重排微积分
Calculus Reordered
David M. Bressoud · 初版 2019 年
6人推荐
6位读者提及
6次提及
《Calculus Reordered》带领读者踏上一段跨越数百年的非凡旅程，讲述了微积分如何演变成我们今天所熟知的面貌。David Bressoud解释了为什么微积分在17世纪被归功于Isaac Newton和Gottfried Leibniz，以及它目前的结构是如何建立在19世纪发展的基础之上的。Bressoud认为，遵循微积分历史演进轨迹的教学法为学生学习这一迷人的数学领域提供了一条更为稳健的途径。深入探讨微积分在地中海东部希腊化时期的诞生——尤其
Hacker News 上怎么说
正在加载完整评论……
要是想搞“严肃”研究——数学方面有大把好书，梳理了几个世纪以来方法论的演变——我读过 David Bressoud 的《微积分的重塑》（Calculus Reordered）和 John Stillwell 的《数学及其历史》（Mathematics and it's history），两本都极力推荐。至于物理学，领域太广了，很难说从哪儿下手。关于量子物理，Jim Baggot 的《量子…
For "serious" studies - for mathematics there are lot of really good books that go through the evolution of the methodologies over the centuries - I've read David Bressoud's "Calculus Reordered" and John Stillwell's "Mathematics and it's history" and can recommend both. For physics the field is so wide it's hard to pinpoint where to start. On Quantum Physics Jim Baggot's "The meaning of Quantum…
……习题，而他的第二本则包含大量物理内容。这些书都偏重文字叙事，并穿插着历史。我觉得这四本都超级引人入胜。微积分：《微积分的重塑：大思想的历史》https://www.amazon.com/Calculus-Reordered-History-Big-Ideas/... https://www.amazon.com/Second-Year-Calculus-Undergraduate-Ma... 分析学：https://www.amazon.com/Approach-Analysis-Mathematical-Associ... https://www.amazon.com/Lebesgues-Integration-Mathematical-As...
…exercises and his second one has a lot of physics. They are all heavy on written narrative and interlaced with history. I find all four of them absolutely fascinating. Calculus: https://www.amazon.com/Calculus-Reordered-History-Big-Ideas/... https://www.amazon.com/Second-Year-Calculus-Undergraduate-Ma... Analysis: https://www.amazon.com/Approach-Analysis-Mathematical-Associ... https://www.amazon.com/Lebesgues-Integration-Mathematical-As...
……就像树形算法一样。如果你有一个对数复杂度的处理过程，输入量暴增一百万倍，实际工作量其实只增加了6倍。所以 log 也就是一个数字里零的个数。有本书叫 Bressoud 写的《微积分的重塑》，里面也讲了纳皮尔对数/自然对数 ln(x)
…like tree algos. If you have a logarithmic process and work increases by a million new inputs then actual work is only 6x increase. So log is also the number of zeros in a number There's a book called Calculus Reordered by Bressoud that described Napier logs/natural ln(x) too
我目前正在读 David M Bressoud 写的《微积分的重塑：大思想的历史》（Calculus Reordered: A history of the big ideas），它真的帮我理清了微积分里所有古怪特性的来龙去脉。之前它确实给人一种东拼西凑、到处严丝合缝不起来的大杂烩感觉，原本需要……
I'm currently reading "Calculus Reordered: A history of the big ideas" by David M Bressoud, which really helped me contextualise all the peculiarities of calculus. It really does feel like a hodgepodge of poorly fitting parts that could use…
> 但你到底应该先学积分还是先学微分？在读 David M. Bressoud 那本极棒的《微积分的重塑》之前，我从没考虑过这种学法。哈，我是从 Ivan Niven 1961 年版的《微积分入门导论》（CALCULUS An Introductory Approach）里先学的积分，那是我小时候在我爸大学工程学教材的阁楼堆里翻出来的。当我后来……
> But should you learn integration before differentiation? I’d never considered this approach until I read David M. Bressoud’s fantastic book Calculus Reordered, Ha, I learned calculus integration first from Ivan Niven's "CALCULUS An Introductory Approach," copyright 1961, that as a kid I found in the attic in my dads undergrad engineering books. When I got…
……可以推荐/提及的：[0] 《烧掉数学书：为你自己重塑数学》（Burn Math Class: And Reinvent Mathematics for Yourself），从 1+1 一路讲到导数和积分。是我最喜欢的数学去神秘化和教学法作品。[1] 《微积分的重塑：大思想的历史》（Calculus Reordered: A History of the Big Ideas），今年刚出的，完全如书名所示。一部通俗易懂的通史，讲述了每个概念登上历史舞台的过程。我才刚开始读，但绝对是……
…can recommend/mention: [0] "Burn Math Class: And Reinvent Mathematics for Yourself" Goes from 1+1 all the way to derivatives and integrals. My favorite work of math demystification and pedagogy. [1] "Calculus Reordered: A History of the Big Ideas" Released this year, exactly as the title says. An accessible history, explaining each idea as it enters the world stage. I've only just started this, but it's a definitely…