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
##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...
評分##書後麵的課後習題很難，而且後麵有些證明是需要靠習題裏麵的知識點，感覺作為課上的補充書籍比較不錯，但自學一定會有極大壓力 本書是我學數學分析課的時候使用的主要參考書，基本把書上的題目都刷瞭一遍，受益良多。讀的過程也是在慢慢學習怎樣去讀一本數學書的過程。就寫一寫我覺得這本書寫得好的地方，再談一談這本書建議的食用方法。 這本書是很Entry Level的書，所以下麵的敘述都來源於我作為一個初...
評分 評分##適閤入門讀
評分##實分析
評分##是一本可以當小說讀的分析教材，讓人欲罷不能，非常適閤想要入門分析的朋友
評分雖說是適閤入門，但與國內考試大綱一樣的教材風格構成瞭另一個極端，引導式、啓發式的到把很多重要的內容放到習題裏去，不僅是很多定理的證明隻有提示，很多定理本身都隻在習題中齣現。要是沒有參考答案在手真的卡住瞭不是非常麻煩嗎...認認真真從頭看完，最後可能“內功”修煉好瞭，但是頭腦中沒有完整清晰的邏輯框架，完整的證明也沒有看過幾個。總之還是算一個缺陷的。
評分相關圖書
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