A concrete introduction to higher algebra:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
New York u.a.
Springer
1995
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| Ausgabe: | 2. ed. |
| Schriftenreihe: | Undergraduate texts in mathematics
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XV, 522 S. graph. Darst. |
| ISBN: | 0387944842 |
Internformat
MARC
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| 245 | 1 | 0 | |a A concrete introduction to higher algebra |c Lindsay N. Childs |
| 250 | |a 2. ed. | ||
| 264 | 1 | |a New York u.a. |b Springer |c 1995 | |
| 300 | |a XV, 522 S. |b graph. Darst. | ||
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| 490 | 0 | |a Undergraduate texts in mathematics | |
| 650 | 7 | |a Algebra abstrata |2 larpcal | |
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Datensatz im Suchindex
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|---|---|
| adam_text | CONTENTS INTRODUCTION VII CHAPTER 1 NUMBERS 1 CHAPTER 2 INDUCTION 8 A.
INDUCTION 8 B. ANOTHER FORM OF INDUCTION 13 C. WELL-ORDERING 16 D.
DIVISION THEOREM 18 E. BASES 20 F. OPERATIONS IN BASE A 23 CHAPTER 3
EUCLID S ALGORITHM 25 A. GREATEST COMMON DIVISORS 25 B. EUCLID S
ALGORITHM 27 C BEZOUT S IDENTITY 29 D. THE EFFICIENCY OF EUCLID S
ALGORITHM 36 E. EUCLID S ALGORITHM AND INCOMMENSURABILITY 40 CHAPTER 4
UNIQUE FACTORIZATION 47 A. THE FUNDAMENTAL THEOREM OF ARITHMETIC 47 B.
EXPONENTIAL NOTATION 50 C. PRIMES 55 D. PRIMES IN AN INTERVAL 59 CHAPTER
5 CONGRUENCES 63 A. CONGRUENCE MODULO M 63 B. BASIC PROPERTIES 65 C.
DIVISIBILITY TRICKS 68 D. MORE PROPERTIES OF CONGRUENCE 71 E. LINEAR
CONGRUENCES AND BEZOUT S IDENTITY 72 CHAPTER 6 CONGRUENCE CLASSES 76 A.
CONGRUENCE CLASSES (MOD M): EXAMPLES 76 B. CONGRUENCE CLASSES AND Z/MZ
80 C. ARITHMETIC MODULO M 82 D. COMPLETE SETS OF REPRESENTATIVES 86 E.
UNITS 88 CHAPTER 7 APPLICATIONS OF CONGRUENCES 91 A. ROUND ROBIN
TOURNAMENTS 91 B. PSEUDORANDOM NUMBERS 92 C. FACTORING LARGE NUMBERS BY
TRIAL DIVISION 100 D. SIEVES 103 E. FACTORING BY THE POLLARD RHO METHOD
105 F. KNAPSACK CRYPTOSYSTEMS 111 CHAPTER 8 RINGS AND FIELDS 118 A.
AXIOMS 118 B. Z/MZ 124 C. HOMOMORPHISMS 127 CHAPTER 9 FERMAT S AND
EULER S THEOREMS 134 A. ORDERS OF ELEMENTS 134 B. FERMAT S THEOREM 138
C. EULER S THEOREM 141 D. FINDING HIGH POWERS MODULO M 145 E. GROUPS OF
UNITS AND EULER S THEOREM 147 F. THE EXPONENT OF AN ABELIAN GROUP 152
CHAPTER 10 APPLICATIONS OF FERMAT S AND EULER S THEOREMS 155 A.
FRACTIONS IN BASE A 155 B. RSA CODES 164 C. 2-PSEUDOPRIMES 169 D. TRIAL
A-PSEUDOPRIME TESTING 175 E. THE POLLARD P - 1 ALGORITHM 177 CHAPTER 11
ON GROUPS 180 A. SUBGROUPS 180 B. LAGRANGE S THEOREM 182 C. A
PROBABILISTIC PRIMALITY TEST 185 D. HOMOMORPHISMS 186 E. SOME NONABELIAN
GROUPS 189 CHAPTER 12 THE CHINESE REMAINDER THEOREM 194 A. THE THEOREM
194 B. PRODUCTS OF RINGS AND EULER S PHI-FUNCTION 202 C. SQUARE ROOTS OF
1 MODULO M 205 CHAPTER 13 MATRICES AND CODES 208 A. MATRIX
MULTIPLICATION 209 B. LINEAR EQUATIONS 212 C. DETERMINANTS AND INVERSES
214 D. M N ,(R) 215 E. ERROR-CORRECTING CODES, I 217 F. HILL CODES 224
CHAPTER 14 POLYNOMIALS 231 CHAPTER 15 UNIQUE FACTORIZATION 239 A.
DIVISION THEOREM 239 B. PRIMITIVE ROOTS 243 C GREATEST COMMON DIVISORS
245 D. FACTORIZATION INTO IRREDUCIBLE POLYNOMIALS 249 CHAPTER 16 THE
FUNDAMENTAL THEOREM OF ALGEBRA 253 A. RATIONAL FUNCTIONS 254 B. PARTIAL
FRACTIONS 255 C. IRREDUCIBLE POLYNOMIALS OVER R 258 D. THE COMPLEX
NUMBERS 260 E. ROOT FORMULAS 263 F. THE FUNDAMENTAL THEOREM 269 G.
