A Field Guide to Algebra

2005
ISBN: 978-0-387-21428-3
Verlag: Springer

Buch, Englisch, 198 Seiten, Format (B × H): 160 mm x 241 mm, Gewicht: 1050 g

Reihe: Undergraduate Texts in Mathematics

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.

Zielgruppe

Lower undergraduate

Autoren/Hrsg.

Chambert-Loir, Antoine

Fachgebiete

• Sozialwissenschaften Pädagogik Lehrerausbildung, Unterricht & Didaktik Allgemeine Didaktik Naturwissenschaften, Mathematik (Unterricht & Didaktik)
• Mathematik | Informatik Mathematik Algebra Zahlentheorie

Inhaltsverzeichnis

Field extensions.- Roots.- Galois theory.- A bit of group theory.- Applications.- Algebraic theory of differential equations.

Über Autor(innen)

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