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Galois Theory
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  • Wiley

More About This Title Galois Theory

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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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Preface.

Notation.

PART I: POLYNOMIALS.

Chapter 1. Cubic Equations.

Chapter 2. Symmetric Polynomials.

Chapter 3. Roots of Polynomials.

PART II: FIELDS.

Chapter 4. Extension Fields.

Chapter 5. Normal and Separable Extensions.

Chapter 6. The Galois Group.

Chapter 7. The Galois Correspondence.

PART III: APPLICATIONS.

Chapter 8. Solvability by Radicals.

Chapter 9. Cyclotomic Extensions.

Chapter 10. Geometric Constructions.

Chapter 11. Finite Fields.

PART IV: FURTHER TOPICS.

Chapter 12. Lagrange, Galois, and Kronecker.

Chapter 13. Computing Galois Groups.

Chapter 14. Solvable Permutation Groups.

Chapter 15. The Lemniscate.

Appendix A: Abstract Algebra.

Appendix B: Hints to Selected Exercises.

References.

Index.

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"This book provides a very detailed and comprehensive presentation of the theory and applications of Galois theory." (Mathematical Reviews, Issue 2006a)

"Happily, Cox's book reads more like a monograph, making a solid case for new subjects rather than rapidly treating a classical one." (CHOICE, September 2005)

" … offers a careful discussion … and will certainly fascinate anyone interested in abstract algebra: a remarkable book!" (Monatshefte fur Mathematik, August 2006)

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