Understanding Analysis

Stephen Abbott

ISBN 10: 1493950266 / ISBN 13: 9781493950263

Published by Springer US, Springer New York Okt 2016, 2016

About this Item

Neuware -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 fromthe first edition, and three more project-style sections have been added. Investigations of Euler¿s computation of ¿(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.Springer Verlag GmbH, Tiergartenstr. 17, 69121 Heidelberg 324 pp. Englisch.

Seller Inventory # 9781493950263

Bibliographic Details

• Title: Understanding Analysis
• Publisher: Springer US, Springer New York Okt 2016
• Publication Date: 2016
• Language: English
• ISBN 10: 1493950266
• ISBN 13: 9781493950263
• Binding: Taschenbuch
• Edition: 1st Edition
• Condition: Neu

About this title

Synopsis

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 fromthe 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.

About the Author

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.