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An Introduction to the Arithmetic of Elliptic Curves

Welcome to the course website (in progress) for the advanced course on elliptic curves at Ross/Ohio 2026. This course is intended as an introduction to the beautiful arithmetic and geometry of elliptic curves for second-year students (i.e. peer mentors) and counselors at Ross.1

Basic information:
  • Instructor: Dhruv Goel [dhruvgoel@princeton.edu]
  • Meeting Times and Locations: See the Ross Calendar for updated times and locations.
  • Topics Covered: The course topics will be adjusted based on the backgrounds and interests of the participants. A tentative list of topics can be found below.
  • Texts/References: I will type up my own lecture notes. For other references, see the section below.
  • Prerequisites: TBD2
  • Assignments and Collaboration Policy: There are no formal assignments, although I will produce weekly exercise sheets. You do not need to turn in solutions, but you are welcome to discuss your solutions with me as well. You are highly encouraged to read the lecture notes carefully and to attempt each problem in the exercise sheets by yourself, having done which, collaboration and discussion with your peers is highly welcome and encouraged.
Elliptic Curve

1. This course is NOT for first-year students at Ross, and first-year students are generally not encouraged to take this course; if you are a first-year student who really wants to sit in, let me and your counselor know and we can discuss your specific situation.↩
2. If you would like to come to this course but are unsure about whether you have enough background, you probably do. Even if you don't, I believe that you will certainly gain something from coming to the lectures, even if you don't understand them fully. You are also welcome to write to me to discuss this.↩

Topics Covered

The current (tentative, possibly slightly ambitious) list of topics I plan to talk about is:
  1. TBD

Lecture Notes

Lecture notes will be updated after the corresponding lecture. Here is the full file (including exercises) [TBD], last updated on [TBD]. Here are the notes sorted by lecture:
  • Lecture 1; posted on [TBD]; introduction

Exercise Sheets

There will be six of these; one for each week. The exercise sheet for a week will be posted at the beginning of that week, so you can start engaging with the problems as soon as possible. Here are the exercise sheets:
  • Exercise Sheet 1; posted on [TBD]

Textbooks and References

Some other useful references at a level similar to that of this course are
  1. [TBD]
If you need assistance in accessing any of these references, please do not hesitate to reach out to me.