This course offers a continued study of the algebraic structures introduced in MATH 305, culminating in the Fundamental Theorem of Galois Theory, a beautiful result that depicts the circle of ideas surrounding field extensions, polynomial rings, and automorphism groups. Applications of Galois theory include the unsolvability of the quintic by radicals and geometric impossibility proofs, such as the trisection of angles and duplication of cubes. Cyclotomic extensions and Sylow theory may be included in the syllabus.

Units: 1

Max Enrollment: 15

Prerequisites: MATH 305

Distribution Requirements: MM - Mathematical Modeling and Problem Solving

Typical Periods Offered: Spring

Semesters Offered this Academic Year: Not Offered; Spring