Applied Number Theory This textbook effectively builds a bridge from basic number theory to recent advances in applied number theory. It presents the first unified account of the four major areas of application where number theory plays a fundamental role namely cryptography coding theory quasi Monte Carlo methods and pseudorandom number generation allowing the authors to delineate the manifold links and interrelations between these areas. Number theory which Carl Friedrich Gauss famously dubbed the queen of mathematics has always been considered a very beautiful field of mathematics producing lovely results and elegant proofs. While only very few real life applications were known in the past today number theory can be found in everyday life: in supermarket bar code scanners in our cars’ GPS systems in online banking etc. Starting with a brief introductory course on number theory in Chapter 1 which makes the book more accessible for undergraduates the authors describe the four main application areas in Chapters 2 5 and offer a glimpse of advanced results that are presented without proofs and require more advanced mathematical skills. In the last chapter they review several further applications of number theory ranging from check digit systems to quantum computation and the organization of raster graphics memory. Upper level undergraduates graduates and researchers in the field of number theory will find this book to be a valuable resource Preface 1 A Review of Number Theory and Algebra 2 Cryptography 3 Coding Theory 4 Quasi Monte Carlo Methods 5 Pseudorandom Numbers 6 Further Applications Bibliography Index