Applied Number Theory

Authors: Niederreiter, Harald, Winterhof, Arne

  • First book that covers all four areas: cryptography, coding theory, quasi-Monte Carlo methods, pseudo-random numbers
  • Contains material for courses on number theory, cryptography, coding theory and quasi-Monte Carlo methods
  • Builds a bridge from basic number theory to recent research in applied number theory
see more benefits

Buy this book

eBook 35,69 €
price for India (gross)
  • ISBN 978-3-319-22321-6
  • Digitally watermarked, DRM-free
  • Included format: EPUB, PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover 24,99 €
44,99 € (listprice)
price for India (gross)
valid through June 30, 2017
  • ISBN 978-3-319-22320-9
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
About this Textbook

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.

About the authors

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

Reviews

“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)


Video

Table of contents (6 chapters)

  • A Review of Number Theory and Algebra

    Niederreiter, Harald (et al.)

    Pages 1-46

    Preview Buy Chapter 24,95 €
  • Cryptography

    Niederreiter, Harald (et al.)

    Pages 47-98

    Preview Buy Chapter 24,95 €
  • Coding Theory

    Niederreiter, Harald (et al.)

    Pages 99-183

    Preview Buy Chapter 24,95 €
  • Quasi-Monte Carlo Methods

    Niederreiter, Harald (et al.)

    Pages 185-306

    Preview Buy Chapter 24,95 €
  • Pseudorandom Numbers

    Niederreiter, Harald (et al.)

    Pages 307-366

    Preview Buy Chapter 24,95 €

Buy this book

eBook 35,69 €
price for India (gross)
  • ISBN 978-3-319-22321-6
  • Digitally watermarked, DRM-free
  • Included format: EPUB, PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover 24,99 €
44,99 € (listprice)
price for India (gross)
valid through June 30, 2017
  • ISBN 978-3-319-22320-9
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Loading...

Recommended for you

Loading...

Bibliographic Information

Bibliographic Information
Book Title
Applied Number Theory
Authors
Copyright
2015
Publisher
Springer International Publishing
Copyright Holder
Springer International Publishing Switzerland
eBook ISBN
978-3-319-22321-6
DOI
10.1007/978-3-319-22321-6
Hardcover ISBN
978-3-319-22320-9
Edition Number
1
Number of Pages
X, 442
Number of Illustrations and Tables
13 b/w illustrations, 7 illustrations in colour
Topics