Number Theory in Science and Communication introductes non-mathematicians to the fascinating and diverse applications of number theory. This best-selling book 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 primituve elements. Their applications to problems in the real world is 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. Engineers and physicists find this an enjoyable and insightful addition to their libraries.
From reviews of an 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
Rezensionen / Stimmen
From reviews of an 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
Reihe
Auflage
3rd ed. 1997. Corr. 2nd printing
Sprache
Verlagsort
Verlagsgruppe
Zielgruppe
Für höhere Schule und Studium
Für Beruf und Forschung
Editions-Typ
Illustrationen
4 farbige Abbildungen, 94 s/w Abbildungen, 4 s/w Tabellen
99 figs.
Maße
Höhe: 23.5 cm
Breite: 15.5 cm
Gewicht
ISBN-13
978-3-540-62006-8 (9783540620068)
DOI
10.1007/978-3-662-03430-9
Schweitzer Klassifikation
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 Transformation 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".- X. Self-Similarity, Fractals and Art.- 30. Self-Similarity, Fractals, Deterministic Chaos and a New State of Matter.- Glossary of Symbols.- References.- Name Index.
