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Beginning with Gauss¿s theory of numbers and Galois¿s ideas, the book progresses to Dedekind and Kronecker, Jordan and Klein, Steinitz, Hilbert, and Emmy Noether. Approaching mathematical topics from a historical perspective, the author explores quadratic forms, quadratic reciprocity, Fermat¿s Last Theorem, cyclotomy, quintic equations, Galois theory, commutative rings, abstract fields, ideal theory, invariant theory, and group theory. Readers will learn what Galois accomplished, how difficult the proofs of his theorems were, and how important Camille Jordan and Felix Klein were in the eventual acceptance of Galois¿s approach to the solution of equations. The book also describes the relationshipbetween Kummer¿s ideal numbers and Dedekind¿s ideals, and discusses why Dedekind felt his solution to the divisor problem was better than Kummer¿s.
Designed for a course in the history of modern algebra, this book is aimed at undergraduate students with an introductory background in algebra but will also appeal to researchers with a general interest in the topic. With exercises at the end of each chapter and appendices providing material difficult to find elsewhere, this book is self-contained and therefore suitable for self-study.
Beginning with Gauss¿s theory of numbers and Galois¿s ideas, the book progresses to Dedekind and Kronecker, Jordan and Klein, Steinitz, Hilbert, and Emmy Noether. Approaching mathematical topics from a historical perspective, the author explores quadratic forms, quadratic reciprocity, Fermat¿s Last Theorem, cyclotomy, quintic equations, Galois theory, commutative rings, abstract fields, ideal theory, invariant theory, and group theory. Readers will learn what Galois accomplished, how difficult the proofs of his theorems were, and how important Camille Jordan and Felix Klein were in the eventual acceptance of Galois¿s approach to the solution of equations. The book also describes the relationshipbetween Kummer¿s ideal numbers and Dedekind¿s ideals, and discusses why Dedekind felt his solution to the divisor problem was better than Kummer¿s.
Designed for a course in the history of modern algebra, this book is aimed at undergraduate students with an introductory background in algebra but will also appeal to researchers with a general interest in the topic. With exercises at the end of each chapter and appendices providing material difficult to find elsewhere, this book is self-contained and therefore suitable for self-study.
Provides a wide-ranging and up-to-date account on the history of abstract algebra
Covers topics from number theory (especially quadratic forms) and Galois theory as far as the origins of the abstract theories of groups, rings and fields
Develops the mathematical and the historical skills needed to understand the subject
Presents material that is difficult to find elsewhere, including translations of Gauss's sixth proof of quadratic reciprocity, parts of Jordan's Traité and Dedekind's 11th supplement, as well as a summary of Klein's work on the icosahedron
| Erscheinungsjahr: | 2018 |
|---|---|
| Fachbereich: | Allgemeines |
| Genre: | Mathematik |
| Rubrik: | Naturwissenschaften & Technik |
| Thema: | Lexika |
| Medium: | Taschenbuch |
| Seiten: | 440 |
| Reihe: | Springer Undergraduate Mathematics Series |
| Inhalt: |
xxiv
415 S. 18 s/w Illustr. 415 p. 18 illus. |
| ISBN-13: | 9783319947723 |
| ISBN-10: | 3319947729 |
| Sprache: | Englisch |
| Herstellernummer: | 978-3-319-94772-3 |
| Ausstattung / Beilage: | Paperback |
| Einband: | Kartoniert / Broschiert |
| Autor: | Gray, Jeremy |
| Auflage: | 1st ed. 2018 |
| Hersteller: |
Springer International Publishing
Springer Undergraduate Mathematics Series |
| Maße: | 235 x 155 x 24 mm |
| Von/Mit: | Jeremy Gray |
| Erscheinungsdatum: | 16.08.2018 |
| Gewicht: | 0,663 kg |
Provides a wide-ranging and up-to-date account on the history of abstract algebra
Covers topics from number theory (especially quadratic forms) and Galois theory as far as the origins of the abstract theories of groups, rings and fields
Develops the mathematical and the historical skills needed to understand the subject
Presents material that is difficult to find elsewhere, including translations of Gauss's sixth proof of quadratic reciprocity, parts of Jordan's Traité and Dedekind's 11th supplement, as well as a summary of Klein's work on the icosahedron
| Erscheinungsjahr: | 2018 |
|---|---|
| Fachbereich: | Allgemeines |
| Genre: | Mathematik |
| Rubrik: | Naturwissenschaften & Technik |
| Thema: | Lexika |
| Medium: | Taschenbuch |
| Seiten: | 440 |
| Reihe: | Springer Undergraduate Mathematics Series |
| Inhalt: |
xxiv
415 S. 18 s/w Illustr. 415 p. 18 illus. |
| ISBN-13: | 9783319947723 |
| ISBN-10: | 3319947729 |
| Sprache: | Englisch |
| Herstellernummer: | 978-3-319-94772-3 |
| Ausstattung / Beilage: | Paperback |
| Einband: | Kartoniert / Broschiert |
| Autor: | Gray, Jeremy |
| Auflage: | 1st ed. 2018 |
| Hersteller: |
Springer International Publishing
Springer Undergraduate Mathematics Series |
| Maße: | 235 x 155 x 24 mm |
| Von/Mit: | Jeremy Gray |
| Erscheinungsdatum: | 16.08.2018 |
| Gewicht: | 0,663 kg |
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