The beginnings and evolution of algebra:
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English Russian |
| Veröffentlicht: |
[Washington, DC]
Mathematical Assoc. of America
2000
|
| Schriftenreihe: | The Dolciani mathematical expositions
23 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XVI, 179 S. graph. Darst. |
| ISBN: | 0883853299 |
Internformat
MARC
| LEADER | 00000nam a2200000 cb4500 | ||
|---|---|---|---|
| 001 | BV013533119 | ||
| 003 | DE-604 | ||
| 005 | 20010829 | ||
| 007 | t | ||
| 008 | 010116s2000 d||| |||| 00||| eng d | ||
| 020 | |a 0883853299 |9 0-88385-329-9 | ||
| 035 | |a (OCoLC)61082784 | ||
| 035 | |a (DE-599)BVBBV013533119 | ||
| 040 | |a DE-604 |b ger |e rakwb | ||
| 041 | 1 | |a eng |h rus | |
| 049 | |a DE-824 | ||
| 050 | 0 | |a QA151 | |
| 082 | 0 | |a 512.009 | |
| 084 | |a SK 200 |0 (DE-625)143223: |2 rvk | ||
| 100 | 1 | |a Bašmakova, Izabella G. |d 1921-2005 |e Verfasser |0 (DE-588)128562072 |4 aut | |
| 245 | 1 | 0 | |a The beginnings and evolution of algebra |c I. G. Bashmakova and G. S. Smirnova |
| 264 | 1 | |a [Washington, DC] |b Mathematical Assoc. of America |c 2000 | |
| 300 | |a XVI, 179 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a The Dolciani mathematical expositions |v 23 | |
| 650 | 4 | |a algebra | |
| 650 | 4 | |a historie | |
| 650 | 4 | |a Geschichte | |
| 650 | 4 | |a Algebra |x History | |
| 650 | 0 | 7 | |a Geschichte |0 (DE-588)4020517-4 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Algebra |0 (DE-588)4001156-2 |2 gnd |9 rswk-swf |
| 655 | 7 | |0 (DE-588)4151278-9 |a Einführung |2 gnd-content | |
| 689 | 0 | 0 | |a Algebra |0 (DE-588)4001156-2 |D s |
| 689 | 0 | |5 DE-604 | |
| 689 | 1 | 0 | |a Algebra |0 (DE-588)4001156-2 |D s |
| 689 | 1 | 1 | |a Geschichte |0 (DE-588)4020517-4 |D s |
| 689 | 1 | |5 DE-604 | |
| 700 | 1 | |a Smirnova, Galina S. |e Verfasser |4 aut | |
| 830 | 0 | |a The Dolciani mathematical expositions |v 23 |w (DE-604)BV001900740 |9 23 | |
| 856 | 4 | 2 | |m HEBIS Datenaustausch Darmstadt |q application/pdf |u http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009238222&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
| 999 | |a oai:aleph.bib-bvb.de:BVB01-009238222 | ||
Datensatz im Suchindex
| _version_ | 1804128327524417536 |
|---|---|
| adam_text | THE DOLC IANI MATHEMATICAL EXPOSITIONS NUMBER TWENTY-THREE THE
BEGINNINGS AND EVOLUTION OF ALGEBRA I. G. BASHMAKOVA AND G. S. SMIRNOVA
TRANSLATED FROM THE RUSSIAN BY ABE SHENITZER WITH THE EDITORIAL
ASSISTANCE OF DAVID A. COX PUBLISHED AND DISTRIBUTED BY THE MATHEMATICAL
ASSOCIATION OF AMERICA CONTENTS INTRODUCTION XIII CHAPTER 1 ELEMENTS OF
ALGEBRA IN ANCIENT BABYLONIA 1 1. BABYLONIAN NUMERICAL ALGEBRA 1 2.
