A history of abstract algebra
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| Format: | Buch |
| Sprache: | English |
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Boston [u.a.]
Birkhäuser
2007
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| 245 | 1 | 0 | |a A history of abstract algebra |c Israel Kleiner |
| 264 | 1 | |a Boston [u.a.] |b Birkhäuser |c 2007 | |
| 300 | |a XIII, 168 S. |b Ill. |c 23 cm | ||
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| 648 | 7 | |a Geschichte 1700-1950 |2 gnd |9 rswk-swf | |
| 650 | 4 | |a Algèbre abstraite - Histoire | |
| 650 | 4 | |a Geschichte | |
| 650 | 4 | |a Algebra, Abstract |x History | |
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Datensatz im Suchindex
| _version_ | 1819624362382196736 |
|---|---|
| adam_text | CONTENTS PREFACE
......................................................... XI PERMISSIONS
..................................................... XV
HISTORYOFCLASSICALALGEBRA ................................... 1 1.1
EARLYROOTS................................................ 1 1.2 THE
GREEKS ................................................ 2 1.3
AL-KHWARIZMI ............................................. 3 1.4 CUBIC
AND QUARTICEQUATIONS.................................. 5 1.5 THE
CUBICAND COMPLEX NUMBERS .............................. 7 1.6
ALGEBRAICNOTATION: VIETEAND DESCARTES ........................ 8 1.7 THE
THEORYOFEQUATIONSAND THEFUNDAMENTAL THEOREM OFALGEBRA . 10 1.8
SYMBOLICALALGEBRA......................................... 13 REFERENCES
..................................................... 14 2
HISTORYOFGROUP THEORY ...................................... 17 2.1
SOURCESOFGROUP THEORY..................................... 17 2.1.1
CLASSICAL ALGEBRA .................................... 18 2.1.2 NUMBER
THEORY ..................................... 19 2.1.3 GEOMETRY
........................................... 20 2.1.4 ANALYSIS
............................................ 21 2.2 DEVELOPMENT
OF SPECIALIZED THEORIESOFGROUPS ................ 22 2.2.1
PERMUTATIONGROUPS .................................. 22 2.2.2
ABELIANGROUPS ...................................... 26 2.2.3
TRANSFORMATIONGROUPS ............................... 28 2.3 EMERGENCE
OFABSTRACTION INGROUP THEORY ...................... 30 2.4
CONSOLIDATIONOFTHEABSTRACT GROUP CONCEPT;DAWN OF ABSTRACT GROUP
THEORY............................................... 33 2.5
DIVERGENCEOFDEVELOPMENTSINGROUP THEORY .................... 35
REFERENCES ..................................................... 38 VIII
CONTENTS 3 HISTORYOFRING THEORY .......................................
