Product Details

• Amazon Sales Rank: #249160 in Books
• Published on: 1997-09-21
• Original language: English
• Number of items: 1
• Binding: Paperback
• 106 pages

Customer Reviews

A classic by he who brought us metric theory of continued fractions
This is a book to be read cover to cover. If metric number theory isn't your thing then it is still worth having just for the early pages.
However, I feel I only digested this more classical material when I worked out how to write it in 2*2 matrix notation. What I'm trying to say is perhaps that I wish there was some discussion of the modular group.

useful book to learn 'assumed mathematical methods'
Introduction

This `Dover' book is an unabridged (1997) English translation of the third Russian reprint (1961). You may come across `Continued Fractions' in other mathematical areas such as Number Theory, Analysis, Probability, and Mechanic's. You may also find 'Continued Fractions' skills are - frustratingly- assumed within general `mathematical techniques' and hard to find a book about its topics?

The book only has 95 pages, but it may be helpful if you are already grasp some principles of analysis, series and recursive-based calculations, but it starts from elemental level, so try not too worry. The book has generous mathematical examples and many graphs.


Down to basics


The book starts from first principles, and allows fundamental skills to be learned. Continued Fractions are positive natural numbers arranged is a way to eventually approximate real numbers and other numerical forms.


Quotation: `Continued Fractions' can be applied to best approximate real or complex numbers, functions of one or several variables'. (Page 19)


To improve accuracy to any level we wish, try representing a number / series with two series, one being the numerator (P), and another series for the denominator (Q). These can be arranged with inequalities. To sew two series - `P' / `Q'- together allows another series to be created by recursive techniques to keep these stages in step.


Summary

If you wish to gain more depth, this book increasing in challenging ideas, such as Chapter 3, `The Measure Theory of Continued Fractions' or further. If you try to stick within boundaries of any previous exposure analysis, (especially) series, and recursive calculation concepts, its starts to make better sense but becomes rather involved at times, but it's a rewarding read. It is fine mathematical books at a 2nd hand price.