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Number Theory in Science and Communication

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

  • Manfred R. Schroeder
Textbook

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

Table of contents

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

    1. Manfred R. Schroeder
      Pages 1-15
    2. Manfred R. Schroeder
      Pages 16-24
    3. Manfred R. Schroeder
      Pages 25-37
    4. Manfred R. Schroeder
      Pages 38-61
  3. Some Simple Applications

    1. Manfred R. Schroeder
      Pages 62-94
  4. Congruences and the Like

    1. Manfred R. Schroeder
      Pages 95-101
    2. Manfred R. Schroeder
      Pages 102-117
    3. Manfred R. Schroeder
      Pages 118-124
  5. Cryptography and Divisors

    1. Manfred R. Schroeder
      Pages 125-134
    2. Manfred R. Schroeder
      Pages 135-141
    3. Manfred R. Schroeder
      Pages 142-153
    4. Manfred R. Schroeder
      Pages 154-155
    5. Manfred R. Schroeder
      Pages 156-172
    6. Manfred R. Schroeder
      Pages 173-176
  6. Residues and Diffraction

    1. Manfred R. Schroeder
      Pages 177-189
  7. Chinese and Other Fast Algorithms

    1. Manfred R. Schroeder
      Pages 199-202
    2. Manfred R. Schroeder
      Pages 203-204
  8. Pseudoprimes, Möbius Transform, and Partitions

    1. Manfred R. Schroeder
      Pages 205-215
    2. Manfred R. Schroeder
      Pages 216-223
    3. Manfred R. Schroeder
      Pages 224-231
  9. Cyclotomy and Polynomials

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      Pages 232-246
    2. Manfred R. Schroeder
      Pages 247-249
    3. Manfred R. Schroeder
      Pages 250-255
  10. Galois Fields and More Applications

    1. Manfred R. Schroeder
      Pages 256-268
    2. Manfred R. Schroeder
      Pages 269-282
    3. Manfred R. Schroeder
      Pages 283-288
    4. Manfred R. Schroeder
      Pages 289-300
    5. Manfred R. Schroeder
      Pages 301-310
  11. Self-Similarity, Fractals and Art

  12. Back Matter
    Pages 336-364

About this book

Introduction

Number Theory in Science and Communication is an introduction for non-mathematicians. The book 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 primituve elements. Their applications to problems in the real world is one of the main themes of the book. This third 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.

Keywords

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

Authors and affiliations

  • Manfred R. Schroeder
    • 1
    • 2
  1. 1.Drittes Physikalisches InstitutUniversität GöttingenGöttingenGermany
  2. 2.Bell LaboratoriesAcoustics Speech and Mechanics ResearchMurray HillUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-662-03430-9
  • Copyright Information Springer-Verlag Berlin Heidelberg 1997
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-540-62006-8
  • Online ISBN 978-3-662-03430-9
  • Series Print ISSN 0720-678X
  • Buy this book on publisher's site
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