Books.org participates in affiliate programs including Bookshop.org and the Amazon Services LLC Associates Program. We may earn a commission from qualifying purchases made through links on this page, at no additional cost to you.
Overview
This book examines the number-theoretic properties of the real numbers. It collects a variety of new ideas and develops connections between different branches of mathematics. An indispensable compendium of basic results, the text also includes important theorems and open problems. The book begins with the classical results of Borel, Khintchine, and Weyl, and then proceeds to Diophantine approximation, GCD sums, Schmidt's method, and uniform distribution. Other topics include generalizations to higher dimensions and various non-periodic problems (for example, restricting approximation to fractions with prime numerator and denominator). It concludes with a chapter on Hausdorf dimensions for exceptional sets of measure zero.
Synopsis
This book examines the number-theoretic properties of the real numbers. It collects a variety of new ideas and develops connections between different branches of mathematics. An indispensable compendium of basic results, the text also includes important theorems and open problems. The book begins with the classical results of Borel, Khintchine, and Weyl, and then proceeds to Diophantine approximation, GCD sums, Schmidt's method, and uniform distribution. Other topics include generalizations to higher dimensions and various non-periodic problems (for example, restricting approximation to fractions with prime numerator and denominator). It concludes with a chapter on Hausdorf dimensions for exceptional sets of measure zero.