Mathematics 410 - Galois Theory

The quadratic formula shows us that the roots of a quadratic polynomial possess a certain symmetry. Galois Theory is the study of the corresponding symmetry for higher degree polynomials. We will develop this theory starting from a basic knowledge of groups, rings, and fields. One of our main goals will be to prove that there is no general version of the quadratic formula for a polynomial of degree five or more. Along the way, we will also show that a circular cake can be divided into 17 (but not 7) equal slices using only a straight-edged knife.

Requisite: MATH 350 or consent of the instructor. Spring semester. Prof. Daniels. 

How to handle overenrollment: Preference is given to seniors.

Students who enroll in this course will likely encounter and be expected to engage in the following intellectual skills, modes of learning, and assessment: Problem sets, In-class group work, In-class quizzes or exams.