Number Theory in Science and Communication [E-Book] : With Applications in Cryptography, Physics, Biology, Digital Information, and Computing / by Manfred R. Schroeder.
"Beauty is the first test: there is no permanent place in the world for ugly mathematics. " - G. H. Hardy N umber 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 Numbe...
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Full text |
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Personal Name(s): | Schroeder, Manfred R., author |
Imprint: |
Berlin, Heidelberg :
Springer,
1984
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Physical Description: |
XVI, 326 p. online resource. |
Note: |
englisch |
ISBN: |
9783662023952 |
DOI: |
10.1007/978-3-662-02395-2 |
Series Title: |
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Springer Series in Information Sciences ;
7 |
Subject (LOC): |
- 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 Transformations 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”
- 30. Conclusion
- A. A Calculator Program for Exponentiation and Residue Reduction
- B. A Calculator Program for Calculating Fibonacci and Lucas Numbers
- C. A Calculator Program for Decomposing an Integer According to the Fibonacci Number System
- Glossary of Symbols.