Applied Number Theory

TRAMA

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.

SOMMARIO

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.

AUTORE

Harald Niederreiter: Full member, Austrian Academy of Sciences; Full member and former member of the presidium, German Academy of Natural Sciences Leopoldina; Cardinal Innitzer Prize for Natural Sciences in Austria; Invited speaker at ICM 1998 (Berlin) and ICIAM 2003 (Sydney): Singapore National Science Award 2003; Fellow of the American Mathematical Society Arne Winterhof: Edmund and Rosa Hlawka Prize 2004; Advancement Award of the Austrian Mathematical Society 2010

ALTRE INFORMAZIONI

• Condizione: Nuovo
• ISBN: 9783319223209
• Dimensioni: 235 x 155 mm
• Formato: Copertina rigida
• Illustration Notes: X, 442 p. 20 illus., 7 illus. in color.
• Pagine Arabe: 442
• Pagine Romane: x