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

Libro 25 de 168: Undergraduate Texts in Mathematics

Chambert-Loir, Antoine

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

Sinopsis

This book has a nonstandard choice of topics, including material on differential galois groups and proofs of the transcendence of e and pi. 

The author uses a conversational tone and has included a selection of stamps to accompany the text.

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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.

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Otras ediciones populares con el mismo título

9781441919472: A Field Guide to Algebra (Undergraduate Texts in Mathematics)

Edición Destacada

ISBN 10:  1441919473 ISBN 13:  9781441919472
Editorial: Springer, 2010
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