MATH 145 - Algebra (Advanced Section)
MATH 145 is an advanced-level version of MATH 135. How the course is taught is flexible and depends on the instructor who is teaching it. In the section I TA'd for, it was more number theoretic, and covered (broadly):
Introduction to rings
Modular arithmetic
Quadratic number domains
Codes and primality tests
Complex numbers
Polynomial Rings
Finite Fields
Below are some documents relating to work I did for the course.
Guest Lecture
I gave a guest lecture on field extensions and properties of finite fields. Because I did the proofs on a separate page on OneNote, the pdf has the proofs awkwardly appended at the end of the document (sorry!)
Supplementary Material
I tried to provide supplementary material which would provide a more ring theoretic perspective to interested students through in-class mini lectures and Piazza posts. These notes summarise some of these lessons.
First Isomorphism Theorem Notes