Galois theory for beginners: a historical perspective
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Weitere Verfasser: | |
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Providence, Rhode Island
American Mathematical Society
2006
|
| Schriftenreihe: | Student mathematical library
Volume 35 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XX, 180 Seiten Illustrationen, Diagramme |
| ISBN: | 9780821838174 0821838172 |
Internformat
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Datensatz im Suchindex
| _version_ | 1804140309407334400 |
|---|---|
| adam_text | Contents
Preface to the English Edition vii
Prefaces to the German Editions ix
Chapter 1. Cubic Equations 1
Chapter 2. Casus Irreducibilis: The Birth of the Complex
Numbers 9
Chapter 3. Biquadratic Equations 23
Chapter 4. Equations of Degree n and Their Properties 27
The Fundamental Theorem of Algebra: Plausibility
and Proof 32
Chapter 5. The Search for Additional Solution Formulas 37
Permutations 42
The Fundamental Theorem on Symmetric
Polynomials 47
Ruffini and the General Equation of Fifth Degree 50
Contents
Chapter 6. Equations That Can Be Reduced in Degree 55
The Decomposition of Integer Polynomials 57
Eisenstein s Irreducibility Criterion 60
Chapter 7. The Construction of Regular Polygons 63
Constructions with Straightedge and Compass 69
The Classical Construction Problems 74
Chapter 8. The Solution of Equations of the Fifth Degree 81
The Transformations of Tschirnhaus and of Bring and
Jerrard 89
Chapter 9. The Galois Group of an Equation 93
Computing the Galois Group H4
A Quick Course in Calculating with Polynomials 119
Chapter 10. Algebraic Structures and Galois Theory 125
Groups and Fields 130
The Fundamental Theorem of Galois Theory: An
Example 144
Artin s Version of the Fundamental Theorem of
Galois Theory 149
The Unsolvability of the Classical Construction
Problems 161
Epilogue 165
Index 177
|
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| author | Bewersdorff, Jörg 1958- |
| author2 | Kramer, David |
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| author_facet | Bewersdorff, Jörg 1958- Kramer, David |
| author_role | aut |
| author_sort | Bewersdorff, Jörg 1958- |
| author_variant | j b jb |
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| callnumber-first | Q - Science |
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| dewey-full | 512.32 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 512 - Algebra |
| dewey-raw | 512.32 |
| dewey-search | 512.32 |
| dewey-sort | 3512.32 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| era | Geschichte gnd |
| era_facet | Geschichte |
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| id | DE-604.BV024122044 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T21:57:56Z |
| institution | BVB |
| isbn | 9780821838174 0821838172 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-018338766 |
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| physical | XX, 180 Seiten Illustrationen, Diagramme |
| publishDate | 2006 |
| publishDateSearch | 2006 |
| publishDateSort | 2006 |
| publisher | American Mathematical Society |
| record_format | marc |
| series | Student mathematical library |
| series2 | Student mathematical library |
| spelling | Bewersdorff, Jörg 1958- Verfasser (DE-588)12862163X aut Algebra für Einsteiger Galois theory for beginners a historical perspective Jörg Bewersdorff. Translated by David Kramer Providence, Rhode Island American Mathematical Society 2006 XX, 180 Seiten Illustrationen, Diagramme txt rdacontent n rdamedia nc rdacarrier Student mathematical library Volume 35 Geschichte gnd rswk-swf Algebraische Gleichung (DE-588)4001162-8 gnd rswk-swf Lösung Mathematik (DE-588)4120678-2 gnd rswk-swf Geschichte (DE-588)4020517-4 gnd rswk-swf Galois-Theorie (DE-588)4155901-0 gnd rswk-swf (DE-588)4151278-9 Einführung gnd-content (DE-588)4123623-3 Lehrbuch gnd-content Galois-Theorie (DE-588)4155901-0 s DE-604 Algebraische Gleichung (DE-588)4001162-8 s Lösung Mathematik (DE-588)4120678-2 s Geschichte z Geschichte (DE-588)4020517-4 s Kramer, David trl Erscheint auch als Online-Ausgabe 978-1-4704-2146-5 Student mathematical library Volume 35 (DE-604)BV013184751 35 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=018338766&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Bewersdorff, Jörg 1958- Galois theory for beginners a historical perspective Student mathematical library Algebraische Gleichung (DE-588)4001162-8 gnd Lösung Mathematik (DE-588)4120678-2 gnd Geschichte (DE-588)4020517-4 gnd Galois-Theorie (DE-588)4155901-0 gnd |
| subject_GND | (DE-588)4001162-8 (DE-588)4120678-2 (DE-588)4020517-4 (DE-588)4155901-0 (DE-588)4151278-9 (DE-588)4123623-3 |
| title | Galois theory for beginners a historical perspective |
| title_alt | Algebra für Einsteiger |
| title_auth | Galois theory for beginners a historical perspective |
| title_exact_search | Galois theory for beginners a historical perspective |
| title_full | Galois theory for beginners a historical perspective Jörg Bewersdorff. Translated by David Kramer |
| title_fullStr | Galois theory for beginners a historical perspective Jörg Bewersdorff. Translated by David Kramer |
| title_full_unstemmed | Galois theory for beginners a historical perspective Jörg Bewersdorff. Translated by David Kramer |
| title_short | Galois theory for beginners |
| title_sort | galois theory for beginners a historical perspective |
| title_sub | a historical perspective |
| topic | Algebraische Gleichung (DE-588)4001162-8 gnd Lösung Mathematik (DE-588)4120678-2 gnd Geschichte (DE-588)4020517-4 gnd Galois-Theorie (DE-588)4155901-0 gnd |
| topic_facet | Algebraische Gleichung Lösung Mathematik Geschichte Galois-Theorie Einführung Lehrbuch |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=018338766&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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