INDETERMINATE EQUATIONS 7 3. THE ORIGIN OF THE FIRST ALGEBRAIC PROBLEMS
9 CHAPTER 2 ANCIENT GREEK GEOMETRIC ALGEBRA 11 1. TRANSFORMATION OF
MATHEMATICS INTO AN ABSTRACT DEDUCTIVE SCIENCE. DISCOVERY OF
INCOMMENSURABILITY 11 2. GEOMETRIC ALGEBRA 15 3. CLASSIFICATION OF
QUADRATIC IRRATIONALITIES 20 4. THE FIRST UNSOLVABLE PROBLEMS 21 5.
CUBIC EQUATIONS 27 6. INDETERMINATE EQUATIONS 30 CHAPTER 3 THE BIRTH OF
LITERAL ALGEBRA 35 1. MATHEMATICS IN THE FIRST CENTURIES CE. DIOPHANTUS
35 2. DIOPHANTUS ARITHMETICA. ITS DOMAIN OF NUMBERS AND SYMBOLISM 37 3.
THE CONTENTS OF ARITHMETICA. DIOPHANTUS METHODS 42 4. ALGEBRA AFTER
DIOPHANTUS 47 IX X THE BEGINNINGS AND EVOLUTION OF ALGEBRA CHAPTER 4
ALGEBRA IN THE MIDDLE AGES IN THE ARABIC EAST AND IN EUROPE 49 1. THE
EMERGENCE OF ALGEBRA AS AN INDEPENDENT DISCIPLINE 49 2. THE FIRST
ADVANCES IN ALGEBRA IN EUROPE 55 3. ALGEBRAIC SYMBOLISM IN EUROPE. THE
GERMAN COSSISTS AND THE DEVELOPMENT OF ALGEBRA IN ITALY 59 CHAPTER 5 THE
FIRST ACHIEVEMENTS OF ALGEBRA IN EUROPE 67 1. THE SOLUTION OF CUBIC AND
QUARTIC EQUATIONS 67 2. THE ALGEBRA OF RAFAEL BOMBELLI. INTRODUCTION OF
COMPLEX NUMBERS 71 3. FRANCOIS VIETE 75 4. CREATION OF A LITERAL
CALCULUS 77 5. GENESIS TRIANGULORUM 80 6. INDETERMINATE EQUATIONS IN THE
WORK OF VIETE 85 7. BEGINNING OF THE THEORY OF DETERMINATE EQUATIONS
.,87 CHAPTER 6 ALGEBRA IN THE 17TH AND 18TH CENTURIES 91 1. THE
ARITHMETIZATION OF ALGEBRA 91 2. DESCARTES TREATMENT OF DETERMINATE
EQUATIONS 93 3. THE FUNDAMENTAL THEOREM OF ALGEBRA 94 4. GAUSS
CRITICISM 98 5. THE PROBLEM OF SOLUTION OF EQUATIONS BY RADICALS 100 6.
PROOF OF THE UNSOLVABILITY OF THE GENERAL QUINTIC BY RADICALS .... 106
CHAPTER 7 THE THEORY OF ALGEBRAIC EQUATIONS IN THE 19TH CENTURY 109 1.
CYCLOTOMIC EQUATIONS 109 2. EQUATIONS WITH AN ABELIAN GROUP 114 3.
GALOIS THEORY 115 4. THE EVOLUTION OF GROUP THEORY IN THE 19TH CENTURY
120 5. THE VICTORIOUS MARCH OF GROUP THEORY 125 CONTENTS XI CHAPTER 8
PROBLEMS OF NUMBER THEORY AND THE BIRTH OF COMMUTATIVE ALGEBRA . 129 1.
DIOPHANTINE EQUATIONS AND THE INTRODUCTION OF ALGEBRAIC NUMBERS 129 2.
