This course is a continuation of Math 333, covering advanced topics in groups, rings, fields and modules that build on the ideas introduced in the fall semester. The course includes an introduction to Galois Theory, and several other topics of great significance in the history of mathematics: insolubility of the quintic equation, angle trisection and constructibility problems
As in Math 333, the course has a strong focus on learning
how to write clear and precise mathematical definitions and proofs.
The math major requires either Math 334 or the second semester of analysis Math 318. Students
considering graduate work in a mathematical field are strongly urged to take both courses.
Prerequisites:
Math 333 (Algebra I)
Who should take this course?
Math majors with research interests in algebra, number theory, geometry, topology, or
combinatorics
Math majors considering graduate work in a mathematical field
Other math majors looking for a 300-level elective
Anyone interested in advanced study of the history of mathematics
Anyone who wants to explore the formal or conceptual side of mathematics in considerable
depth
Topics covered:
Sylow's theorems for groups
Euclidean domains
Field exentions
Introduction to Galois Theory
Constructible numbers
Finite fields
Introduction to modules
Advanced topics in Linear Algebra
For detailed information about Math 334 this year, please consult the list of Fall Courses and Spring Courses linked to the Mathematics and Statistics Home Page.