Mathematics 410 - Galois Theory
M/W/F | 9:00 AM - 9:50 AM
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 answer classical questions about straightedge-and-compass constructions: for example, it is possible to use a straightedge and compass to draw a regular 17-sided polygon, but not a regular 7-sided polygon.
MATH 350 or consent of the instructor is required. Limited to 25 students.
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 quizzes or exams, take-home exams.