Galois Theory

Symmetry. - Rings. - Domains and Fields. - Homomorphisms and Ideals. - Quotient Rings. - Polynomial Rings over Fields. - Prime Ideals and Maximal Ideals. - Irreducible Polynomials. - Classical Formulas. - Splitting Fields. - The Galois Group. - Roots of Unity. - Solvability by Radicals. - Independence of Characters. - Galois Extensions. - The Fundamental Theorem of Galois Theory. - Applications. - Galois's Great Theorem. - Discriminants. - Galois Groups of Quadratics Cubics and Quartics. - Epilogue. - Appendix A: Group Theory Dictionary. - Appendix B: Group Theory Used in the Text. - Appendix C: Ruler-Compass Constructions. - Appendix D: Old-fashioned Galois Theory. - References. Language: English