Advertisement

Number Theory in Science and Communication

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

  • Manfred Schroeder

Table of contents

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

    1. Front Matter
      Pages 1-1
    2. Manfred Schroeder
      Pages 3-20
    3. Manfred Schroeder
      Pages 21-29
    4. Manfred Schroeder
      Pages 31-43
    5. Manfred Schroeder
      Pages 45-69
  3. Some Simple Applications

    1. Front Matter
      Pages 71-71
    2. Manfred Schroeder
      Pages 73-107
  4. Congruences and the Like

    1. Front Matter
      Pages 109-109
    2. Manfred Schroeder
      Pages 111-117
    3. Manfred Schroeder
      Pages 119-137
    4. Manfred Schroeder
      Pages 139-145
    5. Manfred Schroeder
      Pages 147-158
  5. Cryptography and Divisors

    1. Front Matter
      Pages 159-159
    2. Manfred Schroeder
      Pages 161-170
    3. Manfred Schroeder
      Pages 171-177
    4. Manfred Schroeder
      Pages 179-191
    5. Manfred Schroeder
      Pages 193-194
    6. Manfred Schroeder
      Pages 195-211
    7. Manfred Schroeder
      Pages 213-216
  6. Residues and Diffraction

    1. Front Matter
      Pages 217-217
    2. Manfred Schroeder
      Pages 219-232
  7. Chinese and Other Fast Algorithms

    1. Front Matter
      Pages 233-233
    2. Manfred Schroeder
      Pages 245-249
    3. Manfred Schroeder
      Pages 251-252
  8. Pseudoprimes, Möbius Transform, and Partitions

    1. Front Matter
      Pages 253-253
    2. Manfred Schroeder
      Pages 255-266
    3. Manfred Schroeder
      Pages 267-274
    4. Manfred Schroeder
      Pages 275-282
    5. Manfred Schroeder
      Pages 283-285
  9. Cyclotomy and Polynomials

    1. Front Matter
      Pages 287-287
    2. Manfred Schroeder
      Pages 289-304
    3. Manfred Schroeder
      Pages 305-307
    4. Manfred Schroeder
      Pages 309-314
  10. Galois Fields and More Applications

    1. Front Matter
      Pages 315-315
    2. Manfred Schroeder
      Pages 317-329
    3. Manfred Schroeder
      Pages 331-345
    4. Manfred Schroeder
      Pages 347-353
    5. Manfred Schroeder
      Pages 355-366
    6. Manfred Schroeder
      Pages 367-375
  11. Self-Similarity, Fractals and Art

    1. Front Matter
      Pages 377-377
  12. Back Matter
    Pages 405-418

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 fifth edition is augmented by recent advances in coding theory, permutations and derangements and a chapter in quantum cryptography.

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

DES Galois field Number theory Prime algorithms coding coding theory communication cryptography information

Authors and affiliations

  • Manfred Schroeder
    • 1
  1. 1.Universität Göttingen Inst Physik IIIGermany

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-540-85298-8
  • Copyright Information Springer Berlin Heidelberg 2009
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Physics and Astronomy
  • Print ISBN 978-3-540-85297-1
  • Online ISBN 978-3-540-85298-8
  • Buy this book on publisher's site