Aleksander Horawa
Current courses
In Summer 2026, I'm teaching Algebraic Number Theory.
Come to the class to learn how to learn what these pictures mean and how to make them. Or make your own pictures of spectra of number rings using Havard Damm-Johnsen's software drawspec.
This is the splitting field of x^7 - 41.
Summer research
In Summer 2025 (together with Andrew Graham) I supervised an undergraduate research project for Pedro Lack and Zhiyi Luo. Keep your eyes out for their forthcoming paper on Beilinson's conjecture for the universal family of elliptic curves over the modular curve X(4).
Master's students
I'm currently supervising Andrea Robustelli Della Cuna at the University of Bonn.
Previously, I supervised the following master's students at the University of Oxford:
- Lewis Bushen, Torsion in Elliptic Curves, 2023/24.
- Ewan Neumann, Torsion in Abelian Varieties with CM, 2023/24.
- Allan Perez, Torsion in Elliptic Curves, 2023/24.
- Vincent Wellerschoff, Langlands--Tunnell and the Modularity Theorem, 2023/24.
- Tamara Istrate, The Congruent Number Problem, 2022/23.
- Julie Tavernier, The Route to Fermat's Last Theorem, 2022/23.
- Max Mackie, The Congruent Number Problem, 2022/23.
- Gavin Bala, Modular Forms and Elliptic Curves, 2022/23.
Past courses
In Bonn, I taught the following classes:
- Winter 2025/26: Assistant for Algebraic Geometry I (Gebhard Martin).
- Winter 2025/26: Assistant for Representation Theory (Tasho Kaletha).
At Oxford, I taught for the following classes:
- Hilary 2024: tutor for M1 (Linear Algebra II), Merton College.
- Michaelmas 2022: tutor for B3.1 (Galois theory), Intercollegiate class.
At Michigan, I taught the following classes:
- Spring 2022: Math 115 (Calculus 1), Section 101,
- Fall 2020: Math 115 (Calculus 1), Section 037,
- Spring 2020: Math 115 (Calculus 1), Section 105,
- Fall 2019: Graduate Student Mentor (helping coordinators and instructors),
- Winter 2019: Math 116 (Calculus 2), Section 090,
- Fall 2018: Math 115 (Calculus 1), Section 038,
- Winter 2018: Math 115 (Calculus 1), course coordinator,
- Fall 2017: Math 115 (Calculus 1), Section 064,
- Winter 2017: Math 115 (Calculus 1), Section 083,
- Fall 2016: Math 105 (Pre-calculus), Section 024.
In 2021, I received the Department of Mathematics Outstanding Teaching Award.
Previously, I was awarded an Honored Instructor award in Winter 2019.
I was part of the organizing committee of the Directed Reading Program at the University of Michigan.
Check out the website for the newest updates.
I mentored the following students as part of the program:
- Rajas Gupta, The Riemann Hypothesis, Winter 2021.
- Yuqing Liu, Primes of the form x^2 + ny^2, Winter 2020.
- John Haviland, Algebraic curves, Fall 2019.
- Robert Larase, Elliptic curves and cryptography, Winter 2019.
Desmos graphs and other illustrations
These are some illustrations of mathematical concepts (some I made myself, some I found online). Press on "edit graph on Desmos" to see the full, interactive animations.
Area in Polar coordinates
Parametric equations
Taylor Series Approximations
Right Riemann Sums
