分析之道
The way of analysis
Robert S. Strichartz · 初版 1995 年
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6位读者提及
8次提及
数学是一种思维方式。要真正透彻理解数学，绝不仅仅是掌握一系列定理、定义、习题和技巧，而是要理解定理与定义如何与全书展现的整体论证策略融会贯通。这本 real analysis 入门读物包含了详尽完备的证明，辅以生动详实的解析，引导读者领略分析学的基石与精髓。书中对单变量与多变量的 real analysis 进行了系统展开，从实数系的构建一路深入到 Lebesgue 积分的初阶介绍
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…在这方面，以下这几本书帮了我大忙：- 视觉系列。比如《Visual Complex Analysis》和《Visual Group Theory》- 平特的《近世代数基础》（A Book of Abstract Algebra）- 施特里查茨的《分析之道》- 韦尔默的《通过几何看线性代数》（Linear Algebra Through Geometry）。这本书对线性代数概念给出了非常全面的几何解释。它对我理解二次型尤其有帮助。要理解…
…For that matter, the following books helped me a lot: - The visual series. Visual Complex Analysis and Visual Group Theory, for instance - Pinter's A book of Abstract Algebra - Strichartz's The Way of Analysis - Linear Algebra Through Geometry by Wermer. The book offers a comprehensive geometric interpretation to linear algebra concepts. It's especially helpful for me to understand quadratic forms. To understand…
…持怀疑态度，但这是我的书单：* 微积分 * 实分析 * 统计力学 * 概率论。微积分我不太确定有什么好推荐的，但实分析的话，我会推施特里查茨的《分析之道》[0]。统计力学我也没啥好的推荐，因为我还没见过哪本书能不深陷物理学视角，而是纯粹去讲底层…
…skepticism, but here's my list: * Calculus * Real Analysis * Statistical Mechanics * Probability I'm not sure I have any good recommendations for Calculus, but for real analysis, I would recommend "The Way of Analysis" by Strichartz [0]. I don't have good recommendations for books on statistical mechanics, as I haven't found a book that isn't entrenched in coming from a physics perspective and teaches the underlying…
说到微积分相关的书，我很喜欢罗伯特·施特里查茨的《分析之道》。罗伯特在建立核心概念的直觉和动机方面讲得极其细致。他经常先抛出一个符合直觉但有瑕疵的想法，然后一步步修改，直到打磨成严谨成熟的定义或…
Speaking of books about calculus, I like Robert Strichartz's The Way of Analysis. Robert develops intuition and motivation of key concepts in an amazingly detailed way. He often starts with an intuitive but flawed idea, and then gradually revises the idea to a mature definition or…
…125 页全是干货，既清晰又能帮你建立直觉。想看更严谨的替代方案的话：1. 埃利亚斯·M·斯坦因的《实分析：测度论、积分与希尔伯特空间》。2. 罗伯特·S·施特里查茨的《分析之道》。就我个人而言，我会把 Baylis 那本通读，把另外两本作为参考书。此外，还可以去翻翻 mathoverflow.com 和 math.stackexchange.com 上高赞的回答。实用至极。最后，我还有…
…It's 125 pages of clarity and intuition building. More rigorous alternatives would be: 1. Elias M. Stein's 'Real Analysis: Measure Theory, Integration, and Hilbert Spaces'. 2. Robert S. Strichartz 'The Way of Analysis' Personally I would use the Baylis book and the other two as reference. Additional resources include the top voted mathoverflow.com and math.stackexchange.com answers. Beyond useful. Lastly, I have…
…按顺序推荐，这是一份我认为非常出色的书单（极其符合我个人口味）：[0] Garey 和 Johnsen 的《计算机和难解性：NP完全性理论导引》[1] 施特里查茨的《分析之道》[2] Cormen、Leiserson、Rivest 和 Stein 的《算法导论》[3] 叶秀德（Yap）的《算法代数的基本问题》[4] Butler 的《置换群的基本算法》…
…order, here are a list of books I've found exceptional (very much catered to my personal taste): [0] Computers and Intractability: A Guide to the Theory of NP-Completeness by Garey and Johnsen [1] The Way of Analysis by Strichartz [2] Introduction to Algorithms by Cormen, Leiserson, Rivest and Stein [3] Fundamental Problems of Algorithmic Algebra by Yap [4] Fundamental Algorithms for Permutation Groups by Butler…
…我猜这是个人口味问题。我去看了一下，让我特别难受的是，名义上叫‘完备性公理’，它就真的直接当成一条公理给出来了。我的分析课用的是施特里查茨的《分析之道》，它绝对算不上‘短小精悍’——老师形容它‘絮絮叨叨’——但它确实一步步把‘完备性公理’给证明出来了。对比一下完备性公理 > 任何非空…
…guess this is a matter of taste. I went to look at this and it really bothers me that, true to the name they give, the "completeness axiom" is presented as an axiom. My analysis class used Strichartz' The Way of Analysis, which is certainly not "short and sweet" -- the professor described it to us as "chatty" -- but it goes ahead and actually proves the "completeness axiom". Compare the completeness axiom > Every nonempty…