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
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.