Mathematical Writing
I occasionally write expository pieces that develop a mathematical topic beyond the scope of my course and teaching notes.
An Introduction to the Dynamics of Compact Group Automorphisms after Klaus Schmidt
Bachelor thesis | Algebraic dynamics
An introduction to algebraic dynamical systems through actions of countable groups on compact metrizable groups. The thesis develops topological transitivity, ergodicity, mixing, and expansiveness before relating algebraic -actions to modules over Laurent polynomial rings.
Modules over Principal Ideal Domains
Expository note | Algebra
An account of the structure theorems for finitely generated modules over principal ideal domains, followed by applications including the Smith normal form, rational canonical form, and Jordan normal form.
On the Irreducibility of Cyclotomic Polynomials
Expository note | Algebra and number theory
A detailed presentation of Landau’s proof that cyclotomic polynomials are irreducible over , using only foundational results from group, ring, and field theory.