Understanding Analysis (Undergraduate Texts in Mathematics)

4.15 avg rating
( 93 ratings by GoodReads )
 
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.

"synopsis" may belong to another edition of this title.

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 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 … ”

— 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.

"About this title" may belong to another edition of this title.

Top Search Results from the AbeBooks Marketplace

1.

Abbott, Stephen
Published by Springer (2002)
ISBN 10: 0387950605 ISBN 13: 9780387950600
New Hardcover Quantity Available: 1
Seller
Solr Books
(Skokie, IL, U.S.A.)
Rating
[?]

Book Description Springer, 2002. Hardcover. Book Condition: New. Ships Fast! Satisfaction Guaranteed!. Bookseller Inventory # mon0000513125

More Information About This Seller | Ask Bookseller a Question

Buy New
US$ 33.90
Convert Currency

Add to Basket

Shipping: US$ 3.99
Within U.S.A.
Destination, Rates & Speeds

2.

Abbott, Stephen
Published by Springer (2002)
ISBN 10: 0387950605 ISBN 13: 9780387950600
New Hardcover Quantity Available: 1
Seller
Book Deals
(Lewiston, NY, U.S.A.)
Rating
[?]

Book Description Springer, 2002. Book Condition: New. Brand New, Unread Copy in Perfect Condition. A+ Customer Service! Summary: 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. Bookseller Inventory # ABE_book_new_0387950605

More Information About This Seller | Ask Bookseller a Question

Buy New
US$ 52.40
Convert Currency

Add to Basket

Shipping: FREE
Within U.S.A.
Destination, Rates & Speeds

3.

Abbott, Stephen
Published by Springer-Verlag New York Inc., United States (2002)
ISBN 10: 0387950605 ISBN 13: 9780387950600
New Hardcover Quantity Available: 1
Seller
The Book Depository US
(London, United Kingdom)
Rating
[?]

Book Description Springer-Verlag New York Inc., United States, 2002. Hardback. Book Condition: New. 1st ed. 2001. Corr. 2nd printing 2002. 236 x 160 mm. Language: English . Brand New Book. 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. Bookseller Inventory # BZV9780387950600

More Information About This Seller | Ask Bookseller a Question

Buy New
US$ 52.42
Convert Currency

Add to Basket

Shipping: FREE
From United Kingdom to U.S.A.
Destination, Rates & Speeds

4.

Abbott, Stephen
ISBN 10: 0387950605 ISBN 13: 9780387950600
New Hardcover Quantity Available: 1
Seller
AMAZINGBOOKDEALS
(IRVING, TX, U.S.A.)
Rating
[?]

Book Description Hardcover. Book Condition: BRAND NEW. BRAND NEW. Fast Shipping. Prompt Customer Service. Satisfaction guaranteed. Bookseller Inventory # 0387950605BNA

More Information About This Seller | Ask Bookseller a Question

Buy New
US$ 51.95
Convert Currency

Add to Basket

Shipping: US$ 3.99
Within U.S.A.
Destination, Rates & Speeds

5.

Abbott, Stephen
Published by Springer (2002)
ISBN 10: 0387950605 ISBN 13: 9780387950600
New Hardcover Quantity Available: 1
Seller
Irish Booksellers
(Rumford, ME, U.S.A.)
Rating
[?]

Book Description Springer, 2002. Hardcover. Book Condition: New. book. Bookseller Inventory # 0387950605

More Information About This Seller | Ask Bookseller a Question

Buy New
US$ 60.90
Convert Currency

Add to Basket

Shipping: FREE
Within U.S.A.
Destination, Rates & Speeds

6.

Abbott, Stephen
Published by Springer
ISBN 10: 0387950605 ISBN 13: 9780387950600
New Hardcover Quantity Available: 1
Seller
Cloud 9 Books
(West Palm Beach, FL, U.S.A.)
Rating
[?]

Book Description Springer. Hardcover. Book Condition: New. 0387950605 New Condition. Bookseller Inventory # NEW4.0184180

More Information About This Seller | Ask Bookseller a Question

Buy New
US$ 59.99
Convert Currency

Add to Basket

Shipping: US$ 4.99
Within U.S.A.
Destination, Rates & Speeds

7.

Abbott, Stephen
ISBN 10: 0387950605 ISBN 13: 9780387950600
New Quantity Available: 1
Seller
Castle Rock
(Pittsford, NY, U.S.A.)
Rating
[?]

Book Description Book Condition: Brand New. Book Condition: Brand New. Bookseller Inventory # 97803879506001.0

More Information About This Seller | Ask Bookseller a Question

Buy New
US$ 75.29
Convert Currency

Add to Basket

Shipping: US$ 3.99
Within U.S.A.
Destination, Rates & Speeds

8.

Abbott, Stephen
Published by Springer Verlag (2001)
ISBN 10: 0387950605 ISBN 13: 9780387950600
New Hardcover Quantity Available: 1
Seller
Revaluation Books
(Exeter, United Kingdom)
Rating
[?]

Book Description Springer Verlag, 2001. Hardcover. Book Condition: Brand New. 1st ed. 2001. corr. 2nd printing edition. 257 pages. 9.25x6.25x0.75 inches. In Stock. Bookseller Inventory # zk0387950605

More Information About This Seller | Ask Bookseller a Question

Buy New
US$ 81.47
Convert Currency

Add to Basket

Shipping: US$ 7.58
From United Kingdom to U.S.A.
Destination, Rates & Speeds

9.

Abbott, Stephen
Published by Springer (2002)
ISBN 10: 0387950605 ISBN 13: 9780387950600
New Hardcover Quantity Available: 3
Seller
Murray Media
(North Miami Beach, FL, U.S.A.)
Rating
[?]

Book Description Springer, 2002. Hardcover. Book Condition: New. Bookseller Inventory # P110387950605

More Information About This Seller | Ask Bookseller a Question

Buy New
US$ 92.95
Convert Currency

Add to Basket

Shipping: US$ 2.99
Within U.S.A.
Destination, Rates & Speeds

10.

Abbott, Stephen
Published by Springer, U.S.A. (2002)
ISBN 10: 0387950605 ISBN 13: 9780387950600
New Hardcover First Edition Quantity Available: 3
Seller
Wordtown Books
(ferring, United Kingdom)
Rating
[?]

Book Description Springer, U.S.A., 2002. Hardcover. Book Condition: New. 1st Edition. Bookseller Inventory # 0062242

More Information About This Seller | Ask Bookseller a Question

Buy New
US$ 1,300.65
Convert Currency

Add to Basket

Shipping: US$ 8.83
From United Kingdom to U.S.A.
Destination, Rates & Speeds