Galois Theory

David A. Cox

559 pages, parution le 19/11/2004

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Résumé

An Introduction To One Of The Most Celebrated Theories Of Mathematics

Galois theory is one of the jewels of mathematics. Its intrinsic beauty, dramatic history, and deep connections to other areas of mathematics give Galois theory an unequaled richness. David Cox's Galois Theory helps readers understand not only the elegance of the ideas but also where they came from and how they relate to the overall sweep of mathematics.

Galois Theory covers classic applications of the theory, such as solvability by radicals, geometric constructions, and finite fields. The book also delves into more novel topics, including Abel's theory of Abelian equations, the problem of expressing real roots by real radicals (the casus irre-ducibilis), and the Galois theory of origami. Anyone fascinated by abstract algebra will find careful discussions of such topics as:

The contributions of Lagrange, Galois, and Kronecker
How to compute Galois groups
Galois's results about irreducible polynomials of prime or prime-squared degree
Abel's theorem about geometric constructions on the lemniscate

With intriguing Mathematical and Historical Notes that clarify the ideas and their history in detail, Galois Theory brings one of the most colorful and influential theories in algebra to life for professional algebraists and students alike.

L'auteur - David A. Cox

DAVID A.COX is a professor of mathematics at Amherst College. He pursued his undergraduate studies at Rice University and earned his PhD from Princeton in 1975. The main focus of his research is algebraic geometry, though he also has interests in number theory and the history of mathematics. He is the author of Primes of the Form x² + ny², published by Wiley, as well as books on computational algebraic geometry and mirror symmetry.

Sommaire

Preface
Notation
Polynomials
- Cubic Equations
- Symmetric Polynomials
- Roots of Polynomials
Fields
- Extension Fields
- Normal and Separable Extensions
- The Galois Group
- The Galois Correspondence
Applications
- Solvability by Radicals
- Cyclotomic Extensions
- Geometric Constructions
- Finite Fields
Further topics
- Lagrange, Galois, and Kronecker
- Computing Galois Groups
- Solvable Permutation Groups
- The Lemniscate
Appendix A: Abstract Algebra
Appendix B: Hints to Selected Exercises
References
Index

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Caractéristiques techniques

	PAPIER
Éditeur(s)	Wiley
Auteur(s)	David A. Cox
Parution	19/11/2004
Nb. de pages	559
Format	16 x 24
Couverture	Relié
Poids	937g
Intérieur	Noir et Blanc
EAN13	9780471434191
ISBN13	978-0-471-43419-1