In Spring Semester 2025, I taught a graduate topics course on Algorithmic 3-manifold topology at Oklahoma State University. My students typeset some lecture notes (last updated 15 January 2026), which I am making available here as a hopefully useful resource.
These lecture notes build up the theory of crushing normal surfaces, and use this theory to give algorithms for unknot recognition, connected sum decomposition, and 3-sphere recognition. To my knowledge, these notes are the only place one can find all of this material synthesised in a single document.
The notes are currently a bit rough. In future, they will hopefully be cleaned up into a more presentable form.
Science Dalyell Individual Research Project, Semester 2, 2026: Co-supervision of semester-long undergraduate research project
Oklahoma State University, Spring Semester 2025: I taught one section of Calculus III (MATH 2163), plus the aforementioned graduate topics course on Algorithmic 3-manifold topology.
Oklahoma State University, Fall Semester 2024: I taught two sections of Calculus III (MATH 2163).
I have been a tutor (i.e., a teaching assistant) for the following courses at UQ:
Semester 1, 2024: MATH1071 (Advanced Calculus and Linear Algebra I, internal)
Semester 1, 2023: MATH1071 (Advanced Calculus and Linear Algebra I, internal); MATH2301 (Linear & Abstract Algebra & Number Theory, internal)
Semester 2, 2022: MATH2302 (Discrete Mathematics II, internal); MATH7861 (Discrete Mathematics, external)
Semester 1, 2022: MATH2301 (Linear & Abstract Algebra & Number Theory, external); MATH3302 (Coding & Cryptography, internal)
Semester 2, 2021: MATH1061/7861 (Discrete Mathematics, external)
Semester 1, 2021: MATH2301 (Linear & Abstract Algebra & Number Theory, both internal and external); MATH3302 (Coding & Cryptography, external)
Semester 2, 2020: MATH1061 (Discrete Mathematics, internal); MATH3306 (Set Theory & Mathematical Logic, both internal and external)
Semester 1, 2020: MATH1061 (Discrete Mathematics); MATH2301 (Linear & Abstract Algebra & Number Theory); MATH2400 (Mathematical Analysis); MATH4303 (Advanced Combinatorics)
Semester 2, 2019: MATH2100 (Applied Mathematical Analysis)
Semester 1, 2019: MATH1050 (Mathematical Foundations)
The Queensland Mathematics Summer School (QMSS) is a multi-day enrichment programme for Queensland students in Year 11. This summer school has been held annually since 2018, usually in January. The programme typically revolves around a series of lectures and tutorials, with the aim of exposing the students to concepts and challenges that are quite different from those encountered in school. The rest of the time is filled by an assortment of workshops and activities.
I was involved in the first seven editions of QMSS, from 2018 until 2024. My main role in the first five editions (from 2018 to 2022) was as a tutor. I have also presented workshops and lectures at various editions of QMSS, as detailed below.
In the 2018 and 2020 editions of QMSS, the schedule included a 1-hour workshop that remained unfilled until a couple of days before the workshop was supposed to run. As a result, I ended up running semi-impromptu workshops on the following topics:
2018: Non-Euclidean geometry
2020: Distinct distances problem
In 2022, 2023 and 2024, I presented the main lecture series for QMSS.
2022: An abridged, 3-lecture version of Ben Burton's course on Machines and Mathematics, which discusses finite automata and regular expressions.
2023: A 4-lecture version of the course on Machines and Mathematics.
2024: A 3-lecture version of the course on Machines and Mathematics.