Integers, polynomials, and rings: a course in algebra
Gespeichert in:
| Beteilige Person: | |
|---|---|
| Format: | Buch |
| Sprache: | Englisch |
| Veröffentlicht: |
New York
Springer
2004
|
| Schriftenreihe: | Undergraduate texts in mathematics
|
| Schlagwörter: | |
| Links: | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=012859913&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| Umfang: | XV, 284 S. |
| ISBN: | 0387403973 0387201726 |
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Datensatz im Suchindex
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|---|---|
| adam_text | RONALD S. IRVING INTEGERS, POLYNOMIALS, AND RINGS A COURSE IN ALGEBRA
SPRINGER CONTENTS PREFACE VII 1 INTRODUCTION: THE MCNUGGET PROBLEM 1
PART I INTEGERS 2 INDUCTION AND THE DIVISION THEOREM 9 2.1 THE METHOD OF
INDUCTION 9 2.2 THE TOWER OF HANOI 15 2.3 THE DIVISION THEOREM 17 3 THE
EUCLIDEAN ALGORITHM 23 3.1 GREATEST COMMON DIVISORS 23 3.2 THE EUCLIDEAN
ALGORITHM 27 3.3 BEZOUT S THEOREM -. 31 3.4 AN APPLICATION OF BEZOUT S
THEOREM 34 3.5 DIOPHANTINE EQUATIONS 36 4 CONGRUENCES 41 4.1 CONGRUENCES
41 4.2 SOLVING CONGRUENCES 46 4.3 CONGRUENCE CLASSES AND MCNUGGETS 50 5
PRIME NUMBERS 57 5.1 PRIME NUMBERS AND GENERALIZED INDUCTION 57 5.2
UNIQUENESS OF PRIME FACTORIZATIONS 61 5.3 GREATEST COMMON DIVISORS
REVISITED 63 XIV CONTENTS 6 RINGS 69 6.1 NUMBERS 69 6.2 NUMBER RINGS 77
6.3 FRUIT RINGS 83 6.4 MODULAR ARITHMETIC RINGS 88 6.5 CONGRUENCE RINGS
91 7 EULER S THEOREM 9 5 7.1 UNITS 95 7.2 ROOTS OF UNITY 99 7.3 THE
THEOREMS OF FERMAT AND EULER 101 7.4 THE EULER ^-FUNCTION 105 7.5 RSA
ENCRYPTION 110 8 BINOMIAL COEFFICIENTS 115 8.1 PASCAL S TRIANGLE 115 8.2
THE BINOMIAL THEOREM 120 PART II POLYNOMIALS 9 POLYNOMIALS AND ROOTS 127
9.1 POLYNOMIAL EQUATIONS 127 9.2 RINGS OF POLYNOMIALS 128 9.3 FACTORING
A POLYNOMIAL ; 130 9.4 THE ROOTS OF A POLYNOMIAL 133 9.5 MINIMAL
POLYNOMIALS 136 10 POLYNOMIALS WITH REAL COEFFICIENTS 141 10.1 QUADRATIC
POLYNOMIALS 141 10.2 CUBIC POLYNOMIALS 146 10.3 THE DISCRIMINANT OF A
CUBIC POLYNOMIAL 153 10.4 QUARTIC POLYNOMIALS 159 10.5 A CLOSER LOOK AT
QUARTIC POLYNOMIALS 164 10.6 THE DISCRIMINANT OF A QUARTIC POLYNOMIAL
167 10.7 THE FUNDAMENTAL THEOREM OF ALGEBRA 171 11 POLYNOMIALS WITH
RATIONAL COEFFICIENTS 177 11.1 POLYNOMIALS OVER Q 177 11.2 GAUSS S LEMMA
181 11.3 EISENSTEIN S CRITERION . . . 184 11.4 POLYNOMIALS WITH
COEFFICIENTS IN F P 187 CONTENTS XV 12 POLYNOMIAL RINGS 193 12.1 UNIQUE
FACTORIZATION FOR INTEGERS REVISITED 193 12.2 THE EUCLIDEAN ALGORITHM
196 12.3 BEZOUT S THEOREM 198 12.4 UNIQUE FACTORIZATION FOR POLYNOMIALS
199 13 QUADRATIC POLYNOMIALS 201 13.1 SQUARE ROOTS 201 13.2 THE
QUADRATIC FORMULA 204 13.3 SQUARE ROOTS IN FINITE FIELDS 209 13.4
QUADRATIC FIELD CONSTRUCTIONS 214 14 POLYNOMIAL CONGRUENCE RINGS 221
14.1 A CONSTRUCTION OF NEW RINGS 221 14.2 POLYNOMIAL CONGRUENCES 226
14.3 POLYNOMIAL CONGRUENCE RINGS 230 14.4 EQUATIONS AND CONGRUENCES WITH
POLYNOMIAL UNKNOWNS 233 14.5 POLYNOMIAL CONGRUENCE FIELDS 236 PART III
ALL TOGETHER NOW 15 EUCLIDEAN RINGS 241 15.1 FACTORING ELEMENTS IN RINGS
241 15.2 EUCLIDEAN RINGS 245 15.3 UNIQUE FACTORIZATION 249 16 THE RING
OF GAUSSIAN INTEGERS 255 16.1 THE IRREDUCIBLE GAUSSIAN INTEGERS 255 16.2
GAUSSIAN CONGRUENCE RINGS 259 16.3 FERMAT S THEOREM 262 17 FINITE FIELDS
267 17.1 PRIMITIVE ROOTS 267 17.2 QUADRATIC RECIPROCITY 271 17.3
CLASSIFICATION 277 INDEX 281
|
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| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 512 - Algebra |
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| dewey-sort | 3512 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
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| id | DE-604.BV019397503 |
| illustrated | Not Illustrated |
| indexdate | 2024-12-20T11:59:48Z |
| institution | BVB |
| isbn | 0387403973 0387201726 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-012859913 |
| oclc_num | 52799049 |
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| physical | XV, 284 S. |
| publishDate | 2004 |
| publishDateSearch | 2004 |
| publishDateSort | 2004 |
| publisher | Springer |
| record_format | marc |
| series2 | Undergraduate texts in mathematics |
| spellingShingle | Irving, Ronald S. Integers, polynomials, and rings a course in algebra Algebra, Abstract Polynom (DE-588)4046711-9 gnd Ganze Zahl (DE-588)4134668-3 gnd Ring Mathematik (DE-588)4128084-2 gnd |
| subject_GND | (DE-588)4046711-9 (DE-588)4134668-3 (DE-588)4128084-2 |
| title | Integers, polynomials, and rings a course in algebra |
| title_auth | Integers, polynomials, and rings a course in algebra |
| title_exact_search | Integers, polynomials, and rings a course in algebra |
| title_full | Integers, polynomials, and rings a course in algebra Ronald S. Irving |
| title_fullStr | Integers, polynomials, and rings a course in algebra Ronald S. Irving |
| title_full_unstemmed | Integers, polynomials, and rings a course in algebra Ronald S. Irving |
| title_short | Integers, polynomials, and rings |
| title_sort | integers polynomials and rings a course in algebra |
| title_sub | a course in algebra |
| topic | Algebra, Abstract Polynom (DE-588)4046711-9 gnd Ganze Zahl (DE-588)4134668-3 gnd Ring Mathematik (DE-588)4128084-2 gnd |
| topic_facet | Algebra, Abstract Polynom Ganze Zahl Ring Mathematik |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=012859913&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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