Number Theory in Science and Communication : With Applications in Cryptography, Physics, Digital Information, Computing, and Self-Similarity. 5th ed. 2009

種類:

電子ブック

責任表示:

by Manfred Schroeder

出版情報:

Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 2009

著者名:

• Schroeder, Manfred.
• SpringerLink (Online service)

ISBN:

9783540852988 [3540852980]    

注記:

A Few Fundamentals -- The Natural Numbers -- Primes -- The Prime Distribution -- Some Simple Applications -- Fractions: Continued, Egyptian and Farey -- Congruences and the Like -- Linear Congruences -- Diophantine Equations -- The Theorems of Fermat Wilson and Euler -- Permutations Cycles and Derangements -- Cryptography and Divisors -- Euler Trap Doors and Public-Key Encryption -- The Divisor Functions -- The Prime Divisor Functions -- Certified Signatures -- Primitive Roots -- Knapsack Encryption -- Residues and Diffraction -- Quadratic Residues -- Chinese and Other Fast Algorithms -- The Chinese Remainder Theorem and Simultaneous Congruences -- Fast Transformation and Kronecker Products -- Quadratic Congruences -- Pseudoprimes, Möbius Transform, and Partitions -- Pseudoprimes Poker and Remote Coin Tossing -- The Möbius Function and the Möbius Transform -- Generating Functions and Partitions -- From Error Correcting Codes to Covering Sets -- Cyclotomy and Polynomials -- Cyclotomic Polynomials -- Linear Sys
"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 fifth edition is augmented by recent advances in coding theory, permutations and derangements and a chapter in quantum cryptography. 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

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