Number Theory in Science and Communication With Applications in Cryptography, Physics, Digital Information, Computing, and Self-Similarity /

• Main Author: Schroeder, Manfred. (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic
• Language: English
• Published: Berlin, Heidelberg : Springer Berlin Heidelberg, 2009.
• Edition: Fifth Edition.
• Subjects: Physics.; Coding theory.; Number theory.; Distribution (Probability theory).; Mathematical physics.; Mathematical Methods in Physics.; Numerical and Computational Methods.; Coding and Information Theory.; Probability Theory and Stochastic Processes.; Number Theory.
• Online Access: https://ezaccess.library.uitm.edu.my/login?url=http://dx.doi.org/10.1007/978-3-540-85298-8

"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...

Table of Contents:

• Introduction
• The Natural Numbers
• Primes
• The Prime Distribution
• Fractions: Continued, Egyptian and Farey
• Linear Congruences
• Diophantine Equations
• The Theorems of Fermat, Wilson and Euler
• Permutation, Cycles and Derangements
• 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 Transformations and Kronecker Products
• Quadratic Congruences
• Psudoprimes, Poker and Remote Coin Tossing
• The Mb̲ius Function and the Mb̲ius Transform
• From Error Correction Codes to Covering Sets
• 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".