Teaching
Mathematics is often portrayed as something static, where the ideas and results from the distant past are repeated along the generations until it is our turn to learn them. I think this perception is still being reinforced (intentionally and unintentionally), and it hinders both the teaching and the learning of mathematics.
In my lectures I like to provide context and background for the material being covered, and I give students the space to question definitions and proofs. Having a narrative for what is being learned is essential, not just for the initial motivation, but in order to remain engaged with the material.
Mathematics can be a frustrating subject, because sometimes in order to learn something it is not enough to just learn how the textbook solves the problem, you also need to figure out (usually by yourself) whether other methods would also work. We have all experienced the feeling of thinking we have solved a problem only to later realize we made a mistake. This can be a trying experience, yet it is one of the most important ones. Revisiting the material while trying out new proofs is something mathematicians do all the time.
The math that I know is only as good as the math I can explain to others.
Some of my teaching experience
Fall 2023: University of Leeds
Co-instructor of Calculus in the Complex Plane.March 2023: Arizona Winter School on Unlikely Intersections.
Project assistant.Spring 2023: University of Leeds.
Instructor of graduate course on o-minimal complex analysis.Fall 2022: Preliminary Arizona Winter School
Teaching assistant.July 2022: MSRI Summer School.
Teaching assistant for "Algebraic Theory of Differential and Difference Equations, Model Theory and their Applications".2019–2022: Unit 18 Lecturer, UC Berkeley.
Instructor for Introduction to Abstract Algebra, Introduction to Analysis and Introduction to Complex Analysis.2018–2019: Lectureship in mathematics, Corpus Christi College, University of Oxford.
Tutor for first and second year analysis courses.2015–2018: University of Oxford
Tutor and teaching assistant.2010–2015: Pontificia Universidad Católica de Chile
Teaching assistant.
Teaching Material
I have written various notes to help with my teaching. I still revise them from time to time, so in that sense they are not finished, but they are complete enough that I (and others) have used them to teach.
Introduction to Analysis, (version February 2023)
Introduction to Abstract Algebra, (version February 2023)
Introduction to Complex Analysis, (version November 2023)