Quadratic Number Fields (Springer Undergraduate Mathematics Series) - Tapa blanda

Lemmermeyer, Franz

 
9783030786519: Quadratic Number Fields (Springer Undergraduate Mathematics Series)
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ISBN 10: 303078651X ISBN 13: 9783030786519
Editorial: Springer, 2021

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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Acerca del 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.

De la contraportada

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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Editorial
Springer
Año de publicación
2021
Idioma
Inglés
ISBN 10 
303078651X
ISBN 13 
9783030786519
Encuadernación
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Número de edición
1
Número de páginas
356
Contacto del fabricante
Springer Nature Customer Service Center GmbH
ProductSafety@springernature.com

Europaplatz 3,69115 Heidelberg, Germany
Heidelberg
69115
Alemania

Otras ediciones populares con el mismo título

9783030786533: Quadratic Number Fields

Edición Destacada

ISBN 10:  3030786536 ISBN 13:  9783030786533
Editorial: Springer, 2021
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