SYLLABUS
Course outline
A tentative schedule and list of planned topics is available here.
Text Book
There is no required text; lecture notes will be provided. We may make reference to material in the following books and online resources (others may be added as we go along). Additional readings relevant to particular lectures will be posted on the Lectures page.
Algebraic curves: an introduction to algebraic geometry, William Fulton.
Elliptic curves, J.S. Milne.
A course in arithmetic, Jean-Pierre Serre.
Basic algebraic geometry I: varieties in projective space, 3rd edition, Igor Shafarevich.
Algebraic function fields and codes, 2nd edition, Henning Stichtenoth.
The Arithmetic of Elliptic Curves, 2nd edition, Joseph H. Silverman. (errata)
Lectures
All classes will be online because of the pandemic. As a consequence of this format, I will aim to have our meetings be more discussion oriented than a standard lecture. In order to facilitate this, you should read each meeting's reading (listed on the lectures page) and respond in the Zulip stream for that leacture before the start of class. This response can be a question, a remark about something that you found interesting, or a query about where to learn more about something.
Software
Some of the theorems presented in lecture will be demonstrated using the Sage computer algebra system and some of the problem sets will use Sage. You can install Sage on your computer or use it online using CoCalc. Other computer algebra packages such as Magma, Maple, Matlab, and Mathematica are also available to those who wish to use them.
Problem Sets
There will be weekly problem sets.
Problem sets are to be typeset using latex and submitted electronically in pdf format. Collaboration is permitted/encouraged, but you should first attempt to solve the problems on your own, and in any case, you must write up your own solutions. Any collaborators should be identified, as well as any resources you consulted that are not listed above or on the lectures page.
Grading
95% of your grade will be determined by your average problem set score, after dropping your lowest score. There are no exams and no final. The remaining 5% will be determined by participation in the class discussions (on Zulip and on Zoom).
Student Support
If you are dealing with a personal or medical issue that may affect your participation in any MIT class, please discuss it with Student Support Services (S3) at 617-253-4861. They have a Dean on Call 5pm-9am weekdays and 24 hours on weekends at 617-253-1212 or 100 from campus phones. We cannot excuse you from coursework without support from S3.
If you may require disability accommodations, please speak early in the semester with Associate Dean Kathleen Monagle at 617-253-1473 and then let me know so that we can work together to get your accommodation logistics in place.
