Oct 172015

找一本这个书非常非常的困难. 本站好不容易找到了一本, 封面是这个样子的:

Triangle Centers and Central Triangles

Triangle Centers and Central Triangles

“Triangle Centers and Central Triangles” 在近几年欧氏平面几何的研究论文中, 引用频率很高. 这是加拿大 Utilitas Mathematica Publishing Inc 出版社的杂志 “Congressus Numerantium” 1998年的第 129 卷, 讨论了三角形的 400 多个特殊点的性质.

这本书的详细信息, 可以参阅作者 Clark Kimberling 的主页 Triangle Centers and Central Triangles


  1. The Launch Pad: Traditional Triangle Geometry
  2. Definitions
  3. Centers 1 to 180
  4. Centers 181 to 360
  5. Central Lines
  6. Central Triangles
  7. Classes of Triangles
  8. Circles and Other Curves
  9. New Kinds of Problems
 Posted by at 12:23 am
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.

Oct 062014
Step to IMO 2014

Step to IMO 2014

显然的一个 typo 是 151 页浦鸿铭的分数 38 写成了 39.

至于今年 IMO 的解答, 虽然第 3 题本书给出了三种办法, 但证明 3-出自浦鸿铭之手- 是利用余弦定理, 张角定理, 通过大量的计算完成, 可以看成是浪费纸张. 总体而言, 这书的写法不怎么高明.

走向IMO:数学奥林匹克试题集锦(2014)以2014年国家集训队的测试选拔题为主体, 搜集了2013年8月至2014年7月间国内主要的数学竞赛及2014年国际数学奥林匹克试题和解答, 并且附上了2014年美国和俄罗斯数学奥林匹克的试题与解答, 这些试题大都是从事数学奥林匹克教学和研究的专家们的精心创作, 其中的一些解答源自国家集训队和国家队队员, 他们的一些巧思妙解为本书增色不少.



作者: 2014年IMO中国国家集训队教练组
出版社: 华东师范大学出版社
ISBN: 9787567524538
装帧: 平装
字数: 121千字
开本: 新大32开
定价: 22 人民币元

 Posted by at 8:52 am
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.

Sep 152014

喜爱学问的人最喜爱的寻宝, 就是搜刮经典的数学书! 书店, 虽然常去, 但显然的已经越来越成为翻一翻, 体验一下的场所了.

北发图书网价格较低, 但可选的书少; 互动出版网只有国内出版社的书, 并且价格较贵; 北京

Aug 022014
Capital in the Twenty-First Century

Capital in the Twenty-First Century

当前最炙手可热的经济学书 Capital in the Twenty-First Century(二十一世纪资本论)到了

本书是凯恩斯的 “货币通论”以来最牛逼的经济学书, 在全世界引起热议. 本书的最开始应法文出版, 没有引起波澜. 但哈佛大学推出英文版本之后, 世界大惊. 诺贝尔经济学奖得主写好几篇书评, 希拉里赞成作者的观点.

21世纪资本论的中文版将于今年秋季与国内读者见面. 中信出版社拿到了中文版权, 并且邀请了国务院发展研究中心金融研究所研究员巴曙松担纲翻译, 以确保本书相关专业词汇翻译的准确性和可读性, 力求打造一部经得起时间考验的经典之作. 此外, 在中信的邀约下, 作者 Thomas Piketty 已初步定于 2014 年 11 月初来华与中国读者见面, 并讨论这本新书.

今天到的另一本书是 Erwin Kreyszig 的 Differential Geometry. 这书的写法其实很古板, 一些符号已经不怎么使用.

 Posted by at 7:37 pm
Jul 292014

I’ve just received a book named Number Theory in the Spirit of Liouville by Kenneth S. Williams.

Number Theory in the Spirit of Liouville

Number Theory in the Spirit of Liouville

Joseph Liouville is recognised as one of the great mathematicians of the nineteenth century, and one of his greatest achievements was the introduction of a powerful new method into elementary number theory. This book provides a gentle introduction to this method, explaining it in a clear and straightforward manner. The many applications provided include applications to sums of squares, sums of triangular numbers, recurrence relations for divisor functions, convolution sums involving the divisor functions, and many others. All of the topics discussed have a rich history dating back to Euler, Jacobi, Dirichlet, Ramanujan and others, and they continue to be the subject of current mathematical research. Williams places the results in their historical and contemporary contexts, making the connection between Liouville’s ideas and modern theory. This is the only book in English entirely devoted to the subject and is thus an extremely valuable resource for both students and researchers alike.

  • Demonstrates that some analytic formulae in number theory can be proved in an elementary arithmetic manner
  • Motivates students to do their own research
  • Includes an extensive bibliography

Table of Contents

1. Joseph Liouville (1809–1888)
2. Liouville’s ideas in number theory
3. The arithmetic functions \(\sigma_k(n)\), \(\sigma_k^*(n)\), \(d_{k,m}(n)\) and \(F_k(n)\)
4. The equation \(i^2+jk = n\)
5. An identity of Liouville
6. A recurrence relation for \(\sigma^*(n)\)
7. The Girard–Fermat theorem
8. A second identity of Liouville
9. Sums of two, four and six squares
10. A third identity of Liouville
11. Jacobi’s four squares formula
12. Besge’s formula
13. An identity of Huard, Ou, Spearman and Williams
14. Four elementary arithmetic formulae
15. Some twisted convolution sums
16. Sums of two, four, six and eight triangular numbers
17. Sums of integers of the form \(x^2+xy+y^2\)
18. Representations by \(x^2+y^2+z^2+2t^2\), \(x^2+y^2+2z^2+2t^2\) and \(x^2+2y^2+2z^2+2t^2\)
19. Sums of eight and twelve squares
20. Concluding remarks


“… a fascinating exploration and reexamination of both Liouville’s identities and “elementary” methods, providing revealing connections to modern techniques and proofs. Overall, the work contributes significantly to both number theory and the history of mathematics.”

J. Johnson, Choice Magazine

Publisher: Cambridge University Press (November 29, 2010)
Language: English
FORMAT: Paperback
ISBN: 9780521175623
LENGTH: 306 pages
DIMENSIONS: 227 x 151 x 16 mm
CONTAINS: 275 exercises