《量子纠错码》内容简介：量子纠错是量子计算和量子通信得以实现的重要保证.《量子纠错码》介绍量子纠错码的基本数学概念和理论、量子纠错码和经典纠错码之间的密切联系以及构作性能良好量子码的主要数学方法。
《量子纠错码》可作为数学、通信、计算和量子物理等专业的大学生、研究生和教师的教材或教学参考书，也可供相关领域的科研人员阅读参考。

《数学符号理解手册》生动地描述了符号们的成长历程，由浅入深地概括了数学公式，枯燥的数学公式深深地印入你的脑海之中。这一篇篇的小故事幽默地囊括了从小学算术到大学微积分的一系列的数学基础知识，使你在轻松阅读的同时，大大地提高了数学综合应用的能力。读完《数学符号理解手册》，你会发现数学并不可怕，数学公式不比娱乐头条难记。

数学符号是数学文献中用以表示数学概念、数学关系等的记号。本书研究了常见的200余个符号的来龙去脉，着重探讨了常用的100多个符号的产生、发展历史。作者从卷帙浩繁的古算史书中进行考证，以史为据，自成体系，可读性强。
本书可供大、中学师生教学参考、课外阅读，也可供数学史、文化史爱好者阅读。

《混沌、Mel′nikov方法及新发展》内容简介：物理、化学、力学和生物学中物质运动的数学模型往往用微分方程所定义的连续动力系统来模拟，这些动力学模型存在着复杂的动力学行为——混沌性质。《混沌、Mel′nikov方法及新发展》介绍精确地判定Smale马蹄存在意义下具有混沌性质的Mel′nikov方法，并介绍近年来学者们所发展的同宿和异宿到耗散鞍型周期轨道的同宿和异宿缠结理论。
《混沌、Mel′nikov方法及新发展》主要面向从事动力系统应用的读者，亦可作为研究生和对常微分方程与动力系统感兴趣的人员的入门读物。

Scaling laws reveal the fundamental property of phenomena, namely self-similarity - repeating in time and/or space - which substantially simplifies the mathematical modelling of the phenomena themselves. This book begins from a non-traditional exposition of dimensional analysis, physical similarity theory, and general theory of scaling phenomena, using classical examples to demonstrate that the onset of scaling is not until the influence of initial and/or boundary conditions has disappeared but when the system is still far from equilibrium. Numerous examples from a diverse range of fields, including theoretical biology, fracture mechanics, atmospheric and oceanic phenomena, and flame propagation, are presented for which the ideas of scaling, intermediate asymptotics, self-similarity, and renormalisation were of decisive value in modelling.

In this examination of the Babylonian cuneiform "algebra" texts, based on a detailed investigation of the terminology and discursive organization of the texts, Jens Hoyrup proposes that the traditional interpretation must be rejected. The texts turn out to speak not of pure numbers, but of the dimensions and areas of rectangles and other measurable geometrical magnitudes, often serving as representatives of other magnitudes (prices, workdays, etc...), much as pure numbers represent concrete magnitudes in modern applied algebra. Moreover, the geometrical procedures are seen to be reasoned to the same extent as the solutions of modern equation algebra, though not built on any explicit deductive structure.

Reviews the most intriguing applications of fractal analysis in neuroscience with a focus on current and future potential, limits, advantages, and disadvantages. Will bring an understanding of fractals to clinicians and researchers also if they do not have a mathematical background, and will serve as a good tool for teaching the translational applications of computational models to students and scholars of different disciplines. This comprehensive collection is organized in four parts:
(1) Basics of fractal analysis;
(2) Applications of fractals to the basic neurosciences;
(3) Applications of fractals to the clinical neurosciences;
(4) Analysis software, modeling and methodology.
Series: Springer Series in Computational Neuroscience

An effort has been made to present the various topics in the theory of graphs in a logical order, to indicate the historical background, and to clarify the exposition by including figures to illustrate concepts and results. In addition, there are three appendices which provide diagrams of graphs, directed graphs, and trees. The emphasis throughout is on theorems rather than algorithms or applications, which however are occaisionally mentioned.

