Ebook: Number Theory in Science and Communication: With Applications in Cryptography, Physics, Biology, Digital Information, and Computing

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Content:
Front Matter....Pages I-XVI
Introduction....Pages 1-16
The Natural Numbers....Pages 17-25
Primes....Pages 26-39
The Prime Distribution....Pages 40-54
Fractions: Continued, Egyptian and Farey....Pages 55-78
Linear Congruences....Pages 79-86
Diophantine Equations....Pages 87-101
The Theorems of Fermat, Wilson and Euler....Pages 102-109
Euler Trap Doors and Public-Key Encryption....Pages 110-118
The Divisor Functions....Pages 119-126
The Prime Divisor Functions....Pages 127-140
Certified Signatures....Pages 141-142
Primitive Roots....Pages 143-159
Knapsack Encryption....Pages 160-163
Quadratic Residues....Pages 164-175
The Chinese Remainder Theorem and Simultaneous Congruences....Pages 176-185
Fast Transformations and Kronecker Products....Pages 186-190
Quadratic Congruences....Pages 191-192
Pseudoprimes, Poker and Remote Coin Tossing....Pages 193-203
The M?bius Function and the M?bius Transform....Pages 204-211
Generating Functions and Partitions....Pages 212-220
Cyclotomic Polynomials....Pages 221-237
Linear Systems and Polynomials....Pages 238-241
Polynomial Theory....Pages 242-247
Galois Fields....Pages 248-255
Spectral Properties of Galois Sequences....Pages 256-270
Random Number Generators....Pages 271-277
Waveforms and Radiation Patterns....Pages 278-288
Number Theory, Randomness and “Art”....Pages 289-296
Conclusion....Pages 297-297
Back Matter....Pages 298-326

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Content:
Front Matter....Pages I-XVI
Introduction....Pages 1-16
The Natural Numbers....Pages 17-25
Primes....Pages 26-39
The Prime Distribution....Pages 40-54
Fractions: Continued, Egyptian and Farey....Pages 55-78
Linear Congruences....Pages 79-86
Diophantine Equations....Pages 87-101
The Theorems of Fermat, Wilson and Euler....Pages 102-109
Euler Trap Doors and Public-Key Encryption....Pages 110-118
The Divisor Functions....Pages 119-126
The Prime Divisor Functions....Pages 127-140
Certified Signatures....Pages 141-142
Primitive Roots....Pages 143-159
Knapsack Encryption....Pages 160-163
Quadratic Residues....Pages 164-175
The Chinese Remainder Theorem and Simultaneous Congruences....Pages 176-185
Fast Transformations and Kronecker Products....Pages 186-190
Quadratic Congruences....Pages 191-192
Pseudoprimes, Poker and Remote Coin Tossing....Pages 193-203
The M?bius Function and the M?bius Transform....Pages 204-211
Generating Functions and Partitions....Pages 212-220
Cyclotomic Polynomials....Pages 221-237
Linear Systems and Polynomials....Pages 238-241
Polynomial Theory....Pages 242-247
Galois Fields....Pages 248-255
Spectral Properties of Galois Sequences....Pages 256-270
Random Number Generators....Pages 271-277
Waveforms and Radiation Patterns....Pages 278-288
Number Theory, Randomness and “Art”....Pages 289-296
Conclusion....Pages 297-297
Back Matter....Pages 298-326
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