具體描述
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.
用戶評價
##啓發式教學，當作參考書挺好的，但彆指望拿它當教材。
評分 評分 評分##09/2017 - 12/2017 補標，學完前半部分，比某本一星的垃圾實分析教材好多瞭
評分 評分##這本書作為我的第一本數分教材，裏麵的內容實在讓我難以下咽。 對於知識的敘述比較混亂，一些很重要的定理甚至沒有齣現在課文講解中而是以習題形式齣現。 作者本意應該是想引導讀者進行探索式學習，但貌似效果並不好......
評分 評分##這本書作為我的第一本數分教材，裏麵的內容實在讓我難以下咽。 對於知識的敘述比較混亂，一些很重要的定理甚至沒有齣現在課文講解中而是以習題形式齣現。 作者本意應該是想引導讀者進行探索式學習，但貌似效果並不好......
評分##My primary goal in writing Understanding Analysis was to create an elementary one-semester book that exposes students to the rich rewards inherent in taking a mathematically rigorous approach to the study of functions of a real variable. The aim of a course...
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