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Highlighting the importance of Diophantus of Alexandria as a precursor to the study of arithmetic over the rational numbers, this textbook introduces basic notions with an emphasis on Hilbert¿s Nullstellensatz over an arbitrary field. A digression on Euclidian rings is followed by a thorough study of the arithmetic theory of cubic surfaces. Subsequent chapters are devoted to p-adic fields, the Hasse principle, and the subtle notion of Diophantine dimension of fields. All chapters contain exercises, with hints or complete solutions.
Notes on Geometry and Arithmetic will appeal to a wide readership, ranging from graduate students through to researchers. Assuming only a basic background in abstract algebra and number theory, the text uses Diophantine questions to motivate readers seeking an accessible pathway into arithmetic geometry.
Highlighting the importance of Diophantus of Alexandria as a precursor to the study of arithmetic over the rational numbers, this textbook introduces basic notions with an emphasis on Hilbert¿s Nullstellensatz over an arbitrary field. A digression on Euclidian rings is followed by a thorough study of the arithmetic theory of cubic surfaces. Subsequent chapters are devoted to p-adic fields, the Hasse principle, and the subtle notion of Diophantine dimension of fields. All chapters contain exercises, with hints or complete solutions.
Notes on Geometry and Arithmetic will appeal to a wide readership, ranging from graduate students through to researchers. Assuming only a basic background in abstract algebra and number theory, the text uses Diophantine questions to motivate readers seeking an accessible pathway into arithmetic geometry.
Offers readers a 'hands on' introduction to Diophantine geometry
Progresses from introductory to advanced topics using the language of classical geometry
Assumes only modest prerequisites in abstract algebra and number theory
Contains numerous exercises throughout
| Erscheinungsjahr: | 2020 |
|---|---|
| Fachbereich: | Arithmetik & Algebra |
| Genre: | Mathematik |
| Rubrik: | Naturwissenschaften & Technik |
| Medium: | Taschenbuch |
| Seiten: | 196 |
| Reihe: | Universitext |
| Inhalt: |
xii
181 S. 118 s/w Illustr. 3 farbige Illustr. 181 p. 121 illus. 3 illus. in color. |
| ISBN-13: | 9783030437800 |
| ISBN-10: | 3030437809 |
| Sprache: | Englisch |
| Ausstattung / Beilage: | Paperback |
| Einband: | Kartoniert / Broschiert |
| Autor: | Coray, Daniel |
| Übersetzung: |
Steinig, John
Manoil, Constantin |
| Auflage: | 1st ed. 2020 |
| Hersteller: |
Springer International Publishing
Springer International Publishing AG Universitext |
| Maße: | 235 x 155 x 11 mm |
| Von/Mit: | Daniel Coray |
| Erscheinungsdatum: | 07.07.2020 |
| Gewicht: | 0,348 kg |
Offers readers a 'hands on' introduction to Diophantine geometry
Progresses from introductory to advanced topics using the language of classical geometry
Assumes only modest prerequisites in abstract algebra and number theory
Contains numerous exercises throughout
| Erscheinungsjahr: | 2020 |
|---|---|
| Fachbereich: | Arithmetik & Algebra |
| Genre: | Mathematik |
| Rubrik: | Naturwissenschaften & Technik |
| Medium: | Taschenbuch |
| Seiten: | 196 |
| Reihe: | Universitext |
| Inhalt: |
xii
181 S. 118 s/w Illustr. 3 farbige Illustr. 181 p. 121 illus. 3 illus. in color. |
| ISBN-13: | 9783030437800 |
| ISBN-10: | 3030437809 |
| Sprache: | Englisch |
| Ausstattung / Beilage: | Paperback |
| Einband: | Kartoniert / Broschiert |
| Autor: | Coray, Daniel |
| Übersetzung: |
Steinig, John
Manoil, Constantin |
| Auflage: | 1st ed. 2020 |
| Hersteller: |
Springer International Publishing
Springer International Publishing AG Universitext |
| Maße: | 235 x 155 x 11 mm |
| Von/Mit: | Daniel Coray |
| Erscheinungsdatum: | 07.07.2020 |
| Gewicht: | 0,348 kg |
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