# Limits, Limits Everywhere: The Tools of Mathematical Analysis

## David Applebaum

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A 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 ?, 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 theorem-proof 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.

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David Applebaum obtained his PhD at the University of Nottingham in 1984. After postdoctoral appointments in Rome and Nottingham, he became a lecturer in mathematics at Nottingham Trent University (then Trent Polytechnic) in 1987 and was promoted to reader in 1994 and to a chair in 1998. He was Head of Department 1998-2001. He left Nottingham Trent for a chair in Sheffield in 2004 and served as Head of Department of Probability and Statistics there from 2007-10.

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"[H]elpful for college students..." --MAA Reviews

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## 1.Limits, Limits Everywhere: The Tools of Mathematical Analysis

Editorial: Oxford University Press
ISBN 10: 0199640084 ISBN 13: 9780199640089
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Descripción Oxford University Press. PAPERBACK. Estado de conservación: New. 0199640084. Nº de ref. de la librería Z0199640084ZN

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## 2.Limits, Limits Everywhere: The Tools of Mathematical Analysis

Editorial: Oxford University Press 2012-05-04 (2012)
ISBN 10: 0199640084 ISBN 13: 9780199640089
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Descripción Oxford University Press 2012-05-04, 2012. Paperback. Estado de conservación: New. 1. 0199640084. Nº de ref. de la librería Z0199640084ZN

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## 3.Limits, Limits Everywhere: The Tools of Mathematical Analysis

Editorial: Oxford University Press
ISBN 10: 0199640084 ISBN 13: 9780199640089
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## 4.Limits, Limits Everywhere: The Tools of Mathematical Analysis

Editorial: Oxford University Press
ISBN 10: 0199640084 ISBN 13: 9780199640089
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Bookhouse COM LLC
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Descripción Oxford University Press. PAPERBACK. Estado de conservación: New. 0199640084. Nº de ref. de la librería Z0199640084ZN

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## 5.Limits, Limits Everywhere: The Tools of Mathematical Analysis (Paperback)

Editorial: Oxford University Press, United Kingdom (2012)
ISBN 10: 0199640084 ISBN 13: 9780199640089
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The Book Depository
(London, Reino Unido)
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Descripción Oxford University Press, United Kingdom, 2012. Paperback. Estado de conservación: New. Language: English . Brand New Book. A 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 theorem-proof 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. Nº de ref. de la librería AOP9780199640089

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## 6.Limits, Limits Everywhere: The Tools of Mathematical Analysis (Paperback)

Editorial: Oxford University Press, United Kingdom (2012)
ISBN 10: 0199640084 ISBN 13: 9780199640089
Librería
The Book Depository US
(London, Reino Unido)
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Descripción Oxford University Press, United Kingdom, 2012. Paperback. Estado de conservación: New. Language: English . Brand New Book. A 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 theorem-proof 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. Nº de ref. de la librería AOP9780199640089

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## 7.Limits, Limits Everywhere: The Tools Of Mathematical Analysis

ISBN 10: 0199640084 ISBN 13: 9780199640089
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Descripción Estado de conservación: New. Depending on your location, this item may ship from the US or UK. Nº de ref. de la librería 97801996400890000000

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## 8.Limits, Limits Everywhere

Editorial: OUP Oxford 2012-03-01, Oxford (2012)
ISBN 10: 0199640084 ISBN 13: 9780199640089
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Descripción OUP Oxford 2012-03-01, Oxford, 2012. paperback. Estado de conservación: New. Nº de ref. de la librería 9780199640089

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## 9.Limits, Limits Everywhere: The Tools of Mathematical Analysis (Paperback)

ISBN 10: 0199640084 ISBN 13: 9780199640089
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Descripción Estado de conservación: New. Bookseller Inventory # ST0199640084. Nº de ref. de la librería ST0199640084

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## 10.Limits, Limits Everywhere: The Tools of Mathematical Analysis

Editorial: Oxford University Press
ISBN 10: 0199640084 ISBN 13: 9780199640089
Librería
THE SAINT BOOKSTORE
(Southport, Reino Unido)
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Descripción Oxford University Press. Paperback. Estado de conservación: new. BRAND NEW, Limits, Limits Everywhere: The Tools of Mathematical Analysis, David Applebaum, A 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 theorem-proof 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. Nº de ref. de la librería B9780199640089

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