Stephen Abbott

eBook, PDF

Understanding Analysis (eBook, PDF)

Beschreibung

A First Course in Real 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 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 which concludes with a series of questions. The penultimate section of each chapter (the final section is a short epilogue) is written with the exercises incorporated into the exposition.

Technische Details

• Geräte: PC
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• Größe: 23.3MB

Barrierefreiheit

• Text-to-Speech
• E-Mail des Verlags für Barrierefreiheitsfragen: [e-mail]
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Autor

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.          

Produktdetails

• Verlag: Springer US
• Seitenzahl: 260
• Erscheinungstermin: 6. Dezember 2012
• Englisch
• ISBN-13: 9780387215068
• Artikelnr.: 44178351

Rezensionen

"The choice of topics is a happy combination of the essential and the interesting, all truly leading to an understanding of what analysis is and what questions it addresses, aided by the author's extraordinarily lucid exposition. ... Summing Up: Highly recommended. Upper-division undergraduates." (D. Robbins, Choice, Vol. 53 (2), October, 2015)

"This is the second edition of a text for an undergraduate course in single-variable real analysis. ... The topics covered in this book are the ones that have, by now, become standard for a one-semester undergraduate real analysis course ... . Overall, this book represents, to my mind, the gold standard among single-variable undergraduate analysis texts." (Mark Hunacek, MAA Reviews, June,

2015)

"This is a dangerous book. Understanding Analysis is so well-written and the development of the theory so well-motivated that 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; take a look at it next time you're preparing that class."

- Steve Kennedy, MAA Reviews

"Each chapter begins with a discussion section and ends with an epilogue. The discussion serves to motivate the content of the chapter while the epilogue points tantalisingly to more advanced topics. ... I wish I had written this book! The development of the subject follows the tried-and-true path, but the presentation is engaging and challenging. Abbott focuses attention immediately on the topics which make analysis fascinating ... and makes them accessible to an inexperienced audience."

- Scott Sciffer, The Australian Mathematical Society Gazette