街斗数学
Street-fighting mathematics
Sanjoy Mahajan · 初版 2010 年
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38位读者提及
40次提及
为什么值得读
- 展示保留物理单位在抽象数学中的妙用
- 培养科学与工程中的快速直觉推导能力
- 提供开放获取资源且包含大量实用技巧
在解决问题时，正如在街头格斗中一样，规则是给傻瓜制定的：只要管用就行——别傻站在那里！然而，即使不合常规的飞跃可能让我们得出正确的结果，我们却常常对此心存恐惧。传统的数学教学主要是精确地解决表述精确的问题，但现实生活往往抛给我们一些定义不完全的问题，只需要适度精确的解即可。这本引人入胜的著作是一剂解药，用来破除因过度的数学严谨性而带来的僵化，教导我们如何在不需要证明或精确计算的情况下猜测出答案。在 Street-Fighting Mathematics 中，Sanjoy Maha
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……就跟说 1m=1=$1 一样毫无意义。确实，抽象数学经常省去单位，因为有些东西（比如泰勒级数）在特定单位下运算很方便。但这并不意味着单位毫无意义。桑乔伊·马哈詹（Sanjoy Mahajan）的论文/书《街头数学》（Street-Fighting Mathematics）展示了如果你不忘掉单位，在抽象数学里能玩出多么惊人的操作。
…is just as senseless as saying 1m=1=$1. It's true that abstract math often drops units because some things (like Taylor series) work nicely in certain units. That doesn't make the unit meaningless. Street-Fighting Mathematics, thesis/book by Sanjoy Mahajan, shows what amazing things you can die in abstract math if you don't forget units.
如果你想锻炼这类技能，可以试试：MIT 的 Sanjoy Mahajan 写的《Street-Fighting Mathematics》[1] 和《The Art of Insight in Science and Engineering》[2]。免费下载地址：[1] https://mitpress.mit.edu/books/street-fighting-mathematics [2] https://mitpress.mit.edu/books/art-insight-science-and-engin...
If you want to practice skills like these, try: Street-Fighting Mathematics [1] and The Art of Insight in Science and Engineering by Sanjoy Mahajan (MIT) [2]. Free downloads via: [1] https://mitpress.mit.edu/books/street-fighting-mathematics [2] https://mitpress.mit.edu/books/art-insight-science-and-engin...
奥威尔那本书的结构是由出版商决定的，但我依然很喜欢它的内容。我之所以那么类比，是因为纳闷为什么简介非得踩一脚纯数学来给《街头数学》（Street Fighting Mathematics）做宣传。不过就像奥威尔的书一样，《街头数学》的内容看起来确实很有意思，不管他们出于什么原因非要把它当成针对普通数学的“解药”。
Orwell's book's structure was dictated by the publishers, but I still love the content. My allusion was because I am wondering why the description needs to insult pure mathematics in order to promote Street Fighting Mathematics. And similarly to Orwell's book, it seems like Street Fighting Mathematics does actually have interesting content, despite whatever the reason may be that they need an "antidote" for general mathematics.
HN 上之前提过好几次的免费资源：桑乔伊·马哈詹写的《街头数学》（Street-Fighting Mathematics）。https://mitpress.mit.edu/books/street-fighting-mathematics 点击“open access”就能拿到 PDF 链接。
Free resource that has come up a few times on HN in the past: Street-Fighting Mathematics by Sanjoy Mahajan. https://mitpress.mit.edu/books/street-fighting-mathematics Click on "open access" to get to the PDF link.
试试桑乔伊·马哈詹的《街头数学》（Street-Fighting Mathematics）：https://direct.mit.edu/books/oa-monograph/5339/Street-Fighti...
Try Street-Fighting Mathematics by Sanjoy Mahajan: https://direct.mit.edu/books/oa-monograph/5339/Street-Fighti...
……管它是啥样，不断修剪雕琢，直到你的解法从黏土中成型。这完全做得到，也一定会发生。如果你曾尝试过做费米估算（Fermi Estimates）（比如这几本书里介绍的方法：https://www.amazon.com/Street-Fighting-Mathematics-Educated-... 、https://www.amazon.com/Art-Insight-Science-Engineering-Compl... 、https://web.archive.org/web/20160309161649/http://www.its.ca... 、https://www.amazon.com/How-Measure-Anything-Intangibles-Busi...）……
…however it is and keep pruning away at it until your solution is sculpted from the clay. It can and will happen. If you've ever tried doing Fermi Estimates (like those prescribed in https://www.amazon.com/Street-Fighting-Mathematics-Educated-... , https://www.amazon.com/Art-Insight-Science-Engineering-Compl... , https://web.archive.org/web/20160309161649/http://www.its.ca... , https://www.amazon.com/How-Measure-Anything-Intangibles-Busi...),…