INTEGRATING 273 CHAPTER 17 DERIVATIVES 277 A. THE DERIVATIVE OF A
POLYNOMIAL 277 B. STURM S ALGORITHM 280 CHAPTER 18 FACTORING IN Q [X], I
286 A. GAUSS S LEMMA 286 B. FINDING ROOTS 289 C. TESTING FOR
IRREDUCIBILITY 291 CHAPTER 19 THE BINOMIAL THEOREM IN CHARACTERISTIC P
293 A. THE BINOMIAL THEOREM 293 B. FERMAT S THEOREM REVISITED 297 C
MULTIPLE ROOTS 300 CHAPTER 20 CONGRUENCES AND THE CHINESE REMAINDER
THEOREM 302 A. CONGRUENCES MODULO A POLYNOMIAL 302 B. THE CHINESE
REMAINDER THEOREM 308 CHAPTER 21 APPLICATIONS OF THE CHINESE REMAINDER
THEOREM 310 A. THE METHOD OF LAGRANGE INTERPOLATION 310 B. FAST
POLYNOMIAL MULTIPLICATION 313 CHAPTER 22 FACTORING IN F P [X] AND IN
Z[X] 323 A. BERLEKAMP S ALGORITHM 323 B. FACTORING IN Z[X] BY FACTORING
MOD M 333 C. BOUNDING THE COEFFICIENTS OF FACTORS OF A POLYNOMIAL 334 D.
FACTORING MODULO HIGH POWERS OF PRIMES 338 CHAPTER 23 PRIMITIVE ROOTS
346 A. PRIMITIVE ROOTS MODULO M 346 B. POLYNOMIALS WHICH FACTOR MODULO
EVERY PRIME 351 CHAPTER 24 CYCLIC GROUPS AND PRIMITIVE ROOTS 353 A.
CYCLIC GROUPS 353 B. PRIMITIVE ROOTS MODULO P E 356 CHAPTER 25
PSEUDOPRIMES 363 A. LOTS OF CARMICHAEL NUMBERS 363 B. STRONG
A-PSEUDOPRIMES 368 C. RABIN S THEOREM 372 CHAPTER 26 ROOTS OF UNITY IN
Z/MZ 378 A. FOR WHICH A IS M AN A-PSEUDOPRIME? 378 B. SQUARE ROOTS OF -1
IN Z/PZ 381 C. ROOTS OF -1 IN Z/MZ 382 D. FALSE WITNESSES 385 E. PROOF
OF RABIN S THEOREM 388 F. RSA CODES AND CARMICHAEL NUMBERS 392 CHAPTER
27 QUADRATIC RESIDUES 397 A. REDUCTION TO THE ODD PRIME CASE 397 B. THE
LEGENDRE SYMBOL 399 C. PROOF OF QUADRATIC RECIPROCITY 405 D.
APPLICATIONS OF QUADRATIC RECIPROCITY 407 CHAPTER 28 CONGRUENCE CLASSES
MODULO A POLYNOMIAL 414 A. THE RING F[X]/M(X) 414 B. REPRESENTING
CONGRUENCE CLASSES MOD M(X) 418 C. ORDERS OF ELEMENTS 422 D. INVENTING
ROOTS OF POLYNOMIALS 426 E. FINDING POLYNOMIALS WITH GIVEN ROOTS 428
CHAPTER 29 SOME APPLICATIONS OF FINITE FIELDS 432 A. LATIN SQUARES 432
B. ERROR CORRECTING CODES 438 C. REED-SOLOMON CODES 450 CHAPTER 30
CLASSIFYING FINITE FIELDS 464 A. MORE HOMOMORPHISMS 464 B. ON
BERLEKAMP S ALGORITHM 468 C. FINITE FIELDS ARE SIMPLE 469 D. FACTORING X
PN * X IN F P [X] 471 E. COUNTING IRREDUCIBLE POLYNOMIALS 474 F. FINITE
FIELDS 477 G. MOST POLYNOMIALS IN Z [X] ARE IRREDUCIBLE 479 HINTS TO
SELECTED EXERCISES 483 REFERENCES 509 INDEX 513
|
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| dewey-full | 512/.7 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 512 - Algebra |
| dewey-raw | 512/.7 |
| dewey-search | 512/.7 |
| dewey-sort | 3512 17 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| edition | 2. ed. |
| format | Book |
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| indexdate | 2024-07-09T17:54:31Z |
| institution | BVB |
| isbn | 0387944842 |
| language | English |
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| physical | XV, 522 S. graph. Darst. |
| publishDate | 1995 |
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| publisher | Springer |
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| series2 | Undergraduate texts in mathematics |
| spelling | Childs, Lindsay Verfasser aut A concrete introduction to higher algebra Lindsay N. Childs 2. ed. New York u.a. Springer 1995 XV, 522 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Undergraduate texts in mathematics Algebra abstrata larpcal Algebra elementar larpcal Algèbre Algebra Algebra (DE-588)4001156-2 gnd rswk-swf (DE-588)4123623-3 Lehrbuch gnd-content Algebra (DE-588)4001156-2 s DE-604 OEBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007017128&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Childs, Lindsay A concrete introduction to higher algebra Algebra abstrata larpcal Algebra elementar larpcal Algèbre Algebra Algebra (DE-588)4001156-2 gnd |
| subject_GND | (DE-588)4001156-2 (DE-588)4123623-3 |
| title | A concrete introduction to higher algebra |
| title_auth | A concrete introduction to higher algebra |
| title_exact_search | A concrete introduction to higher algebra |
| title_full | A concrete introduction to higher algebra Lindsay N. Childs |
| title_fullStr | A concrete introduction to higher algebra Lindsay N. Childs |
| title_full_unstemmed | A concrete introduction to higher algebra Lindsay N. Childs |
| title_short | A concrete introduction to higher algebra |
| title_sort | a concrete introduction to higher algebra |
| topic | Algebra abstrata larpcal Algebra elementar larpcal Algèbre Algebra Algebra (DE-588)4001156-2 gnd |
| topic_facet | Algebra abstrata Algebra elementar Algèbre Algebra Lehrbuch |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007017128&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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