Applied Number Theory

ISBN-13: 9783319223209 / Angielski / Twarda / 2015 / 442 str.

Harald Niederreiter; Arne Winterhof

Opis

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.

Recenzje

"The authors succeed admirably in their aim of demonstrating that the theory of numbers has applications. ... The account is accessible, well-paced and unified and leads the reader along from the introductory ideas to recent advances. Each chapter has exercises inviting the reader to compute and fill in details in the proofs." (John H. Loxton, Mathematical Reviews, April, 2016)

"The book is intended to be usable as a text ... . It would also be useful for those of us who received our training in number theory in the days before it had any applications and wanted to find out about them. ... The writing is clear and lively. ... The book is pleasant to the eyes, and in the hands. ... It is an estimable book that I hope is successful." (Underwood Dudley, MAA Reviews, maa.org, January, 2016)

Spis treści

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.

O autorze

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