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Mathematics - Number Theory and Discrete Mathematics | Number Theory in Science and Communication - With Applications in Cryptography, Physics, Digital

Number Theory in Science and Communication

With Applications in Cryptography, Physics, Digital Information, Computing, and Self-Similarity

Schroeder, M.R.

4th ed. 2006, XXVI, 367 p. 99 illus., 4 in color.


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"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 Level » Lower undergraduate

Keywords » Coding - Congruance - Encryption - Euler - Fermat - Galois field - Möbius - Polynominals - Prime - Primes - Pseudoprimes - Random Generator - Random Number - number theory

Related subjects » Number Theory and Discrete Mathematics - Probability Theory and Stochastic Processes - Theoretical, Mathematical & Computational Physics - Theoretical Computer Science

Table of contents 

The Natural Numbers.- Primes.- The Prime Distribution.- Fractions: Continued, Egyptian and Farey.- Linear Congruences.- Diophantine Equations.- The Theorems of Fermat, Wilson and Euler.- Euler Trap Doors and Public-Key Encryption.- The Divisor Functions.- The Prime Divisor Functions.- Certified Signatures.- Primitive Roots.- Knapsack Encryption.- Quadratic Residues.- The Chinese Remainder Theorem and Simultaneous Congruences.- Fast Transformation and Kronecker Products.- Quadratic Congruences.- Pseudoprimes, Poker and Remote Coin Tossing.- The Möbius Function and the Möbius Transform.- Generating Functions and Partitions.- Cyclotomic Polynomials.- Linear Systems and Polynomials.- Polynomial Theory.- Galois Fields.- Spectral Properties of Galois Sequences.- Random Number Generators.- Waveforms and Radiation Patterns.- Number Theory, Randomness and “Art”.- Self-Similarity, Fractals, Deterministic Chaos and a New State of Matter.

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