We are all in this together!!
... As a mathematician, one thing I've learned to use while brainstorming on a problem is the hive-mind. :) So, if you ever feel completely stuck on a problem, try to rely on the collective wisdom! You are not alone. It is extremely common to get `stuck' when thinking about a new concept (such as an algebraic variety!?) - so, ask your classmates, not only your professor! Visit the course Campuswire page to throw out a half-baked idea, start an example and pose a question `now what?'. Let yourself be surprised by how creative you are, as a collective!
Afraid? Shy? Unsure? No problem: you may post questions anonymously!
Inspired? Motivated? Post an answer to someone else's question! (And earn participation points while doing it.)
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)
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!
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 can also simply use Overleaf, an online editor; free templates are easily available.
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.