发帖
雷达卡
【新书】这本书能让你学好实分析
提醒：不想阅读废话的读者，可以拉到本文末尾，直接下载书籍。
越来越多的人认识到，现代经济理论根植于实分析，如果不懂《实分析》，很难步入经济学密室，从而难以欣赏经济学的美（或丑陋）。
然而，即使对数学专业的学生来说，《实分析》也是一门大课，由一根根硬骨头组成。民谚云：实分析，学十遍。这是形容《实分析》很难学，很难掌握。
有些鹰派数学家在写《实分析》教程时，从不忌惮自己语言的简洁与高深程度，在他们看来：你看不懂，这是你自己的问题，说明你不是这块料，并不说明他的书写得不好...比如Edmund Landau在他的《分析基础》一书中明确指出：请忘记你在学校里学到的东西，因为你啥也没学到。
与此相反，一些鸽派数学家则希望帮助非数学家读者走得更远一些，因此他们写书时，语言“更友好，更好懂”。这方面的数学家尤其是数学教育家也有很多。
应该使用什么样的教材学《实分析》？标准答案似乎为：Rudin的《数学分析原理》+Royden《实分析》。这也是麻省理工学院这样的大牛校数学系指定的教材。但问题是：这样的教材适合你吗？对于大部分自学者而言，答案似乎是否定的（根据自己的学习体会，无意冒犯高智商读者）。因为这样的教材不是写给“我”这样的人看的。或者说，将它们作为大部分自学者的第一本实分析教材，是不合适的。尽管你早晚要学习它们。人家《实分析》学十遍，你学个五六遍不过分吧。
迂回一点，根据自己的需要选择适合自己的教材，搞得差不多时，也就是你的数学直觉已上升到某个层次时，再学习Rudin的《数学分析原理》+Royden《实分析》可能也不迟。
虽然我写这篇小文的题目叫《这本书能让你学好实分析》，但更准确的题目应该是《这本书能让你爱上实分析》，并让你打下不错的基础。这是一本什么样的书？
这本书是由美国旧金山大学（University of San Francisco）数学系教授John Stillwell于2013年所写得《实数：集合论与实分析导论》。此牛著作等身，文笔巨友好。
下面拷贝这本书的英文介绍（请花点时间读一读）：
While most texts on real analysis are content to assume the real numbers, or to treat them only briefly, this text makes a serious study of the real number system and the issues it brings to light. Analysis needs the real numbers to model the line, and to support the concepts of continuity and measure. But these seemingly simple requirements lead to deep issues of set theory—uncountability, the axiom of choice, and large cardinals. In fact, virtually all the concepts of infinite set theory are needed for a proper understanding of the real numbers, and hence of analysis itself.
By focusing on the set-theoretic aspects of analysis, this text makes the best of two worlds: it combines a down-to-earth introduction to set theory with an exposition of the essence of analysis—the study of infinite processes on the real numbers. It is intended for senior undergraduates, but it will also be attractive to graduate students and professional mathematicians who, until now, have been content to "assume" the real numbers. Its prerequisites are calculus and basic mathematics.
Mathematical history is woven into the text, explaining how the concepts of real number and infinity developed to meet the needs of analysis from ancient times to the late twentieth century. This rich presentation of history, along with a background of proofs, examples, exercises, and explanatory remarks, will help motivate the reader. The material covered includes classic topics from both set theory and real analysis courses, such as countable and uncountable sets, countable ordinals, the continuum problem, the Cantor–Schröder–Bernstein theorem, continuous functions, uniform convergence, Zorn's lemma, Borel sets, Baire functions, Lebesgue measure, and Riemann integrable functions.
本书下载地址（此处），收费：免费一天
The Real Numbers An Introduction to Set Theory and Analysis, Stillwell, 2013.pdf
(3.97 MB, 需要: 8 个论坛币)
专业发布北美最流行数学类与经管类教材，为及时下载，请点一下我头像下方的“关注”，因为我通常免费一天
更多好书...
这本书能让你系统学习回归模型
作者Michael Panik为美国哈德佛德大学（University of Hartford）统计学荣誉退休教授
https://bbs.pinggu.org/thread-2727453-1-1.html
京公网安备 11010802022788号