该书是算子代数一套三册中的第一分册，重点介绍了理论分析和拓扑方面的知识，同时使得读者容易掌握局部紧空间上算子代数和测度论之间的联系。

《最优化理论与方法》全面、系统地介绍了无约束最优化、约束最优化和非光滑最优化的理论和计算方法，它包括了近年来国际上关于优化研究的最新成果。《最优化理论与方法》在经济计划、工程设计、生产管理、交通运输等方面得到了广泛应用。

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。

《现代数学家传略辞典》由江苏教育出版社出版。

A co-publication of the AMS and the London Mathematical Society
Lie groups and algebraic groups are important in many major areas of mathematics and mathematical physics. We find them in diverse roles, notably as groups of automorphisms of geometric structures, as symmetries of differential systems, or as basic tools in the theory of automorphic forms. The author looks at their development, highlighting the evolution from the almost purely local theory at the start to the global theory that we know today. Starting from Lie's theory of local analytic transformation groups and early work on Lie algebras, he follows the process of globalization in its two main frameworks: differential geometry and topology on one hand, algebraic geometry on the other. Chapters II to IV are devoted to the former, Chapters V to VIII, to the latter.
The essays in the first part of the book survey various proofs of the full reducibility of linear representations of SL2(C)
, the contributions of H. Weyl to representations and invariant theory for semisimple Lie groups, and conclude with a chapter on E. Cartan's theory of symmetric spaces and Lie groups in the large.
The second part of the book first outlines various contributions to linear algebraic groups in the 19th century, due mainly to E. Study, E. Picard, and above all, L. Maurer. After being abandoned for nearly fifty years, the theory was revived by C. Chevalley and E. Kolchin, and then further developed by many others. This is the focus of Chapter VI. The book concludes with two chapters on the work of Chevalley on Lie groups and Lie algebras and of Kolchin on algebraic groups and the Galois theory of differential fields, which put their contributions to algebraic groups in a broader context.
Professor Borel brings a unique perspective to this study. As an important developer of some of the modern elements of both the differential geometric and the algebraic geometric sides of the theory, he has a particularly deep understanding of the underlying mathematics. His lifelong involvement and his historical research in the subject area give him a special appreciation of the story of its development.

This book is a history of complex function theory from its origins to 1914, when the essential features of the modern theory were in place. It is the first history of mathematics devoted to complex function theory, and it draws on a wide range of published and unpublished sources. In addition to an extensive and detailed coverage of the three founders of the subject - Cauchy, Riemann, and Weierstrass - it looks at the contributions of authors from d'Alembert to Hilbert, and Laplace to Weyl. Particular chapters examine the rise and importance of elliptic function theory, differential equations in the complex domain, geometric function theory, and the early years of complex function theory in several variables. Unique emphasis has been devoted to the creation of a textbook tradition in complex analysis by considering some seventy textbooks in nine different languages. The book is not a mere sequence of disembodied results and theories, but offers a comprehensive picture of the broad cultural and social context in which the main actors lived and worked by paying attention to the rise of mathematical schools and of contrasting national traditions. The book is unrivaled for its breadth and depth, both in the core theory and its implications for other fields of mathematics. It documents the motivations for the early ideas and their gradual refinement into a rigorous theory.

《基础几何学》分为八章，讲解了连结、分隔与对称－－定性平面几何；平面性与定量平面几何基础理论；圆与三角学；空间中的平行与垂直；向量几何和向量代数；坐标解析几何简介；球面几何和球面三角学；圆锥截线的故事内容。

Algebraic topology is a basic part of modern mathematics and some knowledge of this area is indispensable for any advanced work relating to geometry, including topology itself, differential geometry, algebraic geometry and Lie groups. This book provides a treatment of algebraic topology both for teachers of the subject and for advanced graduate students in mathematics either specializing in this area or continuing on to other fields. J. Peter May's approach reflects the enormous internal developments within algebraic topology, most of which are largely unknown to mathematicians in other fields. But he also retains the classical presentations of various topics where appropriate. Most chapters end with problems that further explore and refine the concepts presented. The final four chapters provide sketches of substantial areas of algebraic topology and the book concludes with a list of suggested readings for those interested in delving further into the field.