Elementary number theory and its applications:
"Elementary Number Theory and Its Applications is noted for its outstanding exercise sets, including basic exercises, exercises designed to help students explore key concepts, and challenging exercises. Computational exercises and computer projects are also provided. In addition to more years o...
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Boston [u.a.]
Addison-Wesley
2005
|
| Ausgabe: | 5. ed., internat. ed. |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Zusammenfassung: | "Elementary Number Theory and Its Applications is noted for its outstanding exercise sets, including basic exercises, exercises designed to help students explore key concepts, and challenging exercises. Computational exercises and computer projects are also provided. In addition to more years of use and professor feedback, the fifth edition of this text has been thoroughly checked to ensure the quality and accuracy of the mathematical content and the exercises. The blending of classical theory with modern applications is a hallmark feature of the text. The Fifth Edition builds on this strength with new examples and exercises, additional applications and increased cryptology coverage. The author devotes a great deal of attention to making this new edition up-to-date, incorporating new results and discoveries in number theory made in the past few years." -- Publisher's description. |
| Beschreibung: | XX, 721 S. |
| ISBN: | 0321263146 |
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Datensatz im Suchindex
| _version_ | 1804132847310602240 |
|---|---|
| adam_text | ELEMENTARY NUMBER THEORY AND ITS APPLICATIONS FIFTH EDITION KENNETH H.
ROSEN AT&T LABORATORIES ADDISON WESLEY BOSTON SAN FRANCISCO NEW YORK
LONDON TORONTO SYDNEY TOKYO SINGAPORE MADRID MEXICO CITY MUNICH PARIS
CAPE TOWN HONG KONG MONTREAL CONTENTS WHAT IS NUMBER THEORY? 1 THE
INTEGERS 5 1.1 NUMBERS AND SEQUENCES 6 1.2 SUMS AND PRODUCTS 16 1.3
MATHEMATICAL INDUCTION 23 1.4 THE FIBONACCI NUMBERS 30 1.5 DIVISIBILITY
37 INTEGER REPRESENTATIONS AND OPERATIONS 43 2.1 REPRESENTATIONS OF
INTEGERS 43 2.2 COMPUTER OPERATIONS WITH INTEGERS 53 2.3 COMPLEXITY OF
INTEGER OPERATIONS 60 PRIMES AND GREATEST COMMON DIVISORS 67 3.1 PRIME
NUMBERS 68 3.2 THE DISTRIBUTION OF PRIMES 77 3.3 GREATEST COMMON
DIVISORS 90 3.4 THE EUCLIDEAN ALGORITHM 97 3.5 THE FUNDAMENTAL THEOREM
OF ARITHMETIC 108 3.6 FACTORIZATION METHODS AND THE FERMAT NUMBERS 123
3.7 LINEAR DIOPHANTINE EQUATIONS 133 XVU XVIII CONTENTS CONGRUENCES 141
4.1 INTRODUCTION TO CONGRUENCES 141 4.2 LINEAR CONGRUENCES 153 4.3 THE
CHINESE REMAINDER THEOREM 158 4.4 SOLVING POLYNOMIAL CONGRUENCES 168 4.5
SYSTEMS OF LINEAR CONGRUENCES 174 4.6 FAPTORING USING THE POLLARD RHO
METHOD 184 APPLICATIONS OF CONGRUENCES 5.1 DIVISIBILITY TESTS 189 5.2
THE PERPETUAL CALENDAR 195 5.3 ROUND-ROBIN TOURNAMENTS 200 5.4 HASHING
FUNCTIONS 202 5.5 CHECK DIGITS 207 189 SOME SPECIAL CONGRUENCES 215 6.1
WILSON S THEOREM AND FERMAT S LITTLE THEOREM 6.2 PSEUDOPRIMES 223 6.3
EULER S THEOREM 233 215 MULTIPLICATIVE FUNCTIONS 239 7.1 THE EULER
PHI-FUNCTION 239 7.2 THE SUM AND NUMBER OF DIVISORS 250 7.3 PERFECT
NUMBERS AND MERSENNE PRIMES 257 7.4 MOBIUS INVERSION 269 8 CRYPTOLOGY
277 8.1 CHARACTER CIPHERS 278 8.2 BLOCK AND STREAM CIPHERS 286 8.3
EXPONENTIATION CIPHERS 305 8.4 PUBLIC KEY CRYPTOGRAPHY 308 8.5 KNAPSACK
CIPHERS 316 8.6 CRYPTOGRAPHIC PROTOCOLS AND APPLICATIONS 323 CONTENTS
XIX PRIMITIVE ROOTS 333 9.1 THE ORDER OF AN INTEGER AND PRIMITIVE ROOTS
334 9.2 PRIMITIVE ROOTS FOR PRIMES 341 9.3 THE EXISTENCE OF PRIMITIVE
ROOTS 347 9.4 INDEX ARITHMETIC 355 9.5 PRIMALITY TESTS USING ORDERS OF
INTEGERS AND PRIMITIVE ROOTS 9.6 UNIVERSAL EXPONENTS 372 365 10
APPLICATIONS OF PRIMITIVE ROOTS AND THE ORDER OF AN INTEGER 379 10.1
PSEUDORANDOM NUMBERS 379 10.2 THE ELGAMAL CRYPTOSYSTEM 389 10.3 AN
APPLICATION TO THE SPLICING OF TELEPHONE CABLES 394 11 QUADRATIC
RESIDUES 401 11.1 QUADRATIC RESIDUES AND NONRESIDUES 402 11.2 THE LAW OF
