具体描述
Stephen D. Abbott is Professor of Mathematics at Middlebury College. He is a two-time winner of Middlebury’s Perkins Award for Excellence in Teaching (1998, 2010). His published work includes articles in the areas of operator theory and functional analysis, the algorithmic foundations of robotics, and the intersection of science, mathematics and the humanities.
This lively introductory text exposes the student to the rewards of a rigorous study of functions of a real variable. In each chapter, informal discussions of questions that give analysis its inherent fascination are followed by precise, but not overly formal, developments of the techniques needed to make sense of them. By focusing on the unifying themes of approximation and the resolution of paradoxes that arise in the transition from the finite to the infinite, the text turns what could be a daunting cascade of definitions and theorems into a coherent and engaging progression of ideas. Acutely aware of the need for rigor, the student is much better prepared to understand what constitutes a proper mathematical proof and how to write one.
Fifteen years of classroom experience with the first edition of Understanding Analysis have solidified and refined the central narrative of the second edition. Roughly 150 new exercises join a selection of the best exercises from the first edition, and three more project-style sections have been added. Investigations of Euler’s computation of ζ(2), the Weierstrass Approximation Theorem, and the gamma function are now among the book’s cohort of seminal results serving as motivation and payoff for the beginning student to master the methods of analysis.
用户评价
##书后面的课后习题很难，而且后面有些证明是需要靠习题里面的知识点，感觉作为课上的补充书籍比较不错，但自学一定会有极大压力 本书是我学数学分析课的时候使用的主要参考书，基本把书上的题目都刷了一遍，受益良多。读的过程也是在慢慢学习怎样去读一本数学书的过程。就写一写我觉得这本书写得好的地方，再谈一谈这本书建议的食用方法。 这本书是很Entry Level的书，所以下面的叙述都来源于我作为一个初...
评分##09/2017 - 12/2017 學完前半部分，比某本一星的垃圾實分析教材好多了
评分虽说是适合入门，但与国内考试大纲一样的教材风格构成了另一个极端，引导式、启发式的到把很多重要的内容放到习题里去，不仅是很多定理的证明只有提示，很多定理本身都只在习题中出现。要是没有参考答案在手真的卡住了不是非常麻烦吗...认认真真从头看完，最后可能“内功”修炼好了，但是头脑中没有完整清晰的逻辑框架，完整的证明也没有看过几个。总之还是算一个缺陷的。
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