I am an undergraduate mathematics student in my third year. Most undergrad programs don't completely prepare you for grad school. I know Ph.D. students are telling me that there is a lot of crucial material that got left out. Here are the subjects I have or plan to study:

Calc sequence and Analysis 1 & 2

Abstract Algebra



Linear alg.

Number theory


Mathematical logic

Calculus on Manifolds

Set theory (I will study separate from M. Logic)

I want to be ready for grad school simply because I struggle with depression and it will take a lot of load off if I can prepare somewhat ahead of time. Which other courses or texts would you recommend to have a solid foundation for grad school? Is learning Mathematica or similar languages a considerable advantage also in grad school?

I would ask faculty but they are always busy and there are two advisors really one of which doesn't have a background in math and the second is a bit of a curmudgeon in the department. Thanks if you can help.