Numbers and symmetry: an introduction to algebra
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Boca Raton [u.a.]
CRC Press
1997
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | 260 S. Ill., graph. Darst. |
| ISBN: | 084930301X |
Internformat
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Datensatz im Suchindex
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|---|---|
| adam_text | NUMBERS AND SYMMETRY AN INTRODUCTION TO ALGEBRA BERNARD L. JOHNSTON FRED
RICHMAN DEPARTMENT OF MATHEMATICAL SCIENCES FLORIDA ATLANTIC UNIVERSITY
BOCA RATON, FLORIDA CRC PRESS BOCA RATON NEW YORK LONDON TOKYO CONTENTS
NEW NUMBERS 1 1.1 A PLANEFUL OF INTEGERS, Z[I] 1 1.2 CIRCULAR NUMBERS, Z
N 8 1.3 MORE INTEGERS ON THE NUMBER LINE, Z [ /2] 11 1.4 NOTES 14 THE
DIVISION ALGORITHM 17 2.1 RATIONAL INTEGERS 17 2.2 NORMS 20 2.2.1
GAUSSIAN INTEGERS 21 2.2.2 Z [S/2] 22 2.3 GAUSSIAN NUMBERS 24 2.4 Q( /2)
27 2.5 POLYNOMIALS 28 2.6 NOTES 33 THE EUCLIDEAN ALGORITHM 35 3.1
BEZOUT S EQUATION 37 3.2 RELATIVELY PRIME NUMBERS 40 3.3 GAUSSIAN
INTEGERS 43 3.4 NOTES 46 UNITS 47 4.1 ELEMENTARY PROPERTIES 47 4.2
BEZOUT S EQUATION 49 4.2.1 CASTING OUT NINES 50 4.3 WILSON S THEOREM 53
4.4 ORDERS OF ELEMENTS: FERMAT AND EULER 54 4.5 QUADRATIC RESIDUES 57
4.6 Z [Y/2 6 0 4.7 NOTES 62 PRIMES 65 5.1 PRIME NUMBERS 65 5.2 GAUSSIAN
PRIMES 70 5.3 Z [Y/2 75 5.4 UNIQUE FACTORIZATION INTO PRIMES 78 5.5 Z N
80 5.6 NOTES 81 6 SYMMETRIES 83 6.1 SYMMETRIES OF FIGURES IN THE PLANE
83 6.2 GROUPS 87 6.2.1 PERMUTATION GROUPS 90 6.2.2 DIHEDRAL GROUPS 92
6.3 THE CYCLE STRUCTURE OF A PERMUTATION 93 6.4 CYCLIC GROUPS 97 6.5 THE
ALTERNATING GROUPS 99 6.5.1 EVEN AND ODD PERMUTATIONS 100 6.5.2 THE SIGN
OF A PERMUTATION 102 6.6 NOTES 104 7 MATRICES 105 7.1 SYMMETRIES AND
COORDINATES 105 7.2 TWO-BY-TWO MATRICES 109 7.3 THE RING OF MATRICES M 2
(R) 114 7.4 UNITS 117 7.5 COMPLEX NUMBERS AND QUATERNIONS 121 7.6 NOTES
124 8 GROUPS 125 8.1 ABSTRACT GROUPS 125 8.2 SUBGROUPS AND COSETS 130
8.3 ISOMORPHISM 133 8.4 THE GROUP OF UNITS OF A FINITE FIELD 137 8.5
PRODUCTS OF GROUPS 140 8.6 THE EUCLIDEAN GROUPS E(L), E{2) AND E(3) 142
8.7 NOTES 148 9 WALLPAPER PATTERNS 149 9.1 ONE-DIMENSIONAL PATTERNS 149
9.2 PLANE LATTICES 153 9.3 FRIEZE PATTERNS 160 9.4 SPACE GROUPS 162 9.5
THE 17 PLANE GROUPS 166 9.6 NOTES 170 10 FIELDS 173 10.1 POLYNOMIALS
OVER A FIELD 173 10.2 KRONECKER S CONSTRUCTION OF SIMPLE FIELD
EXTENSIONS 175 10.2.1 A FOUR-ELEMENT FIELD, KRON(Z 2 ,X 2 + X + 1) . . .
