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This title in other editions

A Field Guide to Algebra (Undergraduate Texts in Mathematics)

by

A Field Guide to Algebra (Undergraduate Texts in Mathematics) Cover

 

Synopses & Reviews

Publisher Comments:

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.

Synopsis:

This book has a nonstandard choice of topics, including material on differential galois groups and proofs of the transcendence of e and pi.  The author uses a conversational tone and has included a selection of stamps to accompany the text.

About the Author

Antoine Chambert-Loir is Professor at Université de Rennes 1.

Table of Contents

Field Extensions.- Roots.- Galois Theory.- A Bit of Group Theory.- Applications.- Algebraic Theory of Differential Equations.- Examination Problems.- References.- Index.

Product Details

ISBN:
9781441919472
Author:
Chambert-loir, Antoine
Publisher:
Springer
Author:
Chambert-Loir, Antoine
Subject:
Mathematics - Algebra
Subject:
Algebra - General
Subject:
Algebra
Subject:
Field Theory and Polynomials
Subject:
Number Theory
Subject:
Commutative Rings and Algebras
Edition Description:
Softcover reprint of hardcover 1st ed. 2005
Series:
Undergraduate Texts in Mathematics
Publication Date:
20101131
Binding:
TRADE PAPER
Language:
English
Pages:
205
Dimensions:
235 x 155 mm 317 gr

Related Subjects


Science and Mathematics » Mathematics » Algebra » Abstract Algebra
Science and Mathematics » Mathematics » Algebra » General
Science and Mathematics » Mathematics » Number Theory

A Field Guide to Algebra (Undergraduate Texts in Mathematics) New Trade Paper
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Product details 205 pages Not Avail - English 9781441919472 Reviews:
"Synopsis" by , This book has a nonstandard choice of topics, including material on differential galois groups and proofs of the transcendence of e and pi.  The author uses a conversational tone and has included a selection of stamps to accompany the text.
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