عنوان

Number Theory in Science and Communication :

شابک

3662023954

شابک

9783662023952

شماره

b579194

عنوان اصلي

Number Theory in Science and Communication :

نام عام مواد

[Book]

ساير اطلاعات عنواني

With Applications in Cryptography, Physics, Biology, Digital Information, and Computing

نام نخستين پديدآور

by Manfred R. Schroeder.

محل نشرو پخش و غیره

Berlin, Heidelberg

نام ناشر، پخش کننده و غيره

Springer Berlin Heidelberg

تاریخ نشرو بخش و غیره

1984

نام خاص و کميت اثر

(xvi, 326 pages)

عنوان فروست

Springer series in information sciences, 7.

متن يادداشت

I A Few Fundamentals --; 1. Introduction --; 2. The Natural Numbers --; 3. Primes --; 4. The Prime Distribution --; II Some Simple Applications --; 5. Fractions: Continued, Egyptian and Farey --; III Congruences and the Like --; 6. Linear Congruences --; 7. Diophantine Equations --; 8. The Theorems of Fermat, Wilson and Euler --; IV Cryptography and Divisors --; 9. Euler Trap Doors and Public-Key Encryption --; 10. The Divisor Functions --; 11. The Prime Divisor Functions --; 12. Certified Signatures --; 13. Primitive Roots --; 14. Knapsack Encryption --; V Residues and Diffraction --; 15. Quadratic Residues --; VI Chinese and Other Fast Algorithms --; 16. The Chinese Remainder Theorem and Simultaneous Congruences --; 17. Fast Transformations and Kronecker Products --; 18. Quadratic Congruences --; VII Pseudoprimes, Möbius Transform, and Partitions --; 19. Pseudoprimes, Poker and Remote Coin Tossing --; 20. The Möbius Function and the Möbius Transform --; 21. Generating Functions and Partitions --; VIII Cyclotomy and Polynomials --; 22. Cyclotomic Polynomials --; 23. Linear Systems and Polynomials --; 24. Polynomial Theory --; IX Galois Fields and More Applications --; 25. Galois Fields --; 26. Spectral Properties of Galois Sequences --; 27. Random Number Generators --; 28. Waveforms and Radiation Patterns --; 29. Number Theory, Randomness and 'Art' --; 30. Conclusion --; A.A Calculator Program for Exponentiation and Residue Reduction --; B.A Calculator Program for Calculating Fibonacci and Lucas Numbers --; C.A Calculator Program for Decomposing an Integer According to the Fibonacci Number System --; Glossary of Symbols.

متن يادداشت

Beauty is the first test: there is no permanent place in the world for ugly mathematics.--G.H. Hardy N umber theory has been considered since time immemorial to be the very paradigm of pure (some would say useless) mathematics. In fact, the Chinese characters for mathematics are Number Science. "Mathematics is the queen of sciences - and number theory is the queen of mathematics," according to Carl Friedrich Gauss, the lifelong Wunderkind, who hirnself enjoyed the epithet "Princeps Mathematicorum." What could be more beautiful than a deep, satisfying relation between whole numbers. {One is almost tempted to call them wholesome numbersJ In fact, it is hard to come up with a more appropriate designation than their learned name: the integers - meaning the "untouched ones". How high they rank, in the realms of pure thought and aesthetics, above their lesser brethren: the real and complex number- whose first names virtually exude unsavory involvement with the complex realities of everyday life! Yet, as we shall see in this book, the theory of integers can provide totally unexpected answers to real-world problems. In fact, discrete mathematics is ta king on an ever more important role. If nothing else, the advent of the digital computer and digital communication has seen to that. But even earlier, in physics the emergence of quantum mechanics and discrete elementary particles put a premium on the methods and, indeed, the spirit of discrete mathematics.

موضوع مستند نشده

Coding theory.

موضوع مستند نشده

Mathematics.

موضوع مستند نشده

Number theory.

مستند نام اشخاص تاييد نشده

by Manfred R. Schroeder.

مستند نام اشخاص تاييد نشده

Manfred R Schroeder

نام الکترونيکي

نوع ماده

[Book]

تكميل شده

Y