Neuware -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.Springer Verlag GmbH, Tiergartenstr. 17, 69121 Heidelberg 356 pp. Englisch.

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T�tulo: Quadratic Number Fields
Editor: Springer International Publishing, Springer International Publishing Sep 2021
Fecha de publicaci�n: 2021
Idioma: Ingl�s
ISBN 10: 303078651X
ISBN 13: 9783030786519
Encuadernaci�n: Taschenbuch
Estado: Neu
Dimensiones: 235�mil�metros de ancho por 155 de alto por 20 de largo
Peso: 540 gramos

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Sinopsis

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.

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

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