Email:
migliore.1@nd.edu
Office hours: (Will be conducted in the zoom classroom until furthermore notice, maybe all semester.) For as long as it remains tenable, I will respond quickly to emails for help whenever you need it (unless it's late at night), and we will switch to zoom if further help is needed.
Time and place of class: MWF 11:40 AM - 12:30 PM, DeBartolo 126.
Textbook: Ideals, varieties and algorithms, 4th Edition by David Cox, John Little and Donal O'Shea, Springer-Verlag.
You already know the drill, but the most important thing is that in this class, as elsewhere on campus, students must comply with all University health and safety protocols. They will not be repeated here. Stay safe!!
At least two of you will not be attending in person, and others might follow suit because of quarantine. As a result, all of my lectures will be recorded on zoom. The notes from each class (pdf) will be posted the same day on my webpage, as will the video of the lecture. The links are below.
Having said that, attending in person is more fun and more conducive to learning. I hope and expect that you will always come in person unless you absolutely have to be there remotely.
Use this link to get to the ZOOM CLASSROOM: https://notredame.zoom.us/j/95544918937. (You can click on it to get there.)
The name of the meeting is SP21-MATH-40510-01 .
Here are the notes from all of the lectures this semester. After every class I'll post that day's lecture. Until then the links will not work.
Here are the videos of the lectures for the semester. After every class I'll post that day's lecture. Obviously I won't post them before the lecture since they won't exist until then!
Here are the links to this semester's problem set, which I will be adding to on a daily basis. It's not in final form until I say it is!! (Make sure you always have the current version!) The links will be made active over the course of the semester.
Here are the problem sets from the last time I taught this class (Spring 2020) as a useful source of study material.
Here is a practice final exam. The solutions are not written up, but please email me with any questions.
Course overview: Algebraic Geometry is the study of systems of polynomial equations and their vanishing loci. This field has important components that lie in the realm of geometry, of algebra and of computation (among others) and countless applications. This course tries to give a flavor of these different aspects of the field and how they fit together. Indeed, much of the fascination of this subject comes from the myriad ways in which arguments squarely in one realm give surprising consequences that fall squarely in a different realm.
Commutative Algebra is a closely related field. This course will also be an introduction to Commutative Algebra, with an emphasis on the interplay between the two fields. We will review the basic notions from algebra (e.g. polynomial rings, ideals, quotient rings), and we will discuss the corresponding geometric objects. Gradually we will build up a Geometry-Algebra dictionary.
Here are some books that might be useful as supplemental reading. Out of courtesy to your classmates, please do not take these out for more than a few days. By far the most important reference is your textbook, but these offer interesting side reading.
Examinations, homework and grades. There will be three problem sets and a final exam. The problem sets can be accessed above. They will be updated regularly. I will let you know when the current version is in final form. Do not assume that the version you see now is in final form before I say that it is!!!
Homework and Reading: There will not be any homework assigned apart from the problem sets. In my lectures I will try to follow the material in the textbooks, although not all of it and not necessarily in the order in which it is presented there. There may also be some additional material not in the books. The problem sets will be based primarily on class lectures, but possibly also from the material in the chapters. Thus it is important to read the material as well as following the lectures.
Honor Code: Both the final exam and the problem sets are conducted under the Notre Dame Honor Code. On the first day of class I will give you a handout and I will give you very clear explanations of what is expected of you in the course and how the Honor Code applies to your work. This is important information, and if for some reason you are not in class on the first day, be sure to talk to me about it!! As always, you are strongly encouraged to come talk to me at any time if you are having any problems with anything.