| |||||||||||||||
 Trade In this Item for up to £3.75
Get an extra £5 when you trade in books worth £10 or more until June 30, 2012. Trade in Metric Spaces: Iteration and Application for an Amazon.co.uk gift card of up to £3.75, which you can then spend on millions of items across the site. Trade-in values may vary (terms apply). Find more products eligible for trade-in.
|
Frequently Bought Together
Product details
|
More About the Author
Product Description
Review
"...a fresh approach to a standard subject in topology and analysis...A healthy, vigorous introduction to analysis." American Scientist
Review
"...a fresh approach to a standard subject in topology and analysis...A healthy, vigorous introduction to analysis." American Scientist
Inside This Book
(Learn More)
First Sentence
Imagine a table top covered with a thin layer of dust. Read the first page
Front Cover | Copyright | Table of Contents | Excerpt | Index | Back Cover
Imagine a table top covered with a thin layer of dust. Read the first page
Explore More
Concordance
Browse Sample PagesConcordance
Front Cover | Copyright | Table of Contents | Excerpt | Index | Back Cover
Tag this product(What's this?)Think of a tag as a keyword or label you consider is strongly related to this product.
Tags will help all customers organise and find favourite items. |
Sell a Digital Version of This Book in the Kindle Store
If you are a publisher or author and hold the digital rights to a book, you can sell a digital version of it in our Kindle Store.
Learn more
What Other Items Do Customers Buy After Viewing This Item?
Customer Reviews
There are no customer reviews yet on Amazon.co.uk.
5 star
4 star
3 star
2 star
1 star
Most Helpful Customer Reviews on Amazon.com (beta)
Amazon.com:
7 reviews
26 of 26 people found the following review helpful
Great Introduction to Metric Spaces. Lively, Informal Style
17 Jun 2000
Format:Paperback
This short book is a gem. Metric Spaces by Victor Bryant is an enjoyable introduction to analysis. I liked the author's informal conversational approach to this rather abstract topic. Nonetheless, I did find it necessary to reread some sections for full understanding.
Bryant motivates the reader immediately with a look at iterative techniques, fixed point functions, converging sequences, and approximation solutions - all in an engaging style. Later topics included distance concepts, function spaces, and the relationship between closed sets, complete sets, and compact sets. The fourth chapter was devoted to the contraction mapping principle and its use in solving differential equations.
Is this book for you? The author says: "The only prerequisite is to have done a course on elementary analysis: it is not a prerequisite to have understood it nor to have remembered it at all." I had never taken any formal courses in analysis, and the highly structured axiomatic approach of analysis texts had never appealed to me. I only had a vague idea as to the properties of a metric space. But I was lured into buying Bryant's short text by the previous Amazon reviewers. And thankfully so.
Bryant certainly enjoys his subject, but he just as clearly recognizes that not everyone might have such an abiding interest. Throughout the text, he points out opportunities where the reader might skip forward if the going has become less interesting. (For the record I refused to be enticed by these short cuts.)
Problems are embedded in the text, one or two at a time, and are used to reinforce points under discussion. Most have clear hints and I found many problems straightforward, but others were more difficult. A few problems were identified as appropriate for the "keen" student. The most abstract mathematics are reserved for the last (optional) chapter, but the author does encourage the reader to stay with it: "It would be a pity to stop ..." Chapter five recasts the first four chapters into a more generalized form of real analysis and addresses the question: "What makes analysis work?"
Bryant had an unusual goal for a mathematics text. "I have tried to provide a readable and natural introduction to an abstract subject in a down-to-earth manner." Also, he says, "My aim is to provide a book which can be read and enjoyed ..." He succeeded in doing just that.
Bryant motivates the reader immediately with a look at iterative techniques, fixed point functions, converging sequences, and approximation solutions - all in an engaging style. Later topics included distance concepts, function spaces, and the relationship between closed sets, complete sets, and compact sets. The fourth chapter was devoted to the contraction mapping principle and its use in solving differential equations.
Is this book for you? The author says: "The only prerequisite is to have done a course on elementary analysis: it is not a prerequisite to have understood it nor to have remembered it at all." I had never taken any formal courses in analysis, and the highly structured axiomatic approach of analysis texts had never appealed to me. I only had a vague idea as to the properties of a metric space. But I was lured into buying Bryant's short text by the previous Amazon reviewers. And thankfully so.
Bryant certainly enjoys his subject, but he just as clearly recognizes that not everyone might have such an abiding interest. Throughout the text, he points out opportunities where the reader might skip forward if the going has become less interesting. (For the record I refused to be enticed by these short cuts.)
Problems are embedded in the text, one or two at a time, and are used to reinforce points under discussion. Most have clear hints and I found many problems straightforward, but others were more difficult. A few problems were identified as appropriate for the "keen" student. The most abstract mathematics are reserved for the last (optional) chapter, but the author does encourage the reader to stay with it: "It would be a pity to stop ..." Chapter five recasts the first four chapters into a more generalized form of real analysis and addresses the question: "What makes analysis work?"
Bryant had an unusual goal for a mathematics text. "I have tried to provide a readable and natural introduction to an abstract subject in a down-to-earth manner." Also, he says, "My aim is to provide a book which can be read and enjoyed ..." He succeeded in doing just that.
16 of 16 people found the following review helpful
Metric Spaces
20 April 2000
Format:Paperback
A short but excellent book for someone who wants a well motivated refresher on analysis. By grounding the ideas with applications of fixed point theorems (such as proving the existence of unique solutions to certain types of differential equations) the author makes accessible an area of mathematics that is often treated in an axiomatic and uninteresting way.
I believe the author is correct when he recommends the book for people who have already had some exposure to analysis. At best a student should already have completed the standard non-rigorous college calculus sequence to get the most out of this book.
12 of 13 people found the following review helpful
This is a great introduction to fixed-point methods.
13 Oct 1998
Format:Paperback
This little book can take a bright high school student or undergraduate through some most interesting territory, previously uncharted at this level of mathematical understanding. Fixed point methods -- approaches to problem solving based on the simple equation f(x)=x -- are ubiquitous and ideally suited for digital computers, but they are seldom introduced in the classroom. Get this book for your high school library. Use it as an independent study for that student you don't want to set loose on calculus quite yet.
Were these reviews helpful?
Let us know
Listmania!
Look for similar items by category
Look for similar items by subject
Feedback
- Would you like to update product info or give feedback on images?
- I am the Author, and I want to comment on my book.
- I am the Publisher, and I want to comment on this book.
|
