实分析的激进方法
A radical approach to real analysis
David M. Bressoud · 初版 1994 年
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“在这部 MAA 经典著作的第二版中，探索依然是核心要素。书中新增了60多道新习题，并对无穷求和、可微性与连续性以及无穷级数敛散性等章节进行了重组，以便更轻松地把握关键思想。A Radical Approach to Real Analysis 是一本实分析入门读物，其立足并取材于塑造其实分析发展的历史课题。它既可用作教材，也适合偏好讲授传统课程的教师作为参考资料，或供
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……关于数学通常教学方式的问题。例如，实分析常常被教成毫无意义的找证明过程（比如去证明那些要么毫无意义、要么显而易见的事情）。但有一本极好的书——David Bressoud 写的《实分析的激进方法》（A Radical Approach to Real Analysis），它把完全相同的知识点，作为数学家们争论了大约 100 年的那些深刻、紧迫且非显然问题的结晶来教授。
…of the way math is often taught. For example, real analysis is often taught as meaningless proof-finding (e.g. proving things that seem either pointless or obvious). But there's a fantastic book, _A Radical Approach to Real Analysis_ by David Bressoud, that teaches the exact same subject matter as the fruit of deep, pressing, and non-obvious questions that stirred debate among mathematicians for around 100 years.
我最喜欢的一本鲜有人讨论的分析学书籍是 Bressoud 写的《实分析的激进方法》。如果你喜欢读数学史和著名数学家的故事，这绝对是必读书。这里的很多人都会推荐 Rudin 或者 Royden，但我见过很多人因此被劝退……
One of my favorite not-much-talked about analysis books is "A Radical Approach to Real Analysis" by Bressoud. Must read if you enjoy reading about the history of mathematics and famous mathematicians. A lot of people here recommend Rudin or Royden, but I have seen many people become turned off to…
……例子，但提到的主题可能太具体了，你的课程里没涵盖。Elinho 的书则简明得多，如果你需要快速总结的话很适合。我还会考虑读读 David Bressoud 的《实分析的激进方法》。这是一本很棒的书，讲清了所有东西背后的历史动机，而且教学分析学的方法非常独树一帜（它肯定会对你学分析有帮助，但可能帮不上太多……
…examples, but mentions topics which may be too specific and not covered in your course. Elinho is much more terse, and great if you need a quick summary. I would also consider reading David Bressod's "A Radical Approach to Real Analysis". It's an awesome book, which mentions historical motivations for everything, and has a really different approach to teaching analysis (it will certainly help you learn analysis, but might not help too…
……它居然行得通。[0] 我脑海里浮现的画面就是 Fourier 点燃了一堆破玩意儿，手算傅里叶系数，然后就指着它们冲 Poisson 和 Lagrange 吼道：“看吧！看到没？！” [0]:《实分析的激进方法》- David Bressoud
…it seemed to work.[0] I picture this in my head as Fourier setting some shit on fire, hand calculating Fourier coefficients, then just pointing and yelling "SEE! SEE!" at Poisson and Lagrange. [0]: A Radical Approach to Real Analysis - David Bressoud
……Weierstraß 等人建立的基于现代极限的体系。真的让人非常困惑 [1]。统计学更糟糕，充斥着以前计算成本高昂时搞出来的各种老旧奇技淫巧。见 [2]。[1]《实分析的激进方法》https://www.davidbressoud.org/aratra/ [2]《统计入门课：托勒密式的课程体系？》https://escholarship.org/uc/item/6hb3k0nz
…modern limit-based field Weierstraß and others built. It's really confusing [1]. Statistics is even worse. A mix of old tricks developed to avoid computations when these were expensive. See [2]. [1] A Radical Approach to Real Analysis https://www.davidbressoud.org/aratra/ [2] The Introductory Statistics Course: A Ptolemaic Curriculum? https://escholarship.org/uc/item/6hb3k0nz