In Spring 2025, I taught MATH 8120 at Ohio State, which was a topics course titled "The Arithmetic of Elliptic Curves". This folder contains all of the files I created for this class when I taught it.

Here are some of my reflections on the class.

-I had 11 students enrolled in my class, ranging from first years to fifth years; I also had several students (grad and undergrad) sitting in on the class.

-Despite algebraic geometry (AG) not being a prerequisite for my class, I think the semester went relatively smooth. The textbook I primarily followed (Silverman's "The arithmetic of elliptic curves") is relatively light on AG for a graduate-level introduction to elliptic curves. I could tell some students wanted more, though -- particularly the all-but-dissertation students. To this end, I had created a few difficult HW problems for the more ambitious students to take on.

-I had introductory algebraic number theory (ANT) be a prerequisite for this course since I wanted to discuss local fields, and this topic was listed on the departmental syllabus for ANT. However, the ANT class offered the previous semester did not cover local fields, and so I decided to create several HW problems on basic facts about local fields and asked students to present on them (in the HW problem session). This course definitely needs students to know some basic facts about local fields.

-I think having HW problem presentations each week instead of written HW went relatively well. Students told me they enjoyed the presentations; I also noticed that some graduate students in my class (particularly the earlier ones) got better at presenting throughout the semester, culminating in lots of quality final presentations. I figured that as they are PhD students, having them prepare and give talks is a good idea.

-The HW presentation lengths varied quite a bit; in the first few weeks, each presentation was at most 10 minutes, but as the semester went on, some solutions were presented for almost 30 minutes! If I teach this class again, I would need to cut some problems out, in anticipation of their solutions being too long to present without asking students to cut details. (Maybe I can check in with students about their solutions before their presentation.)