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Number Theory in Science and Communication

With Applications in Cryptography, Physics, Biology, Digital Information, and Computing

  • Manfred R. Schroeder

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

Table of contents

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

    1. Manfred R. Schroeder
      Pages 1-16
    2. Manfred R. Schroeder
      Pages 17-25
    3. Manfred R. Schroeder
      Pages 26-39
    4. Manfred R. Schroeder
      Pages 40-54
  3. Some Simple Applications

    1. Manfred R. Schroeder
      Pages 55-78
  4. Congruences and the Like

    1. Manfred R. Schroeder
      Pages 79-86
    2. Manfred R. Schroeder
      Pages 87-101
    3. Manfred R. Schroeder
      Pages 102-109
  5. Cryptography and Divisors

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      Pages 110-118
    2. Manfred R. Schroeder
      Pages 119-126
    3. Manfred R. Schroeder
      Pages 127-140
    4. Manfred R. Schroeder
      Pages 141-142
    5. Manfred R. Schroeder
      Pages 143-159
    6. Manfred R. Schroeder
      Pages 160-163
  6. Residues and Diffraction

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      Pages 164-175
  7. Chinese and Other Fast Algorithms

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      Pages 186-190
    2. Manfred R. Schroeder
      Pages 191-192
  8. Pseudoprimes, Möbius Transform, and Partitions

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      Pages 193-203
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      Pages 204-211
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      Pages 212-220
  9. Cyclotomy and Polynomials

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      Pages 221-237
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      Pages 238-241
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      Pages 242-247
  10. Galois Fields and More Applications

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      Pages 248-255
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      Pages 256-270
    3. Manfred R. Schroeder
      Pages 271-277
    4. Manfred R. Schroeder
      Pages 278-288
    5. Manfred R. Schroeder
      Pages 289-296
    6. Manfred R. Schroeder
      Pages 297-297
  11. Back Matter
    Pages 298-326

About this book

Introduction

"Beauty is the first test: there is no permanent place in the world for ugly mathematics. " - G. H. Hardy N umber theory has been considered since time immemorial to be the very paradigm of pure (some would say useless) mathematics. In fact, the Chinese characters for mathematics are Number Science. "Mathematics is the queen of sciences - and number theory is the queen of mathematics," according to Carl Friedrich Gauss, the lifelong Wunderkind, who hirnself enjoyed the epithet "Princeps Mathematicorum. " What could be more beautiful than a deep, satisfying relation between whole numbers. {One is almost tempted to call them wholesome numbersJ In fact, it is hard to come up with a more appropriate designation than their learned name: the integers - meaning the "untouched ones". How high they rank, in the realms of pure thought and aesthetics, above their lesser brethren: the real and complex number- whose first names virtually exude unsavory involvement with the complex realities of everyday life! Yet, as we shall see in this book, the theory of integers can provide totally unexpected answers to real-world problems. In fact, discrete mathematics is ta king on an ever more important role. If nothing else, the advent of the digital computer and digital communication has seen to that. But even earlier, in physics the emergence of quantum mechanics and discrete elementary particles put a premium on the methods and, indeed, the spirit of discrete mathematics.

Keywords

Galois field Symbol Zahlentheorie algorithms communication cryptography diophantine equation discrete mathematics encryption mechanics number theory polynomial prime number quantum mechanics transformation

Authors and affiliations

  • Manfred R. Schroeder
    • 1
    • 2
  1. 1.Drittes Physikalisches InstitutUniversität GöttingenGöttingenFed. Rep. of Germany
  2. 2.Acoustics Speech and Mechanics ResearchBell LaboratoriesMurray HillUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-662-02395-2
  • Copyright Information Springer-Verlag Berlin Heidelberg 1984
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-662-02397-6
  • Online ISBN 978-3-662-02395-2
  • Series Print ISSN 0720-678X
  • Buy this book on publisher's site