Nov 142014
 

相比 Proofs from THE BOOK, Linear Algebra Done Right  没有那么多人注意, 但毫无疑问是一本才华横溢的书. Springer 刚出了这本书的新版: 第三版.

“Linear Algebra Done Right”(线性代数应该这样学)第三版的电子版出来才几天: 11 月 5 日. 纸质版下个月才能买到. 这是一本 “没有” 行列式的线性代数: 避开行列式探讨线性算子的结构, 处理有限维线性空间的诸多定理.

这版 Linear Algebra Done Right  非常精美, 文字色彩鲜明, 配有多幅数学家的肖像.

Nov 132014
 

Proofs from THE BOOK 有一本有名的书. Springer 刚出了这本书的新版.

第五版的 “Proofs from THE BOOK” 的封面与第四版一样, 在内容上增加了四章:

  • 数论部分增加了第 7 章: The spectral theorem and Hadamard’s determinant problem;
  • 几何部分增加了第 15 章: The Borromean rings don’t exist;
  • 组合部分增加了第 34 章: The finite Kakeya problem;
  • 组合部分增加了第 37 章: Permanents and the power of entropy.

第 7 章平淡无奇, 只不过是线性代数常见的材料, 适合刚入大学校门的新生. 为什么归入数论这个部分? 这本书看样子没把数论和代数区别.

第 15 章, 涉及到纽结, 读来趣味盎然, 可能需要一点拓扑的基础.

第 34 章, 日本数学家 Kakeya 的一个问题(挂骨问题)以及高维的推广, 与几何测度论. 问题是大名鼎鼎, 在数学的很多地方出现. 今年第二期的 “数学译林” 的第一页就讨论这个问题.

第 37 章讨论行列式和熵. 行列式恰好是 Linear Algebra Done Right 所 “刻意” 忽视的对象.

Sep 212014
 

网站出了错误, 丢失了九月份的数据. 幸好, 这个月没有多动笔写什么. 现在, 还是来推荐一本书吧, 一本旧书.

More Math Into LaTeX

More Math Into LaTeX

George Grätzer 2007 年出版了他的 More Math Into \(\rm\LaTeX\) 的第四版, 由大名鼎鼎的 Springer 推出.

This is the fourth edition of the standard introductory text and complete reference for scientists in all disciplines, as well as engineers. This fully revised version includes important updates on articles and books as well as information on a crucial new topic: how to create transparencies and computer projections, both for classrooms and professional meetings. The text maintains its user-friendly, example-based, visual approach, gently easing readers into the secrets of \(\rm\LaTeX\) with The Short Course. Then it introduces basic ideas through sample articles and documents. It includes a visual guide and detailed exposition of multiline math formulas, and even provides instructions on preparing books for publishers.

619 页, 内容可谓是相当的全面.

How to introduce \(\rm\LaTeX\) to math students?

Gratzer’s book has always excelled by taking the beginner by hand.

Jan 262014
 

北大清华高教科学这些出版社, 与国外的出版社相差太远了: 人家的内容原创上乘, 书籍杂志都提供电子版(要顾客的银子才能下载天经地义), 网站精美. 单纯从出版物的数量看, 这些出版社也远远不如.

大陆现在还是纸质书绝对称霸!

Handbook on the History of Mathematics Education” 是 Springer 新出的全面展现数学教育历史的研究成果的书: This Handbook strives to present the history of teaching and learning mathematics over the various epochs and civilizations, cultures, and countries.

Jan 252014
 

Springer 刚出来的研究 “Ancient Greek and Medieval Islamic” 的数学史书 “From Alexandria, Through Baghdad: Surveys and Studies in the Ancient Greek and Medieval Islamic Mathematical Sciences in Honor of J.L. Berggren“, 应该是文档体积最大的数学书了, 官方 PDF 达到了惊人的 \(584, 837\) KB! 这个数字很可能会继续增加! 其实, 本书的页码倒不是那么多, 不到 \(600\).

