Applied Number Theory

Applied Number Theory

By: Harald Niederreiter (author), Arne Winterhof (author)Hardback

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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.

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About Author

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


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.

Product Details

  • publication date: 03/09/2015
  • ISBN13: 9783319223209
  • Format: Hardback
  • Year: 2015
  • Number Of Pages: 452
  • ID: 9783319223209
  • weight: 836
  • ISBN10: 3319223208

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