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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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.
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Book Description Springer, 2010. Soft cover. Book Condition: New. Dust Jacket Condition: New. International Edition. Low price guarantee! The book is the brand new international edition textbook with the different ISBN and cover design. The book main content black/white printed in full English as same as the corresponding original US edition. Fast shipments will sent out by DHL/UPS or standard post mail with tracking numbers in one to two working days after the orders confirmed. Bookseller Inventory # ABE-13405600536
Book Description Springer, 2010. Soft cover. Book Condition: New. Dust Jacket Condition: New. International Edition. **INTERNATIONAL EDITION** Read carefully before purchase: This book is the international edition in mint condition with the different ISBN and book cover design, the major content is printed in full English as same as the original North American edition. The book printed in black and white, generally send in twenty-four hours after the order confirmed. All shipments go through via USPS/UPS/DHL with tracking numbers. Great professional textbook selling experience and expedite shipping service. Bookseller Inventory # ABE-13405600539
Book Description Springer, 2001. Paperback. Book Condition: New. Never used!. Bookseller Inventory # P111441928669