Understanding Analysis 2nd Edition by Stephen Abbott (English) Paperback Book

Description: Understanding Analysis by Stephen Abbott 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. FORMAT Paperback LANGUAGE English CONDITION Brand New Publisher Description 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 Eulers computation of ζ(2), the Weierstrass Approximation Theorem, and the gamma function are now among the books cohort of seminal results serving as motivation and payoff for the beginning student to master the methods of analysis. 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 Eulers computation of ζ(2), the Weierstrass Approximation Theorem, and the gamma function are now among the books 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, thats whats going to happen. ... This terrific book will become the text of choice for the single-variable introductory analysis course ... "-- Steve Kennedy, MAA Reviews Author Biography Stephen D. Abbott is Professor of Mathematics at Middlebury College. He is a two-time winner of Middleburys 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. Table of Contents Preface.- 1 The Real Numbers.- 2 Sequences and Series.- 3 Basic Topology of R.- 4 Functional Limits and Continuity.- 5 The Derivative.- 6 Sequences and Series of Functions.- 7 The Riemann Integral.- 8 Additional Topics.- Bibliography.- Index. Review "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 authors 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, thats whats 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 youre 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 Long Description This book outlines an elementary, one-semester course that 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. This new edition is extensively revised and updated with a refocused layout. In addition to the inclusion of extra exercises, the quality and focus of the exercises in this book has improved, which will help motivate the reader. New features include a discussion of infinite products, and expanded sections on metric spaces, the Baire category theorem, multi-variable functions, and the Gamma function. Reviews from the first edition: "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 thats whats 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 youre preparing that class." -Steve Kennedy, The Mathematical Association of America, 2001 "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, 29:3, 2002 Review Quote "The choice of topics is a happy combination of theessential and the interesting, all truly leading to an understanding of whatanalysis is and what questions it addresses, aided by the authors extraordinarilylucid exposition. ... Summing Up: Highly recommended. Upper-divisionundergraduates." (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, thats whats 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 youre 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 Feature Provides a polished and tuned-up version of the same core text that has proved successful with students and instructors for 15 years Includes around 150 new exercises, in addition to around 200 of the best exercises from the first edition, and an accompanying solutions manual for instructors Presents three new self-guided projects exploring Eulers sum, the factorial function and the Weierstrass Approximation Theorem Details ISBN1493950266 Author Stephen Abbott Language English Year 2016 ISBN-10 1493950266 ISBN-13 9781493950263 Format Paperback Publication Date 2016-10-29 Pages 312 Imprint Springer-Verlag New York Inc. Place of Publication New York Country of Publication United States DEWEY 515 Illustrations 36 Illustrations, color; XII, 312 p. 36 illus. in color. Textbook 1 Edition 2nd UK Release Date 2016-10-29 AU Release Date 2016-10-29 NZ Release Date 2016-10-29 US Release Date 2016-10-29 Publisher Springer-Verlag New York Inc. Edition Description Softcover reprint of the original 2nd ed. 2015 Series Undergraduate Texts in Mathematics Alternative 9781493927111 Audience Professional & Vocational We've got this At The Nile, if you're looking for it, we've got it. With fast shipping, low prices, friendly service and well over a million items - you're bound to find what you want, at a price you'll love! TheNile_Item_ID:135366500;

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