Galois Theory

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John Wiley & Sons, 21 sept. 2004 - 559 pages
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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 irreducibilis), 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.

 

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Table des matières

Notation
1
Symmetric Polynomials
25
Roots of Polynomials
55
FIELDS
71
Normal and Separable Extensions
101
The Galois Group
125
The Galois Correspondence
147
APPLICATIONS
189
Finite Fields
289
FURTHER TOPICS
311
Computing Galois Groups
357
Solvable Permutation Groups
407
The Lemniscate
457
Appendix A Abstract Algebra
509
xviii
523
Appendix B Hints to Selected Exercises
543

Cyclotomic Extensions
229
Geometric Constructions
255

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À propos de l'auteur (2004)

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.

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