A Field Guide to Algebra (Electronic book text)


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.

Delivery AdviceNot available

Toggle WishListAdd to wish list
Review this Item

Product Description

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.

Customer Reviews

No reviews or ratings yet - be the first to create one!

Product Details

General

Imprint

Springer Science+Business Media

Country of origin

United States

Series

Undergraduate Texts in Mathematics

Release date

2005

Availability

We don't currently have any sources for this product. If you add this item to your wish list we will let you know when it becomes available.

Authors

Format

Electronic book text

Pages

198

ISBN-13

978-0-387-26955-9

Barcode

9780387269559

Categories

LSN

0-387-26955-X



Trending In Books