## Galois TheoryAn 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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### Contents

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 |