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
A0/00cole Polytechnique, Palaiseau, France. He is now Professor at
UniversitA(c) de Rennes 1.
General
| Imprint: |
Springer-Verlag New York
|
| Country of origin: |
United States |
| Series: |
Undergraduate Texts in Mathematics |
| Release date: |
October 2004 |
| First published: |
2005 |
| Authors: |
Antoine Chambert-Loir
|
| Dimensions: |
235 x 155 x 12mm (L x W x T) |
| Format: |
Hardcover
|
| Pages: |
198 |
| Edition: |
2005 ed. |
| ISBN-13: |
978-0-387-21428-3 |
| Categories: |
Books >
Science & Mathematics >
Mathematics >
Algebra >
General
|
| LSN: |
0-387-21428-3 |
| Barcode: |
9780387214283 |
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