41 3.1 NONCOMMUTATIVE RINGTHEORY ................................. 42
3.1.1 EXAMPLES OFHYPERCOMPLEX NUMBER SYSTEMS ............ 42 3.1.2
CLASSIFICATION ........................................ 43 3.1.3
STRUCTURE ........................................... 45 3.2 COMMUTATIVE
RINGTHEORY .................................... 47 3.2.1 ALGEBRAICNUMBER
THEORY ............................. 48 3.2.2 ALGEBRAICGEOMETRY
.................................. 54 3.2.3 INVARIANT THEORY
..................................... 57 3.3 THE ABSTRACT DEFINITION OFA
RING............................... 58 3.4 EMMY NOETHERAND EMIL ARTIN
............................... 59 3.5 EPILOGUE
.................................................. 60 REFERENCES
..................................................... 60 4
HISTORYOFFIELDTHEORY ....................................... 63 4.1
GALOISTHEORY .............................................. 63 4.2
ALGEBRAICNUMBER THEORY .................................... 64 4.2.1
DEDEKIND SIDEAS ..................................... 65 4.2.2
KRONECKER SIDEAS .................................... 67 4.2.3 DEDEKIND
VS KRONECKER ............................... 68 4.3 ALGEBRAICGEOMETRY
......................................... 68 4.3.1
FIELDSOFALGEBRAICFUNCTIONS .......................... 68 4.3.2
FIELDSOFRATIONALFUNCTIONS ........................... 70 4.4 CONGRUENCES
.............................................. 70 4.5
SYMBOLICALALGEBRA......................................... 71 4.6 THE
ABSTRACT DEFINITION OFA FIELD .............................. 71 4.7
HENSEL SP-ADICNUMBERS ..................................... 73 4.8
STEINITZ ................................................... 74 4.9 A
GLANCEAHEAD ............................................. 76 REFERENCES
..................................................... 77 5
HISTORYOFLINEAR ALGEBRA ..................................... 79 5.1
LINEAREQUATIONS........................................... 79 5.2
DETERMINANTS .............................................. 81 5.3
MATRICESAND LINEARTRANSFORMATIONS........................... 82 5.4
LINEARINDEPENDENCE,BASIS,AND DIMENSION ..................... 84 5.5
VECTORSPACES.............................................. 86 REFERENCES
..................................................... 89 6 EMMY NOETHER
AND THEADVENT OFABSTRACTALGEBRA ............... 91 6.1 INVARIANT THEORY
............................................ 92 6.2 COMMUTATIVE
ALGEBRA....................................... 94 6.3 NONCOMMUTATIVE
ALGEBRAAND REPRESENTATION THEORY.............. 97 6.4
APPLICATIONSOFNONCOMMUTATIVE TOCOMMUTATIVE ALGEBRA......... 98 6.5
NOETHER SLEGACY ........................................... 99
REFERENCES ..................................................... 101
CONTENTS IX 7A COURSE INABSTRACTALGEBRA INSPIREDBY HISTORY
................. 103 PROBLEM I:WHY IS(-1)(-1) = 1?
................................. 104 PROBLEM II:WHAT
ARETHEINTEGERSOLUTIONS OFX2 +2= Y3?............. 105 PROBLEM III:CAN WE
TRISECT A 60 ANGLEUSINGONLYSTRAIGHTEDGE AND COMPASS?
................................................. 106 PROBLEM IV:CAN WE
SOLVEX5 - 6X +3=0 BY RADICALS?.............. 107 PROBLEM V: PAPA,CAN
YOU MULTIPLYTRIPLES? ........................ 108 GENERALREMARKSON
THECOURSE .................................... 109 REFERENCES
..................................................... 110 8
BIOGRAPHIESOFSELECTEDMATHEMATICIANS ......................... 113 8.1
ARTHURCAYLEY(1821-1895) .................................. 113 8.1.1
INVARIANTS ........................................... 115 8.1.2 GROUPS
............................................. 116 8.1.3 MATRICES
............................................ 117 8.1.4 GEOMETRY
........................................... 118 8.1.5 CONCLUSION
......................................... 119 REFERENCES
..................................................... 120 8.2
RICHARDDEDEKIND(1831-1916) ............................... 121 8.2.1
ALGEBRAICNUMBERS ................................... 124 8.2.2
REALNUMBERS ....................................... 126 8.2.3
NATURALNUMBERS .................................... 128 8.2.4 OTHERWORKS
........................................ 129 8.2.5 CONCLUSION
......................................... 131 REFERENCES
..................................................... 132 8.3
