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.

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

“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.

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

• 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.

Step to IMO 2014

目录

2013年全国高中数学联赛
2013年全国高中数学联赛加试

2013年第12届中国女子数学奥林匹克
2013年中国西部数学邀请赛
2013年第10届中国东南地区数学奥林匹克
2014年中国国家集训队测试
2014年中国国家队选拔考试
2014年美国数学奥林匹克
2014年俄罗斯数学奥林匹克
2014年国际数学奥林匹克(第55届IMO)

ISBN: 9787567524538

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.

Capital in the Twenty-First Century

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.

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

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

Preface
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
References
Index.

Review

“… 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