A Field Guide to Algebra (Undergraduate Texts in Mathematics) - Tapa blanda

Libro 25 de 168: Undergraduate Texts in Mathematics

Chambert-Loir, Antoine

 
9781441919472: A Field Guide to Algebra (Undergraduate Texts in Mathematics)
Tapa blanda
ISBN 10: 1441919473 ISBN 13: 9781441919472
Editorial: Springer, 2010

Sinopsis

This unique textbook focuses on the structure of fields and is intended for a second course in abstract algebra. Besides providing proofs of the transcendance of pi and e, the book includes material on differential Galois groups and a proof of Hilbert's irreducibility theorem. The reader will hear about equations, both polynomial and differential, and about the algebraic structure of their solutions. In explaining these concepts, the author also provides comments on their historical development and leads the reader along many interesting paths.

In addition, there are theorems from analysis: as stated before, the transcendence of the numbers pi and e, the fact that the complex numbers form an algebraically closed field, and also Puiseux's theorem that shows how one can parametrize the roots of polynomial equations, the coefficients of which are allowed to vary. There are exercises at the end of each chapter, varying in degree from easy to difficult. To make the book more lively, the author has incorporated pictures from the history of mathematics, including scans of mathematical stamps and pictures of mathematicians.

Antoine Chambert-Loir taught this book when he was Professor at École polytechnique, Palaiseau, France. He is now Professor at Université de Rennes 1.

"Sinopsis" puede pertenecer a otra edición de este libro.

Acerca del autor

Antoine Chambert-Loir is Professor at Université de Rennes 1.

De la contraportada

This unique textbook focuses on the structure of fields and is intended for a second course in abstract algebra. Besides providing proofs of the transcendance of pi and e, the book includes material on differential Galois groups and a proof of Hilbert's irreducibility theorem. The reader will hear about equations, both polynomial and differential, and about the algebraic structure of their solutions. In explaining these concepts, the author also provides comments on their historical development and leads the reader along many interesting paths.

In addition, there are theorems from analysis: as stated before, the transcendence of the numbers pi and e, the fact that the complex numbers form an algebraically closed field, and also Puiseux's theorem that shows how one can parametrize the roots of polynomial equations, the coefficients of which are allowed to vary. There are exercises at the end of each chapter, varying in degree from easy to difficult. To make the book more lively, the author has incorporated pictures from the history of mathematics, including scans of mathematical stamps and pictures of mathematicians.

Antoine Chambert-Loir taught this book when he was Professor at École polytechnique, Palaiseau, France. He is now Professor at Université de Rennes 1.

"Sobre este título" puede pertenecer a otra edición de este libro.

Editorial
Springer
Año de publicación
2010
Idioma
Inglés
ISBN 10 
1441919473
ISBN 13 
9781441919472
Encuadernación
Tapa blanda
Número de páginas
208
Contacto del fabricante
no disponible
Persona responsable
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Otras ediciones populares con el mismo título

9780387214283: A Field Guide to Algebra (Undergraduate Texts in Mathematics)

Edición Destacada

ISBN 10:  0387214283 ISBN 13:  9780387214283
Editorial: Springer, 2004
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