QUADRATIC RECIPROCITY 417 11.3 THE JACOBI SYMBOL 430 11.4 EULER
PSEUDOPRIMES 439 11.5 ZERO-KNOWLEDGE PROOFS 448 12 DECIMAL FRACTIONS AND
CONTINUED FRACTIONS 12.1 DECIMAL FRACTIONS 455 12.2 FINITE CONTINUED
FRACTIONS 468 12.3 INFINITE CONTINUED FRACTIONS 478 12.4 PERIODIC
CONTINUED FRACTIONS 490 12.5 FACTORING USING CONTINUED FRACTIONS 504 455
13 SOME NONLINEAR DIOPHANTINE EQUATIONS 13.1 PYTHAGOREAN TRIPLES 510
13.2 FERMAT S LAST THEOREM 516 13.3 SUMS OF SQUARES 528 13.4 PELL S
EQUATION 539 509 XX CONTENTS 14 B D THE GAUSSIAN INTEGERS 547 14.1
GAUSSIAN INTEGERS AND GAUSSIAN PRIMES 547 14.2 GREATEST COMMON DIVISORS
AND UNIQUE FACTORIZATION 559 14.3 GAUSSIAN INTEGERS AND SUMS OF SQUARES
570 AXIOMS FOR THE SET OF INTEGERS 577 BINOMIAL COEFFICIENTS 581 USING
MAPLE AND MATHEMATICA FOR NUMBER THEORY C.I USING MAPLE FOR NUMBER
THEORY 589 C.2 USING MATHEMATICA FOR NUMBER THEORY 593 589 NUMBER THEORY
WEB LINKS 599 TABLES 601 ANSWERS TO ODD-NUMBERED EXERCISES 617
BIBLIOGRAPHY 689 INDEX OF BIOGRAPHIES 703 INDEX 705 PHOTO CREDITS 721
|
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| spelling | Rosen, Kenneth H. Verfasser aut Elementary number theory and its applications Kenneth H. Rosen 5. ed., internat. ed. Boston [u.a.] Addison-Wesley 2005 XX, 721 S. txt rdacontent n rdamedia nc rdacarrier "Elementary Number Theory and Its Applications is noted for its outstanding exercise sets, including basic exercises, exercises designed to help students explore key concepts, and challenging exercises. Computational exercises and computer projects are also provided. In addition to more years of use and professor feedback, the fifth edition of this text has been thoroughly checked to ensure the quality and accuracy of the mathematical content and the exercises. The blending of classical theory with modern applications is a hallmark feature of the text. The Fifth Edition builds on this strength with new examples and exercises, additional applications and increased cryptology coverage. The author devotes a great deal of attention to making this new edition up-to-date, incorporating new results and discoveries in number theory made in the past few years." -- Publisher's description. Nombres, Théorie des ram Zahlentheorie swd Mathematik Mathematics Number theory Zahlentheorie (DE-588)4067277-3 gnd rswk-swf Numerische Mathematik (DE-588)4042805-9 gnd rswk-swf Elementare Zahlentheorie (DE-588)4294368-1 gnd rswk-swf 1\p (DE-588)4123623-3 Lehrbuch gnd-content Zahlentheorie (DE-588)4067277-3 s DE-604 Elementare Zahlentheorie (DE-588)4294368-1 s 2\p DE-604 Numerische Mathematik (DE-588)4042805-9 s 3\p DE-604 HEBIS Datenaustausch Darmstadt application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=012858224&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 3\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Rosen, Kenneth H. Elementary number theory and its applications Nombres, Théorie des ram Zahlentheorie swd Mathematik Mathematics Number theory Zahlentheorie (DE-588)4067277-3 gnd Numerische Mathematik (DE-588)4042805-9 gnd Elementare Zahlentheorie (DE-588)4294368-1 gnd |
| subject_GND | (DE-588)4067277-3 (DE-588)4042805-9 (DE-588)4294368-1 (DE-588)4123623-3 |
| title | Elementary number theory and its applications |
| title_auth | Elementary number theory and its applications |
| title_exact_search | Elementary number theory and its applications |
| title_full | Elementary number theory and its applications Kenneth H. Rosen |
| title_fullStr | Elementary number theory and its applications Kenneth H. Rosen |
| title_full_unstemmed | Elementary number theory and its applications Kenneth H. Rosen |
| title_short | Elementary number theory and its applications |
| title_sort | elementary number theory and its applications |
| topic | Nombres, Théorie des ram Zahlentheorie swd Mathematik Mathematics Number theory Zahlentheorie (DE-588)4067277-3 gnd Numerische Mathematik (DE-588)4042805-9 gnd Elementare Zahlentheorie (DE-588)4294368-1 gnd |
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