About MATH 3555 A
Modules, vector spaces, linear transformations, rational and Jordan canonical forms. Finite fields, field extensions, and Galois theory leading to the insolvability of quintic equations. Prerequisite: MATH 3551.
Notes
Prereqs enforced by the system: MATH 3551; Open to Degree and PACE students
Section Description
Rings and their modules. Core topics include foundational definitions, ideals and quotients of rings, PIDs and UFDs and polynomial rings, failure of the UFD property for number rings. The fundamental theorem of finitely generated modules over a PID. Time permitting, we will discuss fields and their Galois groups, concluding with a proof that there is a fifth degree polynomial which cannot be solved by an equation using rational numbers, sums, products, and roots. Course goals and objectives include: 1. Proof-based understanding of number systems. Ability to write and understand algebraic proofs. 2. Understand the subtleties in number theory for the integers and more intricate 'rings of integers'. 3. Understand the connection between polynomials, field theory, and group theory.
Section Expectation
No required attendance, but strongly recommend daily attendance.
Evaluation
One midterm exam, one final exam, 10-12 weekly homework assignments.
Important Dates
Note: These dates may change before registration begins.
Note: These dates may not be accurate for select courses during the Summer Session.
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Interest Form
MATH 3555 A is closed to new enrollment.
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