Ebook: Number Theory in Science and Communication: With Applications in Cryptography, Physics, Digital Information, Computing, and Self-Similarity
- Tags: Mathematical Methods in Physics, Numerical and Computational Methods, Coding and Information Theory, Probability Theory and Stochastic Processes, Number Theory
- Series: Springer Series in Information Sciences 7
- Year: 2006
- Publisher: Springer Berlin Heidelberg
- Language: English
- pdf
"Number Theory in Science and Communication" is a well-known introduction for non-mathematicians to this fascinating and useful branch of applied mathematics . It stresses intuitive understanding rather than abstract theory and highlights important concepts such as continued fractions, the golden ratio, quadratic residues and Chinese remainders, trapdoor functions, pseudoprimes and primitive elements. Their applications to problems in the real world are one of the main themes of the book. This revised fourth edition is augmented by recent advances in primes in progressions, twin primes, prime triplets, prime quadruplets and quintruplets, factoring with elliptic curves, quantum factoring, Golomb rulers and "baroque" integers.
From reviews of earlier editions –
"I continue to find [Schroeder’s] Number Theory a goldmine of valuable information. It is a marvellous book, in touch with the most recent applications of number theory and written with great clarity and humor.’ Philip Morrison (Scientific American)
"A light-hearted and readable volume with a wide range of applications to which the author has been a productive contributor – useful mathematics outside the formalities of theorem and proof." Martin Gardner
"Number Theory in Science and Communication" is a well-known introduction for non-mathematicians to this fascinating and useful branch of applied mathematics . It stresses intuitive understanding rather than abstract theory and highlights important concepts such as continued fractions, the golden ratio, quadratic residues and Chinese remainders, trapdoor functions, pseudoprimes and primitive elements. Their applications to problems in the real world are one of the main themes of the book. This revised fourth edition is augmented by recent advances in primes in progressions, twin primes, prime triplets, prime quadruplets and quintruplets, factoring with elliptic curves, quantum factoring, Golomb rulers and "baroque" integers.
From reviews of earlier editions –
"I continue to find [Schroeder’s] Number Theory a goldmine of valuable information. It is a marvellous book, in touch with the most recent applications of number theory and written with great clarity and humor.’ Philip Morrison (Scientific American)
"A light-hearted and readable volume with a wide range of applications to which the author has been a productive contributor – useful mathematics outside the formalities of theorem and proof." Martin Gardner
Content:
Front Matter....Pages I-XXVI
Introduction....Pages 1-18
The Natural Numbers....Pages 19-27
Primes....Pages 28-40
The Prime Distribution....Pages 41-64
Fractions: Continued, Egyptian and Farey....Pages 65-98
Linear Congruences....Pages 99-105
Diophantine Equations....Pages 106-121
The Theorems of Fermat, Wilson and Euler....Pages 122-128
Euler Trap Doors and Public-Key Encryption....Pages 129-138
The Divisor Functions....Pages 139-145
The Prime Divisor Functions....Pages 146-157
Certified Signatures....Pages 158-159
Primitive Roots....Pages 160-176
Knapsack Encryption....Pages 177-180
Quadratic Residues....Pages 181-193
The Chinese Remainder Theorem and Simultaneous Congruences....Pages 194-202
Fast Transformation and Kronecker Products....Pages 203-206
Quadratic Congruences....Pages 207-208
Pseudoprimes, Poker and Remote Coin Tossing....Pages 209-219
The M?bius Function and the M?bius Transform....Pages 220-227
Generating Functions and Partitions....Pages 228-235
Cyclotomic Polynomials....Pages 236-250
Linear Systems and Polynomials....Pages 251-253
Polynomial Theory....Pages 254-259
Galois Fields....Pages 260-272
Spectral Properties of Galois Sequences....Pages 273-286
Random Number Generators....Pages 287-292
Waveforms and Radiation Patterns....Pages 293-304
Number Theory, Randomness and “Art”....Pages 305-314
Self-Similarity, Fractals, Deterministic Chaos and a New State of Matter....Pages 315-339
Back Matter....Pages 340-369
"Number Theory in Science and Communication" is a well-known introduction for non-mathematicians to this fascinating and useful branch of applied mathematics . It stresses intuitive understanding rather than abstract theory and highlights important concepts such as continued fractions, the golden ratio, quadratic residues and Chinese remainders, trapdoor functions, pseudoprimes and primitive elements. Their applications to problems in the real world are one of the main themes of the book. This revised fourth edition is augmented by recent advances in primes in progressions, twin primes, prime triplets, prime quadruplets and quintruplets, factoring with elliptic curves, quantum factoring, Golomb rulers and "baroque" integers.
From reviews of earlier editions –
"I continue to find [Schroeder’s] Number Theory a goldmine of valuable information. It is a marvellous book, in touch with the most recent applications of number theory and written with great clarity and humor.’ Philip Morrison (Scientific American)
"A light-hearted and readable volume with a wide range of applications to which the author has been a productive contributor – useful mathematics outside the formalities of theorem and proof." Martin Gardner
Content:
Front Matter....Pages I-XXVI
Introduction....Pages 1-18
The Natural Numbers....Pages 19-27
Primes....Pages 28-40
The Prime Distribution....Pages 41-64
Fractions: Continued, Egyptian and Farey....Pages 65-98
Linear Congruences....Pages 99-105
Diophantine Equations....Pages 106-121
The Theorems of Fermat, Wilson and Euler....Pages 122-128
Euler Trap Doors and Public-Key Encryption....Pages 129-138
The Divisor Functions....Pages 139-145
The Prime Divisor Functions....Pages 146-157
Certified Signatures....Pages 158-159
Primitive Roots....Pages 160-176
Knapsack Encryption....Pages 177-180
Quadratic Residues....Pages 181-193
The Chinese Remainder Theorem and Simultaneous Congruences....Pages 194-202
Fast Transformation and Kronecker Products....Pages 203-206
Quadratic Congruences....Pages 207-208
Pseudoprimes, Poker and Remote Coin Tossing....Pages 209-219
The M?bius Function and the M?bius Transform....Pages 220-227
Generating Functions and Partitions....Pages 228-235
Cyclotomic Polynomials....Pages 236-250
Linear Systems and Polynomials....Pages 251-253
Polynomial Theory....Pages 254-259
Galois Fields....Pages 260-272
Spectral Properties of Galois Sequences....Pages 273-286
Random Number Generators....Pages 287-292
Waveforms and Radiation Patterns....Pages 293-304
Number Theory, Randomness and “Art”....Pages 305-314
Self-Similarity, Fractals, Deterministic Chaos and a New State of Matter....Pages 315-339
Back Matter....Pages 340-369
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