Galois Theory is the algebraic study of groups that can be associated with polynomial equations. This book covers the basic material of Galois theory and discusses many related topics, such as Abelian equations, solvable equations of prime degree, and the casus irreducibilis, that are not mentioned in most standard treatments. It also describes the rich history of Galois theory, including the work of Lagrange, Gauss, Abel, Galois, Jordan, and Kronecker.
Table of Contents
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.
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.