EVARISTEGALOIS(1811-1832) ................................. 133 8.3.1
MATHEMATICS ........................................ 135 8.3.2 POLITICS
............................................. 135 8.3.3 THE DUEL
............................................ 137 8.3.4 TESTAMENT
.......................................... 137 8.3.5 CONCLUSION
......................................... 138 REFERENCES
..................................................... 139 8.4
CARLFRIEDRICHGAUSS (1777-1855) ............................ 139 8.4.1
NUMBER THEORY...................................... 140 8.4.2
DIFFERENTIAL GEOMETRY,PROBABILITY, AND STATISTICS .......... 142 8.4.3
THE DIARY ........................................... 142 8.4.4
CONCLUSION ......................................... 143 REFERENCES
..................................................... 144 8.5
WILLIAMROWAN HAMILTON (1805-1865) ........................ 144 8.5.1
OPTICS .............................................. 146 8.5.2 DYNAMICS
.......................................... 147 8.5.3 COMPLEX NUMBERS
................................... 149 8.5.4 FOUNDATIONSOFALGEBRA
............................... 150 8.5.5 QUATERNIONS
......................................... 152 8.5.6 CONCLUSION
......................................... 156 REFERENCES
..................................................... 156 X CONTENTS 8.6
EMMY NOETHER(1882-1935) ................................. 157 8.6.1
EARLYYEARS ......................................... 157 8.6.2
UNIVERSITYSTUDIES ................................... 158 8.6.3
GOTTINGEN ........................................... 159 8.6.4
NOETHERASATEACHER ................................. 160 8.6.5 BRYN MAWR
......................................... 161 8.6.6 CONCLUSION
......................................... 162 REFERENCES
..................................................... 162 INDEX
........................................................... 165
|
| any_adam_object | 1 |
| author | Kleiner, Israel |
| author_GND | (DE-588)133618234 |
| author_facet | Kleiner, Israel |
| author_role | aut |
| author_sort | Kleiner, Israel |
| author_variant | i k ik |
| building | Verbundindex |
| bvnumber | BV022525220 |
| callnumber-first | Q - Science |
| callnumber-label | QA162 |
| callnumber-raw | QA162 |
| callnumber-search | QA162 |
| callnumber-sort | QA 3162 |
| callnumber-subject | QA - Mathematics |
| classification_rvk | SG 553 SG 590 SK 200 |
| ctrlnum | (OCoLC)76935733 (DE-599)DNB983487073 |
| dewey-full | 512/.0209 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 512 - Algebra |
| dewey-raw | 512/.0209 |
| dewey-search | 512/.0209 |
| dewey-sort | 3512 3209 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| era | Geschichte 1700-1950 gnd |
| era_facet | Geschichte 1700-1950 |
| format | Book |
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| illustrated | Illustrated |
| indexdate | 2024-12-23T20:07:33Z |
| institution | BVB |
| isbn | 9780817646844 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-015731910 |
| oclc_num | 76935733 |
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| owner | DE-824 DE-12 DE-20 DE-210 DE-11 DE-188 |
| owner_facet | DE-824 DE-12 DE-20 DE-210 DE-11 DE-188 |
| physical | XIII, 168 S. Ill. 23 cm |
| psigel | DHB_JDG_ISBN_1 |
| publishDate | 2007 |
| publishDateSearch | 2007 |
| publishDateSort | 2007 |
| publisher | Birkhäuser |
| record_format | marc |
| spellingShingle | Kleiner, Israel A history of abstract algebra Algèbre abstraite - Histoire Geschichte Algebra, Abstract History Universelle Algebra (DE-588)4061777-4 gnd |
| subject_GND | (DE-588)4061777-4 |
| title | A history of abstract algebra |
| title_auth | A history of abstract algebra |
| title_exact_search | A history of abstract algebra |
| title_full | A history of abstract algebra Israel Kleiner |
| title_fullStr | A history of abstract algebra Israel Kleiner |
| title_full_unstemmed | A history of abstract algebra Israel Kleiner |
| title_short | A history of abstract algebra |
| title_sort | a history of abstract algebra |
| topic | Algèbre abstraite - Histoire Geschichte Algebra, Abstract History Universelle Algebra (DE-588)4061777-4 gnd |
| topic_facet | Algèbre abstraite - Histoire Geschichte Algebra, Abstract History Universelle Algebra |
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