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Dover Books on Mathematics Ser.: Continued Fractions by Herbert Eagle and A. Ya. Khinchin (1997, Trade Paperback)
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Title: Continued Fractions. Language: English. Number of Pages: 112. Weight: 0.28 lbs. Publication Date: 1997-05-14. Publisher: DOVER PUBN INC.
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About this product
Product Identifiers
PublisherDover Publications, Incorporated
ISBN-100486696308
ISBN-139780486696300
eBay Product ID (ePID)108130
Product Key Features
Number of Pages112 Pages
LanguageEnglish
Publication NameContinued Fractions
SubjectArithmetic, Mathematical Analysis
Publication Year1997
FeaturesReprint
TypeTextbook
Subject AreaMathematics
AuthorHerbert Eagle, A. Ya. Khinchin
SeriesDover Books on Mathematics Ser.
FormatTrade Paperback
Dimensions
Item Height0.2 in
Item Weight4.9 Oz
Item Length8.5 in
Item Width5.4 in
Additional Product Features
Intended AudienceCollege Audience
LCCN97-008056
Dewey Edition21
IllustratedYes
Dewey Decimal515/.243
Edition DescriptionReprint
Table Of ContentChapter 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
SynopsisElementary-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, and more. 1964 edition., In this elementary-level text, eminent Soviet mathematician A. Ya. Khinchin offers a superb introduction to the positive-integral elements of the theory of continued functions, a special algorithm that is one of the most important tools in analysis, probability theory, mechanics, and, especially, number theory. Presented in a clear, straightforward manner, the book comprises three major chapters: the properties of the apparatus, the representation of numbers by continued fractions and the measure theory of continued fractions. The last chapter is somewhat more advanced and deals with the metric, or probability, theory of continued fractions, an important field developed almost entirely by Soviet mathematicians, including Khinchin. The present volume reprints an English translation of the third Russian edition published in 1961. It is not only an excellent introduction to the study of continued fractions, but a stimulating consideration of the profound and interesting problems of the measure theory of numbers.
LC Classification NumberQA295.K513 1997
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