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Books > Science & Mathematics > Mathematics > Calculus & mathematical analysis > Real analysis
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Limits, Limits Everywhere - The Tools of Mathematical Analysis (Paperback)
Loot Price: R797
Discovery Miles 7 970
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Limits, Limits Everywhere - The Tools of Mathematical Analysis (Paperback)
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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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