The Axioms of Teaching:
I believe in Federico Ardilla's four axioms of mathematics education, which I use to guide my teaching and interaction with students:
Mathematical potential is distributed equally amongst groups, irrespective of geographic, demographic, and economic boundaries.
Everyone can have joyful, meaningful, and empowering mathematical experiences.
Mathematics is a powerful, malleable tool that can be shaped and used differently by various communities to serve their needs.
Every student deserves to be treated with dignity and respect.
Teaching experience:
Teaching and helping others with mathematics is one of my favorite activities I am involved in Dartmouth's math department as a teaching assistant and mentor for the directed reading program (Directed Reading Program). My experience is outlined below, split between my roles and their chronological order:
As undergraduate TA (Roles: grading homework, holding weekly office hours, proctoring exams, holding midterm and final exam review sessions):
Fall 2025: Math 101, Linear and Multilinear Algebra (under Asher Auel): Math 101: Linear and Multilinear Algebra
Alongside my usual roles, I also held 10 class sessions in the X-hour (Dartmouth's version of discussion section). In these sessions, I taught a mini-course on category theory, roughly following Riehl's Category Theory in Context and MacLane's Categories for the Working Mathematician. My notes have been compiled and posted in the research/notes tab!
Spring 2025: Math 19, Introduction to Set Theory (under Sarah Frei): Math 19: Introduction to Set Theory
Winter 2025: Math 81/111, Abstract Algebra (Field and Galois Theory, under Asher Auel): Abstract Algebra Math 81/111 Winter 2025
Fall 2024: Math 71, Algebra (Group and Ring Theory, under Sarah Frei): Math 71: Algebra
Spring 2024: Math 24, Linear Algebra (under Shiang Tang): Math 24, Spring 2024
As Mathematics Department DRP Mentor (Roles: meeting with students weekly to lecture about, discuss, and tailor reading, writing problem sets for students, advising end-of-term presentation on learning):
Projects in the current term can be found at Directed Reading Program: Projects, projects previously mentored can be found at Directed Reading Program: Past Projects
Winter 2026 (current): "Galois Cohomology"
Students: Frank Gallo (third year undergraduate), Michael Kalinichenko (third year undergraduate), Sair Shaikh (fourth year undergraduate), Aidan Hennessey (first year PhD), Semir Mujevic (first year PhD)
Syllabus to be written.
Notes will be posted in my notes tab once the program has concluded!
Winter 2025: "Category Theory and Further Mathematical Abstraction"
Student: Liam Nokes (fourth year undergraduate)
Miscellaneous:
Summer 2025: Homological Algebra
Students: Ribhu Hooja and Frank Gallo (third-year undergraduates)
Structure: Meeting twice per week for a one-hour lecture with biweekly problem sets. Syllabus available here