数学分析原理

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• ten_fingers · 2012 年

  ……网上有免费的 PDF）。至于数值线性代数，可以参考 Forsythe 和 Moler。用来讲授微积分定理和证明的标准高等微积分教材是 Walter Rudin 的《数学分析原理》（Principles of Mathematical Analysis）。读完那本书之后，像 Knuth 在 TACP 里用的 O( n ln(n) ) 这种记号简直就是小儿科了。注：哈佛大学曾经把 Halmos 的《有限维向量空间》（Finite Dimensional Vector Spaces）和 Rudin 的《原理》用在……

  …available on the Internet in PDF for free). For numerical linear algebra, see Forsythe and Moler. The standard advanced calculus text to teach the theorems and proofs of calculus is Walter Rudin's 'Principles of Mathematical Analysis'. After that book, notation such as O( n ln(n) ) as in Knuth's TACP will be child's play. Note: At one time the Halmos 'Finite Dimensional Vector Spaces' and Rudin's 'Principles' were used in Harvard's…

• graycat · 2016 年

  ……影响深远，而且哪怕在实践中也不会消失，尽管在实际应用中（比如教育统计学）可能没有大家长期以为的那么重要。接着至少把 Rudin 的《数学分析原理》（Principles of Mathematical Analysis，即 Baby Rudin）的前半部分认真刷一遍。至于较新版本后面讲的外代数，额，大概最好从别处学，比如直接看 Cartan 的英文版。Baby Rudin 的前半部分讲的是度量……

  …is profound and won't go away even in practice although is less important in practice than long assumed in, say, educational statistics. Then take a good pass through at least the first parts of Rudin, Principles of Mathematical Analysis, AKA Baby Rudin. For the exterior algebra in the back of the more recent editions, well, likely get that elsewhere, say, now in English, directly from Cartan. The first parts of Baby Rudin cover metric…

• jeffcoat · 2009 年

  你可能不太好找资料，因为完全严谨化的微积分其实叫“分析”（analysis）。最经典但也极其晦涩紧凑的入门教材是 Rudin 的《数学分析原理》（Principles of Mathematical Analysis）。不过如果你是自学，我觉得看一本更亲切的书收获会大得多；我上的第一门分析课用的是 Strichartz 的《分析之道》（The Way of Analysis）。注意：几乎所有……

  You may be having trouble finding things because calculus done with full rigor is called "analysis". The classic introductory-but-extremely-dense text is Rudin's _Principles of Mathematical Analysis_. If you're reading on your own, though, I expect you'll get a lot more out of a friendlier book; my first analysis course was taught out of Strichartz's _The Way of Analysis_. N.B.: Most everything…

• jvreeland · 2014 年

  啃这本书可远没有啃 SICP 那么轻松，但如果你对分析学感兴趣，Walter Rudin 的《数学分析原理》（Principles of Mathematical Analysis，有时也被称为小 Rudin）是个极好的起点。这是一本很难的书，但它基本算得上本科生分析学的标准教材。

  It's not nearly as easy to work through as SICP is but Principles of Mathematical Analysis by Walter Rudin (sometimes referred to as little Rudin) is a great place to start if you're interested in analysis. It's a hard book, but it's pretty much the standard for undergrad analysis.

• karamazov · 2014 年

  ……那些肯花时间和精力去啃完它的人。我会推荐以下三本书，分别覆盖高等数学的三大主要领域（分析、代数和拓扑）：1. Rudin 的《数学分析原理》（Principles of Mathematical Analysis）(http://www.amazon.com/Principles-Mathematical-Analysis-Inter...) 2. Artin 的《代数》（Algebra）(http://www.amazon.com/Algebra-2nd-Featured-Titles-Abstract/d...) 3. Munkres 的《拓扑学》（Topology）(http://www.amazon.com/Topology-2nd-James-Munkres/dp/01318162...)……

  …the people who take the time and effort to go through it. I'd recommend the following three books to similarly cover the three main areas of higher mathematics (analysis, algebra, and topology): 1. Principles of Mathematical Analysis by Rudin (http://www.amazon.com/Principles-Mathematical-Analysis-Inter...) 2. Algebra by Artin (http://www.amazon.com/Algebra-2nd-Featured-Titles-Abstract/d...) 3. Topology by Munkres (http://www.amazon.com/Topology-2nd-James-Munkres/dp/01318162...)…

• nextos · 2018 年

  ……微积分。高中水平非常棒的有：* Lang 的《基础数学》（Basic Mathematics）* Thompson 的《简易微积分》（Calculus Made Easy）。如果觉得太简单，可以试试类似 Math 55 的路子：* Axler 的《线性代数应该这样学》（Linear Algebra Done Right）* Rudin 的《数学分析原理》（Principles of Mathematical Analysis）。你也可以把 Axler 换成 Halmos 的《有限维向量空间》（Finite-Dimensional Vector Spaces），不过难度更高。遗憾的是 Axler 最新版里加了各种让人分心的配图和排版框，反而失掉了一些原有的……

  …calculus. A great high school level one is: * Basic Mathematics by Lang * Calculus Made Easy by Thompson If that is too simplistic, try a Math 55 like approach: * Linear Algebra Done Right by Axler * Principles of Mathematical Analysis by Rudin You can replace Axler by Finite-Dimensional Vector Spaces by Halmos. But it's harder. Sadly the latest edition of Axler has distracting pictures and boxes that have done away with some of it's…

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