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)
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.
Solutions must be typeset using latex and submitted electronically in pdf format. Collaboration is permitted and encouraged, but you should first attempt to solve the problems on your own. In any case, you must write up your own solutions independently. Any collaborators should be identified, as well as any resources you consulted that are not listed above or on the lectures page.
Late work policy:
Any request for late submission must be emailed to shivac@mit.edu 48 hours before submission deadline. If the request is granted, the extension will be for 2 days, except in extraordinary circumstances. A maximum of two late submissions are allowed.
Final Project
There will be a final research project instead of a final or exams. In consultation with the instructor, students will choose a book chapter or research article related to the course. They will write and present an article summarizing (an interesting part of) its contents, pose a research question naturally arising in this work, and then, if time permits, try to answer it. The approximate length should be 5-10 pages, and the intended audience is your peers. Depending on your choice of topic, you may get quite far into this sequence, or the summary itself may comprise the majority of your paper. Project plan/outline due by April 25: Project ideas
Grading
Grades will be based on your performance on the problem sets (80%) and the final project (20%). The lowest score among your problem sets scores will be dropped. (This includes any problem set you did not submit.) There are no exams and no final exam.
Student Support
Student Support Services (S3)
Personal and medical issues can make it hard to focus on academics. If you find that something is getting in the way of your ability to attend class, complete work, or take an exam, you should contact a dean in Student Support Services (S3). The deans will provide you with support and help you work with us to determine next steps. We ask that you go to S3 so we know you have had a chance to talk through your situation with someone and to connect with any resources you might need. You can reach out to a dean you have worked with in the past, join their virtual help queue (https://sicp-s3.mit.edu/queue), or e-mail s3- support@mit.edu.
Disability and Access Services (DAS)
MIT is committed to the principle of equal access and we want all of our students to feel welcome here. Students who need disability accommodations are encouraged to speak with Kathleen Monagle, Associate Dean, prior to or early in the semester so that accommodation requests can be evaluated and addressed in a timely fashion. Even if you are not planning to use accommodations, it is recommended that you meet with DAS staff to familiarize yourself with the services and resources of the office. You may also consult with Disability and Access Services in 5-104 or at 617-253-1674. If you have already been approved for accommodations, please contact me early in the semester so that we can work together to get your accommodation logistics in place.