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A Field Guide to Algebra (Undergraduate Texts in Mathematics) Paperback - 2010
by Chambert-Loir, Antoine
- Used
- Good
- Paperback
Description
Details
- Title A Field Guide to Algebra (Undergraduate Texts in Mathematics)
- Author Chambert-Loir, Antoine
- Binding Paperback
- Edition 1st ed.
- Condition Used - Good
- Pages 198
- Volumes 1
- Language ENG
- Publisher Springer
- Date 2010-11-29
- Bookseller's Inventory # 1441919473.G
- ISBN 9781441919472 / 1441919473
- Weight 0.66 lbs (0.30 kg)
- Dimensions 9.21 x 6.14 x 0.44 in (23.39 x 15.60 x 1.12 cm)
- Dewey Decimal Code 512.3
About Bonita California, United States
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.