
Limits, Limits Everywhere: The Tools of Mathematical Analysis (Paperback)
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Dispatched in 1 business day When will my order arrive?  DescriptionA quantity can be made smaller and smaller without it ever vanishing. This fact has profound consequences for science, technology, and even the way we think about numbers. In this book, we will explore this idea by moving at an easy pace through an account of elementary real analysis and, in particular, will focus on numbers, sequences, and series. Almost all textbooks on introductory analysis assume some background in calculus. This book doesn't and, instead, the emphasis is on the application of analysis to number theory. The book is split into two parts. Part 1 follows a standard university course on analysis and each chapter closes with a set of exercises. Here, numbers, inequalities, convergence of sequences, and infinite series are all covered. Part 2 contains a selection of more unusual topics that aren't usually found in books of this type. It includes proofs of the irrationality of e and pi, continued fractions, an introduction to the Riemann zeta function, Cantor's theory of the infinite, and Dedekind cuts. There is also a survey of what analysis can do for the calculus and a brief history of the subject. A lot of material found in a standard university course on "real analysis" is covered and most of the mathematics is written in standard theoremproof style. However, more details are given than is usually the case to help readers who find this style daunting. Both set theory and proof by induction are avoided in the interests of making the book accessible to a wider readership, but both of these topics are the subjects of appendices for those who are interested in them. And unlike most university texts at this level, topics that have featured in popular science books, such as the Riemann hypothesis, are introduced here. As a result, this book occupies a unique position between a popular mathematics book and a first year college or university text, and offers a relaxed introduction to a fascinating and important branch of mathematics.
 Publisher: Oxford University Press
 Published: 04 May 2012
 Format: Paperback 224 pages
 See: Full bibliographic data
 Categories: Calculus & Mathematical Analysis  Calculus
 ISBN 13: 9780199640089 ISBN 10: 0199640084
 Sales rank: 477,417
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Full bibliographic data for Limits, Limits Everywhere
 Title
 Limits, Limits Everywhere
 Subtitle
 The Tools of Mathematical Analysis
 Authors and contributors
 Physical properties
 Format: Paperback
Number of pages: 224
Width: 153 mm
Height: 234 mm
Thickness: 12 mm
Weight: 337 g  Language
 English
 ISBN
 ISBN 13: 9780199640089
ISBN 10: 0199640084  Classifications
BIC E4L: MAT
B&T Book Type: NF
Nielsen BookScan Product Class 3: S7.9T
B&T Modifier: Region of Publication: 03
B&T Modifier: Academic Level: 01
B&T General Subject: 710
LC classification: QA
Ingram Subject Code: MA
Libri: IMA
B&T Modifier: Text Format: 06
LC subject heading:
DC22: 515
Abridged Dewey: 515
WarengruppenSystematik des deutschen Buchhandels: 26270
BISAC V2.8: MAT005000
LC subject heading:
BIC subject category V2: PBK
B&T Merchandise Category: UP
DC23: 515
Thema V1.0: PBK Illustrations note
 33 black and white line drawings
 Publisher
 Oxford University Press
 Imprint name
 Oxford University Press
 Publication date
 04 May 2012
 Publication City/Country
 Oxford
 Table of contents
 INTRODUCTION ; I APPROACHING LIMITS ; 1. A Whole Lot of Numbers ; 2. Let's Get Real ; 3. The Joy of Inequality ; 4. Where Do You Go To, My Lovely ; 5. Bounds for Glory ; 6. You Cannot be Series ; II EXPLORING LIMITS ; 7. Wonderful Numbers ; 8. Infinite Products ; 9. Continued Fractions ; 10. How Infinite Can You Get? ; 11. Constructing the Real Numbers ; 12. Where to Next in Analysis? The Calculus ; 13. Some Brief Remarks About the History of Analysis ; FURTHER READING ; APENDICES ; 1. The Binomial Theorem ; 2. The Language of Set Theory ; 3. Proof by Mathematical Induction ; 4. The Algebra of Numbers ; HINTS AND SELECTED SOLUTIONS