Symmetry 1
Rings 7
Domains and Fields 13
Homomorphisms and Ideals 17
Quotient Rings 21
Polynomial Rings over Fields 24
Prime Ideals and Maximal Ideals 31
Irreducible Polynomials 38
Classical Formulas 44
Splitting Fields 50
The Galois Group 59
Roots of Unity 63
Solvability by Radicals 71
Independence of Characters 76
Galois Extensions 79
The Fundamental Theorem of Galois Theory 83
Applications 85
Galois's Great Theorem 90
Discriminants 95
Galois Groups of Quadratics,Cubics,and Quartics 100
Epilogue 107
Appendix A:Group Theory Dictionary 109
Appendix B:Group Theory Used in the Text 112
Appendix C:Ruler-Compass Constructions 129
Appendix D:Old-fashioned Galois Theory 138
References 151
Index 153