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Applied Number Theory

  • Harald Niederreiter
  • Arne Winterhof

Table of contents

  1. Front Matter
    Pages i-x
  2. Harald Niederreiter, Arne Winterhof
    Pages 1-46
  3. Harald Niederreiter, Arne Winterhof
    Pages 47-98
  4. Harald Niederreiter, Arne Winterhof
    Pages 99-183
  5. Harald Niederreiter, Arne Winterhof
    Pages 185-306
  6. Harald Niederreiter, Arne Winterhof
    Pages 307-366
  7. Harald Niederreiter, Arne Winterhof
    Pages 367-424
  8. Back Matter
    Pages 425-442

About this book

Introduction

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.

Keywords

coding theory cryptography number theory pseudo-random numbers quasi-Monte Carlo methods

Authors and affiliations

  • Harald Niederreiter
    • 1
  • Arne Winterhof
    • 2
  1. 1.Austrian Academy of SciencesJohann Radon Inst. for Computational and Applied Mathematics (RICAM)LinzAustria
  2. 2.Austrian Academy of SciencesJohann Radon Inst. for Computational and Applied Mathematics (RICAM)LinzAustria

Bibliographic information