<電子ブック>
A Field Guide to Algebra / by Antoine Chambert-Loir
(Undergraduate Texts in Mathematics. ISSN:21975604)
版 | 1st ed. 2005. |
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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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電子ブック | 配架場所 | 資料種別 | 巻 次 | 請求記号 | 状 態 | 予約 | コメント | ISBN | 刷 年 | 利用注記 | 指定図書 | 登録番号 |
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電子ブック | オンライン | 電子ブック |
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Springer eBooks | 9780387269559 |
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EB00230768 |
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※2017年9月4日以降