COURSE SCHEDULE

Nonlinear algebra

The following schedule is tentative; it will be updated each week in case we change pace during any topics. You are expected to cover (at least at a high level) the assigned readings before coming to the lecture. This will help you follow the course and organize your notes. In the reading schedule below, "CLO" refers to Cox, Little and O'Shea, Ideals, Varieties and Algorithms.

Homework problem sets are naturally related to the material covered in the course; hence, homework numbers are listed next to the corresponding topic.

  • Homework assignments will be posted at least one week before the due date.

  • It is your responsibility to check the course assignments by logging into the course Campuswire page, which will link you directly to the Google Classroom page where you can obtain and submit work.

  • You are expected to start working on the homework sets early (not the day they are due or right before). It is extremely difficult to answer last-minute homework questions; particularly if you have not been participating in the Campuswire discussion beforehand.

... "and how do I figure out when to do what??"

Help with writing up assignments

To improve your mathematical writing quickly, start by writing draft solutions to homework early. A day or two later after you have had time to forget what you wrote, read it. If it doesn’t make sense or convince you, rewrite it. Writing a solution requires saying what you mean and meaning what you say. Be intellectually honest. Intellectual dishonesty includes: 1) stating a “reason” without understanding its relevance. 2) Claiming a conclusion when you know you haven’t proved it. 3) Giving an example and claiming you have proved the statement for all instances.

(This text borrowed from Prof. Kaul)

Help @MathCenter

Mathematics graduate students who are TAs hold office hours in our department's Virtual Math Center; check out the Virtual Math Tutoring Center here.
Any TA can help with any course they have some knowledge about, when they are not busy with students in their assigned courses. Make sure you use this great resource!

Software help

If you decide to use Macaulay2, you might want to consult a chapter by Bernd Sturmfels from a book on Macaulay2. Information on how to use Mathematica/Maple for computations with Gröbner bases may be found in Appendix C of the textbook. (Note: Maple packages tend to be rather slow in comparison with a dedicated system such as Macaulay2.

Help with typing math: TeX, etc.

You are encouraged to type your assignments. You can access LaTeX in the computer labs; more information and help can be found on this departmental page. Note: for Macs, I recommend TeXShop. You can also simply use Overleaf.

You might also consider using the what-you-see-is-what-you-get text editor TeXmacs; it makes it unnecessary for you to learn the LaTeX typesetting language while producing output of comparable quality. The program is freely downloadable, available for various platforms, able to import and export LaTeX files, and offers a plugin for Macaulay 2.