Symmetries of Equations: An Introduction to Galois Theory

Shared by Natalia Suárez • mathematics, galois theory • 1950

Contents: 1. What is Galois Theory? 2. Rings I: Polynomials 3. Roots and Irreducibility 4. Fields I: Basics, Extensions and Concrete Examples 5. Rings II: Quotients 6. Fields II: Constructions and More Examples 7. Ruler and Compass Constructions I 8. Linear Algebra I: Dimensions 9. Fields III: A Menagerie 10. Ruler and Compass Constructions II 11. Groups I: A Miscellany 12. Groups II: Symmetries of Fields 13. Linear Algebra II: Solving Equations 14. The Fundamental Theorem of Galois Theory 15. Applications of the Galois Correspondence 16. (Not) Solving Equations 17. Selected Solutions. Lecture