Verfügbarkeit: Primes and programming | Technische Universität München

Primes and programming: an introduction to number theory with computing

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Bibliographische Detailangaben
Beteilige Person:	Giblin, Peter 1943- (VerfasserIn)
Format:	Buch
Sprache:	Englisch
Veröffentlicht:	Cambridge Cambridge Univ. Press 1993
Ausgabe:	1. publ.
Schlagwörter:	Nombres premiers - Informatique Datenverarbeitung Zahlentheorie Primzahlzerlegung PASCAL > Programmiersprache Numerisches Verfahren
Links:	http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=005537816&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA
Umfang:	X, 235 S. graph. Darst.
ISBN:	0521401828 0521409888

Internformat

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Datensatz im Suchindex

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adam_text	Contents Preface vii Logical dependence of chapters xi 1. The Fundamental Theorem, Greatest Common Divisors and Least Common Multiples 1 1. Primes and the fundamental theorem 1 2. Greatest common divisor and least common multiple 7 3. Euclid s algorithm for the gcd 12 4. [x] and applications 24 5*. Further projects 29 2. Listing Primes 37 1. Primes by division 37 2. Primes by multiplication (elimination of composites) 50 3. Approximations to tt(x) 52 4. The sieve of Eratosthenes 55 3. Congruences 69 1. Congruences: basic properties 69 2. Inverses mod m and solutions of certain congruences 74 3. Further examples of congruences 81 4. Powers and Pseudoprimes 86 1. Fermat s (little) theorem 86 2. The power algorithm 89 3. Head s algorithm for multiplication mod m 93 vi 4. Pseudoprimes 98 5. Wilson s theorem 102 5. Miller s Test and Strong Pseudoprimes 104 1. Miller s test 104 2. Probabilistic primality testing 109 6. Euler s Theorem, Orders and Primality Testing 112 1. Euler s function (the (^ function or totient function) 112 2. Euler s theorem and the concept of order 119 3. Primality tests 124 4. Periods of decimals 130 7. Cryptography 133 1. Exponentiation ciphers 134 2. Public key cryptography: RSA ciphers 136 3. Coin tossing by telephone 145 8. Primitive Roots 147 1. Properties and applications of primitive roots 147 2. Existence and nonexistence of primitive roots 149 9. The Number of Divisors d and the Sum of Divisors a 158 1. The function d(n) 158 2. Multiplicative functions and the sum function cr(n) 162 3. Tests for primality of the Mersenne numbers 2m — 1 170 10. Continued Fractions and Factoring 174 1. Continued fractions: initial ideas and definitions 175 2. The continued fraction for ^/n 180 3. Proofs of some properties of continued fractions 186 4. Pell s equation 189 5. The continued fraction factoring method 191 11. Quadratic Residues 200 1. Definitions and examples 200 2. The quadratic character of 2 203 3. Quadratic reciprocity 206 4. The Jacobi symbol and a program for finding (^) 211 5. Solving the equation x2 = a (mod p): quadratic congruences 217 Bibliography 225 Index 231 Index of Listed Programs 236 Index of Notation 237
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spellingShingle	Giblin, Peter 1943- Primes and programming an introduction to number theory with computing Nombres premiers - Informatique ram Datenverarbeitung (DE-588)4011152-0 gnd Zahlentheorie (DE-588)4067277-3 gnd Primzahlzerlegung (DE-588)4175717-8 gnd PASCAL Programmiersprache (DE-588)4044804-6 gnd Numerisches Verfahren (DE-588)4128130-5 gnd
subject_GND	(DE-588)4011152-0 (DE-588)4067277-3 (DE-588)4175717-8 (DE-588)4044804-6 (DE-588)4128130-5
title	Primes and programming an introduction to number theory with computing
title_auth	Primes and programming an introduction to number theory with computing
title_exact_search	Primes and programming an introduction to number theory with computing
title_full	Primes and programming an introduction to number theory with computing Peter Giblin
title_fullStr	Primes and programming an introduction to number theory with computing Peter Giblin
title_full_unstemmed	Primes and programming an introduction to number theory with computing Peter Giblin
title_short	Primes and programming
title_sort	primes and programming an introduction to number theory with computing
title_sub	an introduction to number theory with computing
topic	Nombres premiers - Informatique ram Datenverarbeitung (DE-588)4011152-0 gnd Zahlentheorie (DE-588)4067277-3 gnd Primzahlzerlegung (DE-588)4175717-8 gnd PASCAL Programmiersprache (DE-588)4044804-6 gnd Numerisches Verfahren (DE-588)4128130-5 gnd
topic_facet	Nombres premiers - Informatique Datenverarbeitung Zahlentheorie Primzahlzerlegung PASCAL Programmiersprache Numerisches Verfahren
url	http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=005537816&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA
work_keys_str_mv	AT giblinpeter primesandprogramminganintroductiontonumbertheorywithcomputing

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