From Alexandria, Through Baghdad

From Alexandria, Through Baghdad

本书内容, 分为三个部分:

  • Part I Surveys
  • Part II Studies
  • Part III The Story of \(\mathrm \pi\)

This book honors the career of historian of mathematics J.L. Berggren, his scholarship, and service to the broader community. The first part, of value to scholars, graduate students, and interested readers, is a survey of scholarship in the mathematical sciences in ancient Greece and medieval Islam. It consists of six articles (three by Berggren himself) covering research from the middle of the 20th century to the present. The remainder of the book contains studies by eminent scholars of the ancient and medieval mathematical sciences. They serve both as examples of the breadth of current approaches and topics, and as tributes to Berggren’s interests by his friends and colleagues.

Jan 222014
 

Springer 刚刚推出了 2010 年出版的 “The Abel Prize 2003–2007” 的续集 “The Abel Prize 2008–2012“.

The Abel Prize 2008-2012

The Abel Prize 2008-2012

Covering the years 2008-2012, this book profiles the life and work of recent winners of the Abel Prize: John G. Thompson and Jacques Tits, 2008; Mikhail Gromov, 2009; John T. Tate Jr., 2010; John W. Milnor, 2011; Endre Szemerédi, 2012.

The profiles feature autobiographical information as well as a description of each mathematician’s work. In addition, each profile contains a complete bibliography, a curriculum vitae, as well as photos — old and new. As an added feature, interviews with the Laureates can be streamed from the Abel Prize web site.

The book also presents a  history of the Abel Prize written by the historian Kim Helsvig, and includes a facsimile of a letter from Niels Henrik Abel, which is transcribed, translated into English, and placed into historical perspective by Christian Skau.

Jan 092014
 

世界图书出版公司北京公司在三月会影印一些新的数学书. 下面是朕觉得不错的几本:

1. Galois Cohomology, Jean-Pierre Serre, Springer, 1997

2. Algebraic Cobordism, Marc Levine, Fabien Morel, Springer, 2007

3. Sheaves on Manifolds, Masaki Kashiwara, Pierre Schapira, Springer, 2002

4. Simplicial Homotopy Theory, Paul G. Goerss, John F. Jardine, Birkhäuser, 2009

5. The Seiberg-Witten Equations and Applications to the Topology of Smooth Four-Manifolds, John W. Morgan, Princeton University Press, 1995

6. Complex Analysis on Infinite Dimensional Spaces, Sean Dineen, Springer, 1999

7. Class Field Theory, Nancy Childress, 2nd, Springer, 2008

这些书其实都很旧了: 日期最近的 Simplicial Homotopy Theory 已经是五年前.

这里仅仅列出了七本, 很明显, 除了一本是 Princeton University 出版社授权, 其余皆来自 Springer!

由于现在书还没有面世, 目前还无法确定每本书是不是最新. 世界图书出版公司影印的书, 不一定是最新的版本, 比如前不久刚出版的第三版”Vector Calculus, Linear Algebra, and Differential Forms”, 其实这书第四版已经出来几年了, 比如 “Ideals, Varieties, and Algorithms”, 虽然第三版是最新的, 但其实 Springer 已经在新的重印本改正了很多的错误.

世界图书出版公司的出版情况, 实际也是中国学术目前窘境的缩影.

Jan 012014
 

Springer 开始出版一个新的数学系列 “Mathematical Lectures from Peking University”. 这套书是北京国际数学研究中心(Beijing International Center for Mathematical Research, 简称 BICMR)的数学讲义.

Mathematical Lectures from Peking University includes monographs, lecture notes, and proceedings based on research pursued and events held at Beijing International Center for Mathematical Research (BICMR). BICMR is a mathematical research institute sponsored by the national government of China. The center was created in 2005 by national government decree. Its goal is to build a world-class mathematical center for research and training young talents; to foster a new generation of leading world-class mathematicians in China; to support the application of mathematics in sciences and practical fields; to promote research and improve the level of mathematics education at Peking University, as well as all over China.

目前已经出版两册:

1. Conformal Field Theories and Tensor Categories: Proceedings of a Workshop Held at Beijing International Center for Mathematical

2. Some Topics in Algebra: An Advanced Undergraduate Course at PKU