Number Theory in Science and Communication [E-Book] : With Applications in Cryptography, Physics, Digital Information, Computing, and Self-Similarity / by Manfred R. Schroeder.
Schroeder, Manfred R., (author)
Second Enlarged Edition.
Berlin, Heidelberg : Springer, 1986
XIX, 374 p. online resource.
Springer Series in Information Sciences ; 7
Full Text
Table of Contents:
  • A Few Fundamentals
  • The Natural Numbers
  • Primes
  • The Prime Distribution
  • Some Simple Applications
  • Fractions: Continued, Egyptian and Farey
  • Congruences and the Like
  • Linear Congruences
  • Diophantine Equations
  • The Theorems of Fermat, Wilson and Euler
  • Cryptography and Divisors
  • Euler Trap Doors and Public-Key Encryption
  • The Divisor Functions
  • The Prime Divisor Functions
  • Certified Signatures
  • Primitive Roots
  • Knapsack Encryption
  • Residues and Diffraction
  • Quadratic Residues
  • Chinese and Other Fast Algorithms
  • The Chinese Remainder Theorem and Simultaneous Congruences
  • Fast Transformations and Kronecker Products
  • Quadratic Congruences
  • Pseudoprimes, Möbius Transform, and Partitions
  • Pseudoprimes, Poker and Remote Coin Tossing
  • The Möbius Function and the Möbius Transform
  • Generating Functions and Partitions
  • Cyclotomy and Polynomials
  • Cyclotomic Polynomials
  • Linear Systems and Polynomials
  • Polynomial Theory
  • Galois Fields and More Applications
  • Galois Fields
  • Spectral Properties of Galois Sequences
  • Random Number Generators
  • Waveforms and Radiation Patterns
  • Number Theory, Randomness and “Art”
  • Self Similarity, Fractals and Art
  • Self-Similarity, Fractals, Deterministic Chaos and a New State of Matter.