. 178 10.2.2 A SIXTEEN-ELEMENT FIELD, KRON(Z 2 ,X 4 + X + 1) . . . 179
10.3 FINITE FIELDS 180 10.4 NOTES 185 11 LINEAR ALGEBRA 187 11.1 VECTOR
SPACES 187 11.2 MATRICES 193 11.3 ROW SPACE AND ECHELON FORM 195 11.4
INVERSES AND ELEMENTARY MATRICES 198 11.5 DETERMINANTS 201 11.6 NOTES
207 12 ERROR-CORRECTING CODES 209 12.1 CODING FOR REDUNDANCY 209 12.2
LINEAR CODES 213 12.2.1 A HAMMING CODE 215 12.3 PARITY-CHECK MATRICES
218 12.4 CYCLIC CODES 223 12.5 BCH CODES 230 12.5.1 A
TWO-ERROR-CORRECTING CODE 230 12.5.2 DESIGNER CODES 232 12.6 CDS 237
12.7 NOTES 239 13 APPENDIX: INDUCTION 241 13.1 FORMULATING THE N-TH
STATEMENT 242 13.2 THE DOMINO THEORY: ITERATION 244 13.3 FORMULATING THE
INDUCTION STATEMENT 244 13.3.1 SUMMARY OF STEPS 246 13.4 SQUARES 247
13.5 TEMPLATES 251 13.6 RECURSION 253 13.7 NOTES 254 14 APPENDIX: THE
USUAL RULES 255 14.1 RINGS 255 14.2 NOTES 256 INDEX 257
|
| any_adam_object | 1 |
| author | Johnston, Bernard L Richman, Fred 1938- |
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| callnumber-first | Q - Science |
| callnumber-label | QA154 |
| callnumber-raw | QA154.2 |
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| ctrlnum | (OCoLC)35741513 (DE-599)BVBBV012130768 |
| dewey-full | 512/.02 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 512 - Algebra |
| dewey-raw | 512/.02 |
| dewey-search | 512/.02 |
| dewey-sort | 3512 12 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV012130768 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T18:22:13Z |
| institution | BVB |
| isbn | 084930301X |
| language | English |
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| physical | 260 S. Ill., graph. Darst. |
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| spelling | Johnston, Bernard L Verfasser aut Numbers and symmetry an introduction to algebra Bernard L. Johnston ; Fred Richman Boca Raton [u.a.] CRC Press 1997 260 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Algebra Algebra (DE-588)4001156-2 gnd rswk-swf (DE-588)4151278-9 Einführung gnd-content Algebra (DE-588)4001156-2 s DE-604 Richman, Fred 1938- Verfasser (DE-588)109792009 aut GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008215606&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Johnston, Bernard L Richman, Fred 1938- Numbers and symmetry an introduction to algebra Algebra Algebra (DE-588)4001156-2 gnd |
| subject_GND | (DE-588)4001156-2 (DE-588)4151278-9 |
| title | Numbers and symmetry an introduction to algebra |
| title_auth | Numbers and symmetry an introduction to algebra |
| title_exact_search | Numbers and symmetry an introduction to algebra |
| title_full | Numbers and symmetry an introduction to algebra Bernard L. Johnston ; Fred Richman |
| title_fullStr | Numbers and symmetry an introduction to algebra Bernard L. Johnston ; Fred Richman |
| title_full_unstemmed | Numbers and symmetry an introduction to algebra Bernard L. Johnston ; Fred Richman |
| title_short | Numbers and symmetry |
| title_sort | numbers and symmetry an introduction to algebra |
| title_sub | an introduction to algebra |
| topic | Algebra Algebra (DE-588)4001156-2 gnd |
| topic_facet | Algebra Einführung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008215606&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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