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# Limits, Limits Everywhere: The Tools of Mathematical Analysis

De (autor)
en Limba Engleză Paperback – March 2012
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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## Specificații

ISBN-13: 9780199640089
ISBN-10: 0199640084
Pagini: 218
Ilustrații: 33 black and white line drawings
Dimensiuni: 153 x 234 x 12 mm
Greutate: 0.34 kg
Editura: Oxford University Press
Colecția OUP Oxford
Locul publicării: Oxford, United Kingdom

## Recenzii

This book does not offer an easy ride but its informal and enthusiastic literary style hold ones attention. Perhaps mindful of the content of much current popular mathematical exposition, the author draws many illustrations from number theory.
The author is able to mix both styles relating informal language to mathematical language and giving proofs that are deep but easy to read and follow.
Written in a style that is easy to read and follow, the author gives clear and succinct explanations and meets his desire for this to be between a textbook and a popular book on mathematics.
Recommended in the Times Higher Education's Textbook Guide 2012.
This is an excellent book which should appeal to teachers and pre-University or undergraduate students looking for a hands-on introduction to mathematical analysis.
The book is devoted to the discussion of one of the most difficult concepts of mathematical analysis, the concept of limits. The presentation is instructive and informal. It allows the author to go much deeper than is usually possible in a standard course of calculus. Moreover, each portion of the material is supplied by an explanation why and what for it is necessary to study (and to teach) the corresponding part of calculus ... the book can be recommended forinterested students as well as for teachers in mathematics.

## Notă biografică

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 from2007-10.