Skip to main content
SpringerLink
Log in
Book cover

Number Theory in Science and Communication

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

  • Textbook
  • © 1986

Overview

Authors:
  1. Manfred R. Schroeder

    1. Drittes Physikalisches Institut, Universität Göttingen, Göttingen, Fed. Rep. of Germany
      Acoustics Speech and Mechanics Research, Bell Laboratories, Murray Hill, USA

    View author publications

    You can also search for this author in PubMed   Google Scholar

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

This is a preview of subscription content, log in via an institution to check access.

Access this book

Log in via an institution
eBook USD 34.99
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

Licence this eBook for your library

Institutional subscriptions

Table of contents (30 chapters)

  1. Front Matter

    Pages I-XIX
    Download chapter PDF

  2. A Few Fundamentals

    1. Introduction

      • Manfred R. Schroeder
      Pages 1-16

    2. The Natural Numbers

      • Manfred R. Schroeder
      Pages 17-25

    3. Primes

      • Manfred R. Schroeder
      Pages 26-39

    4. The Prime Distribution

      • Manfred R. Schroeder
      Pages 40-54

  3. Some Simple Applications

    1. Fractions: Continued, Egyptian and Farey

      • Manfred R. Schroeder
      Pages 55-86

  4. Congruences and the Like

    1. Linear Congruences

      • Manfred R. Schroeder
      Pages 87-94

    2. Diophantine Equations

      • Manfred R. Schroeder
      Pages 95-110

    3. The Theorems of Fermat, Wilson and Euler

      • Manfred R. Schroeder
      Pages 111-117

  5. Cryptography and Divisors

    1. Euler Trap Doors and Public-Key Encryption

      • Manfred R. Schroeder
      Pages 118-126

    2. The Divisor Functions

      • Manfred R. Schroeder
      Pages 127-134

    3. The Prime Divisor Functions

      • Manfred R. Schroeder
      Pages 135-148

    4. Certified Signatures

      • Manfred R. Schroeder
      Pages 149-150

    5. Primitive Roots

      • Manfred R. Schroeder
      Pages 151-167

    6. Knapsack Encryption

      • Manfred R. Schroeder
      Pages 168-171

  6. Residues and Diffraction

    1. Quadratic Residues

      • Manfred R. Schroeder
      Pages 172-185

  7. Chinese and Other Fast Algorithms

    1. The Chinese Remainder Theorem and Simultaneous Congruences

      • Manfred R. Schroeder
      Pages 186-195

    2. Fast Transformations and Kronecker Products

      • Manfred R. Schroeder
      Pages 196-200

    3. Quadratic Congruences

      • Manfred R. Schroeder
      Pages 201-202

  8. Pseudoprimes, Möbius Transform, and Partitions

    1. Pseudoprimes, Poker and Remote Coin Tossing

      • Manfred R. Schroeder
      Pages 203-214
Back to top

Keywords

About this book

"Beauty is the first test: there is no permanent place in the world for ugly mathematics. " - G. H. Hardy Number 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 himself 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 numbers') 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 taking 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.

Reviews

..."A lighthearted and readable volume with a wide range of applications to which the author has been a productive contributor - useful mathematics given outside the formalities of theorem and proof"... #Scientific American#1

Authors and Affiliations

  • Drittes Physikalisches Institut, Universität Göttingen, Göttingen, Fed. Rep. of Germany

    Manfred R. Schroeder

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

    Manfred R. Schroeder

Bibliographic Information

Publish with us

Policies and ethics

Back to top

Search

Navigation