Mathematical thought from ancient to modern times
Morris Kline 的经典名著 “Mathematical thought: from ancient to modern times(古今数学思想)” 中文版由上海科学技术出版社推出了新版.
新版最大的变化就是不再是四册, 而是分三册出版. 至于书的内容, 应该没什么变化, 最大的可能就是更正排版错误.
一下子读完全书可能不是最优. 建议学习一门科目的时候, 参考阅读本大部头的相关章节.
Another name for general topology is point-set topology. 一般拓扑学又称为点集拓扑学.
1. John B. Conway, A Course in Point Set Topology, Springer, 2014
It turns out that for all their diversity, the strikingly successful groups in America today share three traits that, together, propel success. The first is a superiority complex — a deep-seated belief in their exceptionality. The second appears to be the opposite — insecurity, a feeling that you or what you’ve done is not good enough. The third is impulse control.
这是”The New York Times(纽约时报)” 25 日文章 “What Drives Success?” 的第十三个段落. 昨天(1 月 30 日, 应该是北京时间. 这一天是”纽约时报中文网” 2014 年的最后一次更新. 该网站 1 月 31 日至 2 月 6 日休刊), “纽约时报中文网”把这文章译成了中文, 标题是”成功人士的品质“. 上面那一段对应的中文是:
事实证明, 尽管存在各种差异, 如今在美国社会非常成功的族群都有三大利于成功的法宝. 首先是至上情结, 即深信自己卓尔不群. 第二点似乎刚好相反, 是缺乏安全感, 也就是觉得自己或自己的所作所为还不够好的那种感觉. 第三则是自我控制.
俺觉得第三点最不容易做到. 这就是自我管理, 自律.
美国联邦最高法院大法官 Sonia Sotomayor(June 25, 1954-) 的奋斗故事可以说明, 一个人想克服自己面临的困难, 必须得多么优秀. Sonia Sotomayor 的父母来自波多黎各. 她出生在纽约市布朗克斯区一个政府为低收入人群提供的住宅区内. 她在感人至深的自传 “我至爱的世界(My Beloved World)’中说, 父亲酗酒, 母亲“对此的办法是避免”和父亲“同时在家”. Sonia Sotomayor 9 岁那年, 父亲去世, 抛下两个孩子. 她的母亲在一家戒毒诊所当护士, 靠微薄薪水养活一家三口. 因为患有糖尿病, Sonia Sotomayor 从 8 岁左右开始就要给自己注射胰岛素, 这个过程很痛苦, 但她“有幸拥有”一种“顽强的毅力”. 她刚开始并不是尖子生. 五年级时, 她“成绩平平”. 但很快, 她的成绩就名列前茅了. 她于 1976 年至 1979 年在普林斯顿大学和耶鲁大学求学, 1979 年获得法学博士学位. 2009 年 5 月 26 日, 美国总统奥巴马提名 Sonia Sotomayor 为美国联邦最高法院大法官. 2009 年 8 月 6 日获美国参议院以 68-31 票, 通过任命 Sonia Sotomayor 为美国最高法院大法官.
Eminent Kazakh mathematician Mukhtarbay Otelbaev, Prof. Dr. has published a full proof of the Clay Navier-Stokes Millennium Problem in “Mathematical Journal” (2013, v.13 , № 4 (50))
The area of Muhtarbay Otelbaev’s scientific interests included spectral theory of operators, theory of operators’ contraction and expansion, investment theory of functional spaces, approximation theory, computational mathematics, inverse problems.
Mukhtarbay Otelbaev 已经发表超过 \(200\) 篇论文, 指导了超过 \(70\) 个博士.
[Update, Feb 7, 2014: Terence Tao 已经向 J. Amer. Math. Soc. 投了一篇论文 “Finite time blowup for an averaged three-dimensional Navier-Stokes equation”. 同时, 他也把文章传到了 arXiv: Finite time blowup for an averaged three-dimensional Navier-Stokes equation. 参看他 4 日的博客.]
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.
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
本书内容, 分为三个部分:
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.
The derivative \(\dfrac{\mathrm dy}{\mathrm dx}\) is not a ratio.
Leibniz 引进了符号 \(\dfrac{\mathrm dy}{\mathrm dx}\), 人们认为它是商: \(x\) 的改变导致的 \(y\) 的无穷小改变与 \(x\) 的无穷小改变的商.
但实际上, \(\dfrac{\mathrm dy}{\mathrm dx}\) 仅仅是一个符号, 用来表示导数, 其定义是一个极限. 我们不能把 \(\dfrac{\mathrm dy}{\mathrm dx}\) 解释为”比”.
诚然, Leibniz 的符号非常有启发性, 也很有用. 比如, 反函数定理是这么说的:
\[\frac{\mathrm dx}{\mathrm dy} = \frac1{\frac{\mathrm dy}{\mathrm dx}}.\]
这非常自然, 如若把导数理解为分数. 再如, 复合函数求导的链式法则(the Chain Rule):
\[\frac{\mathrm dz}{\mathrm dx} = \frac{\mathrm dz}{\mathrm dy}\frac{\mathrm dy}{\mathrm dx}.\]
这”显而易见”, 如果观众认为导数是分数. 这些事实显示: 导数, 其行为在许多方面来说, 又仿佛是商. 就是因为这符号如此美好, 所以才能在被保留, 并得到了广泛的使用. 但是, 我们必须记住: 导数实际不是商, 仅仅是一个极限. 隐函数定理告诉大家,
\[\frac{\mathrm dy}{\mathrm dx} = -\frac{\frac{\partial F}{\partial x}}{\frac{\partial F}{\partial y}}.\]
嗯, 这很有说服力! 我们书写 \(\frac{\mathrm dy}{\mathrm dx}\), 似乎是分数, 其行为也很像分数, 但确确实实不是分数.
首先, 实数有一个重要的性质, 所谓的 Archimedean Property: 对任意实数 \(\epsilon\gt0\), \(M\gt0\), 总存在正整数 \(n\), 使得 \(n\epsilon\gt M\). 但是, 对于”无穷小”, 不存在这样的特点.
其次, 对于曲线的切线,
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
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.