当长的一段时间之内，这套书只有题目，并无标准解法，直到20世纪八十年代初由我国著名数学家费定晖，周学圣等人将其全部解出，并且反复演算，最终集结成册，由山东科学技术出版社出版，这就是在数学界大名鼎鼎的《1.Б.П.吉米多维奇数学分析习题集》。从《吉米多维奇数学分析习题集》到《吉米多维奇数学分析习题集题解》虽然两字之差，但是包含了一代数学大师们无数的心血。 直至1977年吉米多维奇去世，全套题集共计4462道，由浅入深的涵盖了数学分析题目的全部变化形式，部分习题难度很大，因此无论是自学、提高还是考研，这《吉米多维奇数学分析习题集题解5》都是适合的。 特别是费定晖、周学圣版本题解，历经三十年风雨，三次改版，各种解法已经得到了最大的优化，错误基本全部修正，是同类习题所无法模仿的。

《流形拓扑学:理论与概念的实质》是一部关于流形的拓扑学专著，较全面和系统地介绍了拓扑学大多数重要领域中的理论与方法。内容涉及微分拓扑、同调论、同伦论、微分形式与谱序列、不动点理论、Morse理论，以及向量丛的示性类理论。同时，书中也介绍了作者新发展的流形共轭结构理论，主要结果包括共轭对称性定理，上、下同调群的几何化定理，最小共轭元球面定理.在这些定理基础上，同调论和同伦论中许多重要定理与结果，如Poincare对偶，Lefschetz对偶，Kunneth公式，上、下同调群，以及Hurewicz定理等的实质及直观意义变得更清楚了。 《流形拓扑学:理论与概念的实质》适合于数学、理论物理等相关专业的高年级大学生、研究生、教师及研究人员学习和参考。

Now updated with new research and even more intuitive explanations, a demystifying explanation of how managers can inform themselves to make less risky, more profitable business decisions This insightful and eloquent book will show you how to measure those things in your own business that, until now, you may have considered "immeasurable," including customer satisfaction, organizational flexibility, technology risk, and technology ROI. Adds even more intuitive explanations of powerful measurement methods and shows how they can be applied to areas such as risk management and customer satisfaction Continues to boldly assert that any perception of "immeasurability" is based on certain popular misconceptions about measurement and measurement methods Shows the common reasoning for calling something immeasurable, and sets out to correct those ideas Offers practical methods for measuring a variety of "intangibles" Adds recent research, especially in regards to methods that seem like measurement, but are in fact a kind of "placebo effect" for management - and explains how to tell effective methods from management mythology Written by recognized expert Douglas Hubbard-creator of Applied Information Economics-"How to Measure Anything, Second Edition" illustrates how the author has used his approach across various industries and how any problem, no matter how difficult, ill defined, or uncertain can lend itself to measurement using proven methods.