KUMMER S IDEAL FACTORS 135 3. ARITHMETIC IN ARBITRARY FIELDS OF
ALGEBRAIC NUMBERS. IDEAL THEORY 137 4. IDEAL THEORY IN FIELDS OF
ALGEBRAIC FUNCTIONS 140 CHAPTER 9 LINEAR AND NONCOMMUTATIVE ALGEBRA 149
1. INTRODUCTION OF DETERMINANTS 149 2. LINEAR TRANSFORMATIONS AND
MATRICES 151 3. THE ENGLISH SCHOOL OF SYMBOLIC ALGEBRA. HAMILTON S
QUATERNIONS 155 4. ALGEBRAS 158 CONCLUSION 161 APPENDIX: A NEW VIEW OF
THE GEOMETRIC ALGEBRA OF THE ANCIENTS .... 163 REFERENCES 175 INDEX 177
|
| any_adam_object | 1 |
| author | Bašmakova, Izabella G. 1921-2005 Smirnova, Galina S. |
| author_GND | (DE-588)128562072 |
| author_facet | Bašmakova, Izabella G. 1921-2005 Smirnova, Galina S. |
| author_role | aut aut |
| author_sort | Bašmakova, Izabella G. 1921-2005 |
| author_variant | i g b ig igb g s s gs gss |
| building | Verbundindex |
| bvnumber | BV013533119 |
| callnumber-first | Q - Science |
| callnumber-label | QA151 |
| callnumber-raw | QA151 |
| callnumber-search | QA151 |
| callnumber-sort | QA 3151 |
| callnumber-subject | QA - Mathematics |
| classification_rvk | SK 200 |
| ctrlnum | (OCoLC)61082784 (DE-599)BVBBV013533119 |
| dewey-full | 512.009 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 512 - Algebra |
| dewey-raw | 512.009 |
| dewey-search | 512.009 |
| dewey-sort | 3512.009 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
| fullrecord | <?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>01826nam a2200481 cb4500</leader><controlfield tag="001">BV013533119</controlfield><controlfield tag="003">DE-604</controlfield><controlfield tag="005">20010829 </controlfield><controlfield tag="007">t</controlfield><controlfield tag="008">010116s2000 d||| |||| 00||| eng d</controlfield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">0883853299</subfield><subfield code="9">0-88385-329-9</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(OCoLC)61082784</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-599)BVBBV013533119</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-604</subfield><subfield code="b">ger</subfield><subfield code="e">rakwb</subfield></datafield><datafield tag="041" ind1="1" ind2=" "><subfield code="a">eng</subfield><subfield code="h">rus</subfield></datafield><datafield tag="049" ind1=" " ind2=" "><subfield code="a">DE-824</subfield></datafield><datafield tag="050" ind1=" " ind2="0"><subfield code="a">QA151</subfield></datafield><datafield tag="082" ind1="0" ind2=" "><subfield code="a">512.009</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">SK 200</subfield><subfield code="0">(DE-625)143223:</subfield><subfield code="2">rvk</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Bašmakova, Izabella G.</subfield><subfield code="d">1921-2005</subfield><subfield code="e">Verfasser</subfield><subfield code="0">(DE-588)128562072</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">The beginnings and evolution of algebra</subfield><subfield code="c">I. G. Bashmakova and G. S. Smirnova</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="a">[Washington, DC]</subfield><subfield code="b">Mathematical Assoc. of America</subfield><subfield code="c">2000</subfield></datafield><datafield tag="300" ind1=" " ind2=" "><subfield code="a">XVI, 179 S.</subfield><subfield code="b">graph. Darst.</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="b">n</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="b">nc</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="490" ind1="1" ind2=" "><subfield code="a">The Dolciani mathematical expositions</subfield><subfield code="v">23</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">algebra</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">historie</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Geschichte</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Algebra</subfield><subfield code="x">History</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Geschichte</subfield><subfield code="0">(DE-588)4020517-4</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Algebra</subfield><subfield code="0">(DE-588)4001156-2</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="655" ind1=" " ind2="7"><subfield code="0">(DE-588)4151278-9</subfield><subfield code="a">Einführung</subfield><subfield code="2">gnd-content</subfield></datafield><datafield tag="689" ind1="0" ind2="0"><subfield code="a">Algebra</subfield><subfield code="0">(DE-588)4001156-2</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2=" "><subfield code="5">DE-604</subfield></datafield><datafield tag="689" ind1="1" ind2="0"><subfield code="a">Algebra</subfield><subfield code="0">(DE-588)4001156-2</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="1" ind2="1"><subfield code="a">Geschichte</subfield><subfield code="0">(DE-588)4020517-4</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="1" ind2=" "><subfield code="5">DE-604</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Smirnova, Galina S.