Quadratic Number Fields

Franz Lemmermeyer

ISBN 10: 303078651X / ISBN 13: 9783030786519

Verlag: Springer International Publishing, Springer Nature Switzerland, 2021

Beschreibung

Druck auf Anfrage Neuware - Printed after ordering - This undergraduate textbook provides an elegant introduction to the arithmetic of quadratic number fields, including many topics not usually covered in books at this level. Quadratic fields offer an introduction to algebraic number theory and some of its central objects: rings of integers, the unit group, ideals and the ideal class group. This textbook provides solid grounding for further study by placing the subject within the greater context of modern algebraic number theory. Going beyond what is usually covered at this level, the book introduces the notion of modularity in the context of quadratic reciprocity, explores the close links between number theory and geometry via Pell conics, and presents applications to Diophantine equations such as the Fermat and Catalan equations as well as elliptic curves. Throughout, the book contains extensive historical comments, numerous exercises (with solutions), and pointers to further study.Assuming a moderate background in elementary number theory and abstract algebra, Quadratic Number Fields offers an engaging first course in algebraic number theory, suitable for upper undergraduate students.

Bestandsnummer des Verkäufers 9783030786519

Bibliografische Details

• Titel: Quadratic Number Fields
• Verlag: Springer International Publishing, Springer Nature Switzerland
• Erscheinungsjahr: 2021
• Sprache: Englisch
• ISBN-10: 303078651X
• ISBN-13: 9783030786519
• Einband: Taschenbuch
• Zustand: Neu
• Abmessungen: 235B x 155 H x 20 T Millimeter Breite: 235 mm, Höhe: 155 mm, Tiefe: 20 mm
• Gewicht: 540 Gramm

Über diesen Titel

Inhaltsangabe

This undergraduate textbook provides an elegant introduction to the arithmetic of quadratic number fields, including many topics not usually covered in books at this level.

Quadratic fields offer an introduction to algebraic number theory and some of its central objects: rings of integers, the unit group, ideals and the ideal class group. This textbook provides solid grounding for further study by placing the subject within the greater context of modern algebraic number theory. Going beyond what is usually covered at this level, the book introduces the notion of modularity in the context of quadratic reciprocity, explores the close links between number theory and geometry via Pell conics, and presents applications to Diophantine equations such as the Fermat and Catalan equations as well as elliptic curves. Throughout, the book contains extensive historical comments, numerous exercises (with solutions), and pointers to further study.

Assuming a moderate background in elementary number theory and abstract algebra, Quadratic Number Fields offers an engaging first course in algebraic number theory, suitable for upper undergraduate students.

Über die Autorin bzw. den Autor

Franz Lemmermeyer has worked in algebraic number theory and has published several books on the history of number theory, in particular on reciprocity laws.