Galois Theory This course is a tutorial in Galois theory for students who have completed Abstract Algebra. Starting from the concept of a ring, we will develop the theory of polynomial rings over fields, and use this to carry out an in-depth investigation of field extensions. Our work together will culminate in proving the fundamental theorem of Galois theory. Working independently and in small groups, students will explore related areas of algebra and communicate their insights in expository writing and oral presentations. This course fulfills the capstone senior work requirement for the mathematics major.