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A Field Guide to Algebra (Electronic book text)
A Field Guide to Algebra (Electronic book text): Antoine Chambert-Loir

A Field Guide to Algebra (Electronic book text)

Antoine Chambert-Loir

Series: Undergraduate Texts in Mathematics

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This unique textbook focuses on the structure of fields and is intended for a second course in abstract algebra. Besides providing proofs of the transcendence 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 Icole Polytechnique, Palaiseau, France. He is now Professor at Universiti de Rennes 1.


Imprint: Springer Science+Business Media
Country of origin: United States
Series: Undergraduate Texts in Mathematics
Release date: 2005
Authors: Antoine Chambert-Loir
Format: Electronic book text
Pages: 198
ISBN-13: 978-0-387-26955-9
Categories: Books > Science & Mathematics > Mathematics > Algebra > General
Books > Science & Mathematics > Mathematics > Number theory > General
LSN: 0-387-26955-X
Barcode: 9780387269559

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