Understanding Analysis (Undergraduate Texts in Mathematics)

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9780387950600: Understanding Analysis (Undergraduate Texts in Mathematics)

This elementary presentation exposes readers to both the process of rigor and the rewards inherent in taking an axiomatic approach to the study of functions of a real variable. The aim is to challenge and improve mathematical intuition rather than to verify it. The philosophy of this book is to focus attention on questions which give analysis its inherent fascination. Each chapter begins with the discussion of some motivating examples and concludes with a series of questions.

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From the Back Cover:

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.

Review of the first edition:

“This is a dangerous book. Understanding Analysis is so well-written and the development of the theory so well-motivated t

hat exposing students to it could well lead them to expect such excellence in all their textbooks. ... Understanding Analysis is perfectly titled; if your students read it, that’s what’s going to happen. ... This terrific book will become the text of choice for the single-variable introductory analysis course ... ”

― Steve Kennedy, MAA Reviews           

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.          

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Abbott, Stephen
Editore: Springer (2001)
ISBN 10: 0387950605 ISBN 13: 9780387950600
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Descrizione libro Springer, 2001. Hardcover. Condizione libro: Neubuch. XII, 257 S. verlagsneu – Introduction to the Problems in Analysis outlines an elementary, one semester course which exposes students to both the process of rigor, and the rewards inherent in taking an axiomatic approach to the study of functions of a real variable. The aim of a course in real analysis should be to challenge and improve mathematical intuition rather than to verify it. The philosophy of this book is to focus attention on questions which give analysis its inherent fascination. Does the Cantor set contain any irrational numbers? Can the set of points where a function is discontinuous be arbitrary? Can the rational numbers be written as a countable intersection of open sets? Is an infinitely differentiable function necessarily the limit of its Taylor series? Giving these topics center stage, the motivation for a rigorous approach is justified by the fact that they are inaccessible without it. Codice libro della libreria 18004081

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Descrizione libro Springer, 2002. Hardcover. Condizione libro: New. book. Codice libro della libreria 0387950605

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Descrizione libro Springer, 2001. Hardcover. Condizione libro: New. This item is printed on demand. Codice libro della libreria DADAX0387950605

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Descrizione libro Springer, 2002. Hardcover. Condizione libro: New. Codice libro della libreria P110387950605

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Descrizione libro Springer. Hardcover. Condizione libro: New. 0387950605 New Condition. Codice libro della libreria NEW6.0184155

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Descrizione libro Hardcover. Condizione libro: BRAND NEW. BRAND NEW. Fast Shipping. Prompt Customer Service. Satisfaction guaranteed. Codice libro della libreria 0387950605BNA

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