直观理解分析
Understanding Analysis
Stephen Abbott · 初版 2001 年
31人推荐
38位读者提及
42次提及
为什么值得读
- 对数学分析证明的推导阐释极佳
- 阅读体验温和且不易卡壳
- 为后续学习测度论概率打下平缓基础
Introduction to the Problems in Analysis 勾勒了一门一学期的初级课程，引导学生既领会严谨求证的过程，又体会采用公理化方法研究实变量函数所带来的收获。实分析课程的目标应当是挑战并提升数学直觉，而不仅仅是对其进行验证。本书的理念是将注意力集中在赋予分析学固有魅力的问题上。Cantor set 中是否包含无理数？函数不连续点的集合可以是任意的吗？……能否……
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…Velleman 的《How to Prove It - A Structured Approach》，或者 Hammack 的《Book of Proof》（第2版，这本是免费的！）。4. 数学分析（Mathematical Analysis）：4a. 分析学的优质前置准备：Alcock 的《How to Think About Analysis》；4b. Abbott 的《Understanding Analysis》（第2版），或者 Bryant 的《Yet Another Introduction to Analysis》（有完整解答），或者 Sasane 的《The How and Why of One Variable Calculus》，或者《Mathematical Analysis - A Straightforward Approach》（第2…
…How to Prove It - A Structured Approach - Velleman OR Book of Proof (2nd ed) - Hammack (it's free!) 4. Mathematical Analysis: 4a. Good prep for Analysis: How to Think About Analysis - Alcock 4b. Understanding Analysis (2nd ed) - Abbott OR Yet Another Introduction to Analysis - Bryant (has full solutions) OR The How and Why of One Variable Calculus - Sasane OR Mathematical Analysis - A Straightforward Approach (2nd…
…做前10章里的一些习题。如果你能轻松搞定，就直接进入分析学（analysis）；如果不行，就先把这10章啃完。2）我个人最喜欢的自学书是 Abbott 的《Understanding Analysis》，尤其是如果你能搞到 solutions manual（习题解答）的话，我觉得里面对证明的解释写得特别好。3）我还推荐 Lara Alcock 的书《How to Think About Analysis》，这本书并不是教材，…
…do some exercises from the first 10 chapters. If you can do them easily, move onto analysis, if not, work through those 10 chapters first. 2) The book I personally like best for self-study is Abbott, “Understanding analysis” particularly if you can get the solutions manual, I think the explanations of the proofs are very good. 3) I would also recommend Lara Alcock’s book “How to think about analysis”, which is NOT a textbook,…
赞同楼上。如果你卡住了，把小 Rudin（little Rudin）和一本更友好的书（比如 Abbott 的《Understanding Analysis》）搭配着看，是搞懂这些内容的绝佳办法。
Echo the above. Pairing little Rudin with a more user-friendly book like Understanding Analysis by Abbott is a great way to learn the material if you get stuck.
…沉迷于绝对纯粹的数学，而且大概率只存在于学术圈里；但我感兴趣的是应用和自学。在现代教材中，考虑到你的兴趣，我会推荐看看 Abbott 的《Understanding Analysis》和 Capinski 的《Measure, Integral and Probability》，两本读起来都很顺畅，合在一起能为你提供一条通往测度论概率论（measure-theoretic probability）的平缓路径。
…in love with absolutely pure mathematics and most likely only in an academic setting, while I am interested in applications and self-studying. From modern texts, given your interests, I would look at "Understanding analysis" by Abbott and "Measure, Integral and Probability" by Capinski, both pleasant to read and together providing a not too steep path toward measure-theoretic probability.
如果你喜欢 Axler 的书，不妨看看 Abbott 的《Understanding Analysis》，同样出自 Springer UTM 系列。我觉得它涵盖的内容比 Rudin 稍微少一些（比如看 baby Rudin 的目录，我敢肯定 Abbott 没涉及勒贝格积分 Lebesgue integration），但它是一本非常棒的…
If you liked Axler, you might check out Abbott's Understanding Analysis, also in the Springer UTM series. I think it covers somewhat less than Rudin (e.g. looking at baby Rudin's contents, I'm pretty sure Abbott doesn't touch Lebesgue integration) but it's a pretty great…
我现在正用 Stephen Abbott 的《Understanding Analysis》自学分析学。强烈推荐。它的解释非常清晰，有助于建立对每个概念的直觉，而且我认为它挑的习题也都很棒。
Right now, I'm self-studying analysis with Stephen Abbott's "Understanding Analysis". I strongly recommend it. It has clear explanations that help to develop the intuition about each concept and what I think are well chosen exercises.