From the rear cover
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 cole polytechnique, Palaiseau, France. He is now Professor at Universit de Rennes 1.
Details
- Title A Field Guide to Algebra
- Author Antoine Chambert-Loir
- Binding Hardcover
- Edition INTERNATIONAL ED
- Pages 198
- Volumes 1
- Language ENG
- Publisher Springer, New York
- Date 2004-10-01
- Illustrated Yes
- Features Bibliography, Illustrated, Index
- ISBN 9780387214283 / 0387214283
- Weight 1.05 lbs (0.48 kg)
- Dimensions 9.46 x 6.4 x 0.65 in (24.03 x 16.26 x 1.65 cm)
- Library of Congress subjects Algebraic fields
- Library of Congress Catalog Number 2004048103
- Dewey Decimal Code 512.3
Media reviews
Citations
- Choice, 06/01/2005, Page 1856
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