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Limits, Limits EverywhereThe Tools of Mathematical AnalysisNormal Price: $44.95
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Limits, Limits Everywhere by David ApplebaumBook Description 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 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.Buy Limits, Limits Everywhere book by David Applebaum from Australia's Online Bookstore, Boomerang Books. Book Details ISBN: 9780199640089ISBN10: 0199640084
(234mm x 153mm x 12mm) Pages: 224 Imprint: Oxford University Press Publisher: Oxford University Press Publish Date: 1Mar2012 Country of Publication: United Kingdom 

Books By Author David Applebaum
Levy Processes and Stochastic Calculus, Paperback (April 2009)
A fully revised and appended edition of this unique volume, which develops together these two important subjects.
Probability and Information, Paperback (August 2008)
» View all books by David Applebaum
An update of this popular introduction to probability theory and information theory with new material on Markov chains. Reviews» Have you read this book? We'd like to know what you think about it  write a review about Limits, Limits Everywhere book by David Applebaum and you'll earn 50c in Boomerang Bucks loyalty dollars (you must be a member  it's free to sign up!) Author Biography  David ApplebaumDavid 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 19982001. He left Nottingham Trent for a chair in Sheffield in 2004 and served as Head of Department of Probability and Statistics there from 200710. 
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