</subfield><subfield code="e">Verfasser</subfield><subfield code="4">aut</subfield></datafield><datafield tag="830" ind1=" " ind2="0"><subfield code="a">The Dolciani mathematical expositions</subfield><subfield code="v">23</subfield><subfield code="w">(DE-604)BV001900740</subfield><subfield code="9">23</subfield></datafield><datafield tag="856" ind1="4" ind2="2"><subfield code="m">HEBIS Datenaustausch Darmstadt</subfield><subfield code="q">application/pdf</subfield><subfield code="u">http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009238222&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA</subfield><subfield code="3">Inhaltsverzeichnis</subfield></datafield><datafield tag="999" ind1=" " ind2=" "><subfield code="a">oai:aleph.bib-bvb.de:BVB01-009238222</subfield></datafield></record></collection> |
| genre | (DE-588)4151278-9 Einführung gnd-content |
| genre_facet | Einführung |
| id | DE-604.BV013533119 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T18:47:29Z |
| institution | BVB |
| isbn | 0883853299 |
| language | English Russian |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-009238222 |
| oclc_num | 61082784 |
| open_access_boolean | |
| owner | DE-824 |
| owner_facet | DE-824 |
| physical | XVI, 179 S. graph. Darst. |
| publishDate | 2000 |
| publishDateSearch | 2000 |
| publishDateSort | 2000 |
| publisher | Mathematical Assoc. of America |
| record_format | marc |
| series | The Dolciani mathematical expositions |
| series2 | The Dolciani mathematical expositions |
| spelling | Bašmakova, Izabella G. 1921-2005 Verfasser (DE-588)128562072 aut The beginnings and evolution of algebra I. G. Bashmakova and G. S. Smirnova [Washington, DC] Mathematical Assoc. of America 2000 XVI, 179 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier The Dolciani mathematical expositions 23 algebra historie Geschichte Algebra History Geschichte (DE-588)4020517-4 gnd rswk-swf Algebra (DE-588)4001156-2 gnd rswk-swf (DE-588)4151278-9 Einführung gnd-content Algebra (DE-588)4001156-2 s DE-604 Geschichte (DE-588)4020517-4 s Smirnova, Galina S. Verfasser aut The Dolciani mathematical expositions 23 (DE-604)BV001900740 23 HEBIS Datenaustausch Darmstadt application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009238222&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Bašmakova, Izabella G. 1921-2005 Smirnova, Galina S. The beginnings and evolution of algebra The Dolciani mathematical expositions algebra historie Geschichte Algebra History Geschichte (DE-588)4020517-4 gnd Algebra (DE-588)4001156-2 gnd |
| subject_GND | (DE-588)4020517-4 (DE-588)4001156-2 (DE-588)4151278-9 |
| title | The beginnings and evolution of algebra |
| title_auth | The beginnings and evolution of algebra |
| title_exact_search | The beginnings and evolution of algebra |
| title_full | The beginnings and evolution of algebra I. G. Bashmakova and G. S. Smirnova |
| title_fullStr | The beginnings and evolution of algebra I. G. Bashmakova and G. S. Smirnova |
| title_full_unstemmed | The beginnings and evolution of algebra I. G. Bashmakova and G. S. Smirnova |
| title_short | The beginnings and evolution of algebra |
| title_sort | the beginnings and evolution of algebra |
| topic | algebra historie Geschichte Algebra History Geschichte (DE-588)4020517-4 gnd Algebra (DE-588)4001156-2 gnd |
| topic_facet | algebra historie Geschichte Algebra History Algebra Einführung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009238222&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV001900740 |
| work_keys_str_mv | AT basmakovaizabellag thebeginningsandevolutionofalgebra AT smirnovagalinas thebeginningsandevolutionofalgebra |