{"product_id":"continued-fractions-revised","title":"Continued Fractions (Revised)","description":"\n\u003ctable align=\"center\" border=\"0\" cellpadding=\"2\" cellspacing=\"0\" width=\"100%\"\u003e\n\u003ctr\u003e\n\u003ctd class=\"productDetailSmallElements\"\u003e\n\u003cp\u003e\n\u003cstrong\u003eTable of Contents\u003c\/strong\u003e:\u003cbr\u003e\n\t\t\t\t\t\t\t\tChapter I. Properties of the Apparatus \n\u003cbr\u003e 1. Introduction \n\u003cbr\u003e 2. Convergents \n\u003cbr\u003e 3. Infinite continued fractions \n\u003cbr\u003e 4. Continued fractions with natural elements \n\u003cbr\u003eChapter II. The Representation of Numbers by Continued Fractions \n\u003cbr\u003e 5. Continued fractions as an apparatus for representing real numbers \n\u003cbr\u003e 6. Convergents as best approximations \n\u003cbr\u003e 7. The order of approximation \n\u003cbr\u003e 8. General approximation theorems \n\u003cbr\u003e 9. The approximation of algebraic irrational numbers and Liouville's transcendental numbers \n\u003cbr\u003e 10. Quadratic irrational numbers and periodic continued fractions \n\u003cbr\u003eChapter III. The Measure Theory of Continued Fractions \n\u003cbr\u003e 11. Introduction \n\u003cbr\u003e 12. The elements as functions of the number represented \n\u003cbr\u003e 13. Measure-theoretic evaluation of the increase in the elements \n\u003cbr\u003e 14. Measure-theoretic evaluation of the increase in the denominators of the convergents. The fundamental theorem of the measure theory of approximation \n\u003cbr\u003e 15. Gauss's problem and Kuz'min's theorem \n\u003cbr\u003e 16. Average values \n\u003cbr\u003e Index\u003cbr\u003e\u003cbr\u003e\n\u003cstrong\u003ePublisher Marketing\u003c\/strong\u003e:\u003cbr\u003e\n\t\t\t\t\t\t\t\tIn 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. \n\u003cbr\u003ePresented 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. \n\u003cbr\u003eThe 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.\u003cbr\u003e\u003cbr\u003e\n\u003c\/p\u003e\n\u003cbr\u003e\n\u003cbr\u003e\n\u003c\/td\u003e\n\u003c\/tr\u003e\n\u003c\/table\u003e\n","brand":"Dover Publications","offers":[{"title":"Default Title","offer_id":46431154602115,"sku":"SPTM-9780486696300","price":8.95,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0564\/6830\/8099\/files\/9780486696300_spiral.png?v=1769660484","url":"https:\/\/sebink.com\/products\/continued-fractions-revised","provider":"Sebink","version":"1.0","type":"link"}