Applied Number Theory / by Harald Niederreiter, Arne Winterhof.

Format:

Book

Author/Creator:

Niederreiter, Harald., Author.

Winterhof, Arne., Author.

Language:

English

Subjects (All):

Number theory.

Information theory.

Data structures (Computer science).

Number Theory.

Information and Communication, Circuits.

Data Structures and Information Theory.

Local Subjects:

Number Theory.

Information and Communication, Circuits.

Data Structures and Information Theory.

Physical Description:

1 online resource (X, 442 p. 20 illus., 7 illus. in color.)

Edition:

1st ed. 2015.

Place of Publication:

Cham : Springer International Publishing : Imprint: Springer, 2015.

Language Note:

English

Summary:

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.

Contents:

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.

Notes:

Bibliographic Level Mode of Issuance: Monograph

Description based on publisher supplied metadata and other sources.

ISBN:

3-319-22321-6

OCLC:

920524960