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Number Theory in Science and Communication

With Applications in Cryptography, Physics, Digital Information, Computing, and Self-Similarity

  • Manfred R. Schroeder

Part of the Springer Series in Information Sciences book series (SSINF, volume 7)

Table of contents

  1. Front Matter
    Pages I-XXVI
  2. A Few Fundamentals

    1. Pages 1-18
    2. Pages 19-27
    3. Pages 28-40
  3. Some Simple Applications

  4. Congruences and the Like

  5. Cryptography and Divisors

  6. Residues and Diffraction

    1. Pages 181-193
  7. Chinese and Other Fast Algorithms

  8. Pseudoprimes, Möbius Transform, and Partitions

  9. Cyclotomy and Polynomials

    1. Pages 236-250
    2. Pages 254-259
  10. Galois Fields and More Applications

  11. Self-Similarity, Fractals and Art

  12. Back Matter
    Pages 340-369

About this book

Introduction

"Number Theory in Science and Communication" is a well-known introduction for non-mathematicians to this fascinating and useful branch of applied mathematics . It stresses intuitive understanding rather than abstract theory and highlights important concepts such as continued fractions, the golden ratio, quadratic residues and Chinese remainders, trapdoor functions, pseudoprimes and primitive elements. Their applications to problems in the real world are one of the main themes of the book. This revised fourth edition is augmented by recent advances in primes in progressions, twin primes, prime triplets, prime quadruplets and quintruplets, factoring with elliptic curves, quantum factoring, Golomb rulers and "baroque" integers.

From reviews of earlier editions –

"I continue to find [Schroeder’s] Number Theory a goldmine of valuable information. It is a marvellous book, in touch with the most recent applications of number theory and written with great clarity and humor.’ Philip Morrison (Scientific American)

"A light-hearted and readable volume with a wide range of applications to which the author has been a productive contributor – useful mathematics outside the formalities of theorem and proof." Martin Gardner

Keywords

Coding Congruance Encryption Euler Fermat Galois field Möbius Polynominals Prime Primes Pseudoprimes Random Generator Random Number number theory

Authors and affiliations

  • Manfred R. Schroeder
    • 1
  1. 1.Drittes Physikalisches InstitutUniversität GöttingenGöttingenGermany

Bibliographic information

  • DOI https://doi.org/10.1007/b137861
  • Copyright Information Springer-Verlag Berlin Heidelberg 2006
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Physics and Astronomy
  • Print ISBN 978-3-540-26596-2
  • Online ISBN 978-3-540-26598-6
  • Series Print ISSN 0720-678X
  • Buy this book on publisher's site