Please note: In order to keep Hive up to date and provide users with the best features, we are no longer able to fully support Internet Explorer. The site is still available to you, however some sections of the site may appear broken. We would encourage you to move to a more modern browser like Firefox, Edge or Chrome in order to experience the site fully.

Supporting your high street Find out how »
Limits, Limits Everywhere : The Tools of Mathematical Analysis, EPUB eBook

Limits, Limits Everywhere : The Tools of Mathematical Analysis EPUB

EPUB

Download - Immediately Available
Please note: eBooks can only be purchased with a UK issued credit card and all our eBooks (ePub and PDF) are DRM protected.

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 ofthis type.

It includes proofs of the irrationality of e and π, 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 mostuniversity 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 afascinating and important branch of mathematics.

Information

Other Formats

Save 15%

£24.57

£20.88

Download - Immediately Available
Add to Basket
Sign in to add to wishlist
 
Delivered to your inbox

to transfer to your device

eBook Help

Is this the right eBook for
my device? How do I download
this eBook? See help and FAQs pages

Information