Abstract Algebra and Famous Impossibilities:
Saved in:
| Main Author: | |
|---|---|
| Format: | Electronic eBook |
| Language: | English |
| Published: |
New York, NY
Springer New York
1991
|
| Series: | Universitext
|
| Subjects: | |
| Links: | https://doi.org/10.1007/978-1-4419-8552-1 |
| Item Description: | The famous problems of squaring the circle, doubling the cube and trisecting an angle captured the imagination of both professional and amateur mathematicians for over two thousand years. Despite the enormous effort and ingenious attempts by these men and women, the problems would not yield to purely geometrical methods. It was only the development. of abstract algebra in the nineteenth century which enabled mathematicians to arrive at the surprising conclusion that these constructions are not possible. In this book we develop enough abstract algebra to prove that these constructions are impossible. Our approach introduces all the relevant concepts about fields in a way which is more concrete than usual and which avoids the use of quotient structures (and even of the Euclidean algorithm for finding the greatest common divisor of two polynomials). Having the geometrical questions as a specific goal provides motivation for the introduction of the algebraic concepts and we have found that students respond very favourably. We have used this text to teach second-year students at La Trobe University over a period of many years, each time refining the material in the light of student performance |
| Physical Description: | 1 Online-Ressource (X, 189 p) |
| ISBN: | 9781441985521 9780387976617 |
| ISSN: | 0172-5939 |
| DOI: | 10.1007/978-1-4419-8552-1 |
Staff View
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Record in the Search Index
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| discipline | Mathematik |
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| indexdate | 2024-12-20T17:10:40Z |
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| isbn | 9781441985521 9780387976617 |
| issn | 0172-5939 |
| language | English |
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| publishDateSearch | 1991 |
| publishDateSort | 1991 |
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| spellingShingle | Jones, Arthur Abstract Algebra and Famous Impossibilities Mathematics Number theory Number Theory Mathematik Geometrie (DE-588)4020236-7 gnd Ungelöstes Problem (DE-588)4186869-9 gnd Geometrische Konstruktion (DE-588)4156714-6 gnd Problemlösen (DE-588)4076358-4 gnd Galois-Theorie (DE-588)4155901-0 gnd Universelle Algebra (DE-588)4061777-4 gnd Algebraische Methode (DE-588)4141841-4 gnd |
| subject_GND | (DE-588)4020236-7 (DE-588)4186869-9 (DE-588)4156714-6 (DE-588)4076358-4 (DE-588)4155901-0 (DE-588)4061777-4 (DE-588)4141841-4 (DE-588)4143389-0 |
| title | Abstract Algebra and Famous Impossibilities |
| title_auth | Abstract Algebra and Famous Impossibilities |
| title_exact_search | Abstract Algebra and Famous Impossibilities |
| title_full | Abstract Algebra and Famous Impossibilities by Arthur Jones, Kenneth R. Pearson, Sidney A. Morris |
| title_fullStr | Abstract Algebra and Famous Impossibilities by Arthur Jones, Kenneth R. Pearson, Sidney A. Morris |
| title_full_unstemmed | Abstract Algebra and Famous Impossibilities by Arthur Jones, Kenneth R. Pearson, Sidney A. Morris |
| title_short | Abstract Algebra and Famous Impossibilities |
| title_sort | abstract algebra and famous impossibilities |
| topic | Mathematics Number theory Number Theory Mathematik Geometrie (DE-588)4020236-7 gnd Ungelöstes Problem (DE-588)4186869-9 gnd Geometrische Konstruktion (DE-588)4156714-6 gnd Problemlösen (DE-588)4076358-4 gnd Galois-Theorie (DE-588)4155901-0 gnd Universelle Algebra (DE-588)4061777-4 gnd Algebraische Methode (DE-588)4141841-4 gnd |
| topic_facet | Mathematics Number theory Number Theory Mathematik Geometrie Ungelöstes Problem Geometrische Konstruktion Problemlösen Galois-Theorie Universelle Algebra Algebraische Methode Aufgabensammlung |
| url | https://doi.org/10.1007/978-1-4419-8552-1 |
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