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Continued Fractions 3RD Edition

by

Continued Fractions 3RD Edition Cover

 

Synopses & Reviews

Publisher Comments:

Elementary-level text by noted Soviet mathematician offers superb introduction to positive-integral elements of theory of continued fractions. Clear, straightforward presentation of the properties of the apparatus, the representation of numbers by continued fractions, and the measure theory of continued fractions. 1964 edition. Prefaces.

Synopsis:

Elementary-level text by noted Soviet mathematician offers superb introduction to positive-integral elements of theory of continued fractions. Properties of the apparatus, representation of numbers by continued fractions, more. 1964 edition.

Table of Contents

Chapter I. Properties of the Apparatus

  1. Introduction

  2. Convergents

  3. Infinite continued fractions

  4. Continued fractions with natural elements

Chapter II. The Representation of Numbers by Continued Fractions

  5. Continued fractions as an apparatus for representing real numbers

  6. Convergents as best approximations

  7. The order of approximation

  8. General approximation theorems

  9. The approximation of algebraic irrational numbers and Liouville's transcendental numbers

  10. Quadratic irrational numbers and periodic continued fractions

Chapter III. The Measure Theory of Continued Fractions

  11. Introduction

  12. The elements as functions of the number represented

  13. Measure-theoretic evaluation of the increase in the elements

  14. Measure-theoretic evaluation of the increase in the denominators of the convergents. The fundamental theorem of the measure theory of approximation

  15. Gauss's problem and Kuz'min's theorem

  16. Average values

  Index

Product Details

ISBN:
9780486696300
Translator:
Scripta Technica, Inc
Author:
Eagle, Herbert
Author:
Mathematics
Author:
Khinchin, Aleksandra
Author:
Khinchin, A. Ya
Author:
Khinchin, A. Ya.
Author:
Scripta Technica, Inc
Publisher:
Dover Publications
Location:
Mineola, N.Y. :
Subject:
General
Subject:
Mathematics
Subject:
Number Theory
Subject:
Fractions
Subject:
Infinity
Subject:
Continued fractions.
Subject:
Fractions, continued
Subject:
General Mathematics
Subject:
Mathematics - General
Subject:
Arithmetic
Edition Description:
Trade Paper
Series:
Dover Books on Mathematics
Series Volume:
93-1
Publication Date:
19970531
Binding:
TRADE PAPER
Language:
English
Illustrations:
Yes
Pages:
112
Dimensions:
8.5 x 5.38 in 0.29 lb

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Related Subjects


Science and Mathematics » Mathematics » Analysis General
Science and Mathematics » Mathematics » Calculus » Precalculus
Science and Mathematics » Mathematics » General
Science and Mathematics » Mathematics » Number Theory
Science and Mathematics » Mathematics » Probability and Statistics » General
Science and Mathematics » Mathematics » Probability and Statistics » Statistics
Science and Mathematics » Physics » General

Continued Fractions 3RD Edition New Trade Paper
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Product details 112 pages Dover Publications - English 9780486696300 Reviews:
"Synopsis" by ,
Elementary-level text by noted Soviet mathematician offers superb introduction to positive-integral elements of theory of continued fractions. Properties of the apparatus, representation of numbers by continued fractions, more. 1964 edition.

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