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)
Third Edition.
Berlin, Heidelberg : Springer, 1997
XXII, 364 p. online resource.
englisch
9783662034309
10.1007/978-3-662-03430-9
Springer Series in Information Sciences ; 7
Full Text
Table of Contents:
  • I. A Few Fundamentals
  • 1. Introduction
  • 2. The Natural Numbers
  • 3. Primes
  • 4. The Prime Distribution
  • II. Some Simple Applications
  • 5. Fractions: Continued, Egyptian and Farey
  • III. Congruences and the Like
  • 6. Linear Congruences
  • 7. Diophantine Equations
  • 8. The Theorems of Fermat, Wilson and Euler
  • IV. Cryptography and Divisors
  • 9. Euler Trap Doors and Public-Key Encryption
  • 10. The Divisor Functions
  • 11. The Prime Divisor Functions
  • 12. Certified Signatures
  • 13. Primitive Roots
  • 14. Knapsack Encryption
  • V. Residues and Diffraction
  • 15. Quadratic Residues
  • VI. Chinese and Other Fast Algorithms
  • 16. The Chinese Remainder Theorem and Simultaneous Congruences
  • 17. Fast Transformation and Kronecker Products
  • 18. Quadratic Congruences
  • VII. Pseudoprimes, Möbius Transform, and Partitions
  • 19. Pseudoprimes, Poker and Remote Coin Tossing
  • 20. The Möbius Function and the Möbius Transform
  • 21. Generating Functions and Partitions
  • VIII. Cyclotomy and Polynomials
  • 22. Cyclotomic Polynomials
  • 23. Linear Systems and Polynomials
  • 24. Polynomial Theory
  • IX. Galois Fields and More Applications
  • 25. Galois Fields
  • 26. Spectral Properties of Galois Sequences
  • 27. Random Number Generators
  • 28. Waveforms and Radiation Patterns
  • 29. Number Theory, Randomness and “Art”
  • X. Self-Similarity, Fractals and Art
  • 30. Self-Similarity, Fractals, Deterministic Chaos and a New State of Matter
  • Glossary of Symbols
  • References
  • Name Index.