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＜電子ブック＞
A Field Guide to Algebra / by Antoine Chambert-Loir
(Undergraduate Texts in Mathematics. ISSN:21975604)

版	1st ed. 2005.
出版者	(New York, NY : Springer New York : Imprint: Springer)
出版年	2005
本文言語	英語
大きさ	X, 198 p : online resource
著者標目	*Chambert-Loir, Antoine author SpringerLink (Online service)
件　名	LCSH:Algebra LCSH:Algebraic fields LCSH:Polynomials LCSH:Number theory LCSH:Commutative algebra LCSH:Commutative rings FREE:Algebra FREE:Field Theory and Polynomials FREE:Number Theory FREE:Commutative Rings and Algebras
一般注記	Field extensions -- Roots -- Galois theory -- A bit of group theory -- Applications -- Algebraic theory of differential equations 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 HTTP:URL=https://doi.org/10.1007/b138364

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