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Galois Theory
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Galois Theory

Galois Theory

David A. Cox

559 pages, parution le 19/11/2004

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
Voir tout
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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

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