000 04082nam a22005295i 4500
001 978-3-540-26598-6
003 DE-He213
005 20160302162214.0
007 cr nn 008mamaa
008 100301s2006 gw | s |||| 0|eng d
020 _a9783540265986
_9978-3-540-26598-6
024 7 _a10.1007/b137861
_2doi
050 4 _aQA241-247.5
072 7 _aPBH
_2bicssc
072 7 _aMAT022000
_2bisacsh
082 0 4 _a512.7
_223
100 1 _aSchroeder, Manfred R.
_eauthor.
245 1 0 _aNumber Theory in Science and Communication
_h[electronic resource] :
_bWith Applications in Cryptography, Physics, Digital Information, Computing, and Self-Similarity /
_cby Manfred R. Schroeder.
250 _aFourth Edition.
264 1 _aBerlin, Heidelberg :
_bSpringer Berlin Heidelberg,
_c2006.
300 _aXXVI, 367 p. 99 illus., 4 illus. in color.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
490 1 _aSpringer Series in Information Sciences,
_x0720-678X ;
_v7
505 0 _aThe 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.
520 _a"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.
650 0 _aMathematics.
650 0 _aCoding theory.
650 0 _aNumber theory.
650 0 _aProbabilities.
650 0 _aPhysics.
650 1 4 _aMathematics.
650 2 4 _aNumber Theory.
650 2 4 _aMathematical Methods in Physics.
650 2 4 _aNumerical and Computational Physics.
650 2 4 _aCoding and Information Theory.
650 2 4 _aProbability Theory and Stochastic Processes.
710 2 _aSpringerLink (Online service)
773 0 _tSpringer eBooks
776 0 8 _iPrinted edition:
_z9783540265962
830 0 _aSpringer Series in Information Sciences,
_x0720-678X ;
_v7
856 4 0 _uhttp://dx.doi.org/10.1007/b137861
912 _aZDB-2-PHA
999 _c176153
_d176153