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  • Textbook
  • © 1997

Number Theory in Science and Communication

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

  • Excellent introduction to the field
  • Suited for the non-specialist
  • Very successful book now in a completely revised new edition
  • Includes supplementary material: sn.pub/extras

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

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Table of contents (30 chapters)

  1. Front Matter

    Pages I-XXII
  2. A Few Fundamentals

    1. Introduction

      • Manfred R. Schroeder
      Pages 1-15
    2. The Natural Numbers

      • Manfred R. Schroeder
      Pages 16-24
    3. Primes

      • Manfred R. Schroeder
      Pages 25-37
    4. The Prime Distribution

      • Manfred R. Schroeder
      Pages 38-61
  3. Some Simple Applications

    1. Fractions: Continued, Egyptian and Farey

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

    1. Linear Congruences

      • Manfred R. Schroeder
      Pages 95-101
    2. Diophantine Equations

      • Manfred R. Schroeder
      Pages 102-117
    3. The Theorems of Fermat, Wilson and Euler

      • Manfred R. Schroeder
      Pages 118-124
  5. Cryptography and Divisors

    1. Euler Trap Doors and Public-Key Encryption

      • Manfred R. Schroeder
      Pages 125-134
    2. The Divisor Functions

      • Manfred R. Schroeder
      Pages 135-141
    3. The Prime Divisor Functions

      • Manfred R. Schroeder
      Pages 142-153
    4. Certified Signatures

      • Manfred R. Schroeder
      Pages 154-155
    5. Primitive Roots

      • Manfred R. Schroeder
      Pages 156-172
    6. Knapsack Encryption

      • Manfred R. Schroeder
      Pages 173-176
  6. Residues and Diffraction

    1. Quadratic Residues

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

    1. Fast Transformation and Kronecker Products

      • Manfred R. Schroeder
      Pages 199-202
    2. Quadratic Congruences

      • Manfred R. Schroeder
      Pages 203-204
  8. Pseudoprimes, Möbius Transform, and Partitions

    1. Pseudoprimes, Poker and Remote Coin Tossing

      • Manfred R. Schroeder
      Pages 205-215

About this book

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 primitive 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.

Reviews

From reviews of an 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

Authors and Affiliations

  • Drittes Physikalisches Institut, Universität Göttingen, Göttingen, Germany

    Manfred R. Schroeder

  • Bell Laboratories, Acoustics Speech and Mechanics Research, Murray Hill, USA

    Manfred R. Schroeder

Bibliographic Information

Buy it now

Buying options

eBook USD 74.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever

Tax calculation will be finalised at checkout

Other ways to access