I'm an undergraduate studying materials science and engineering with a concentration in polymer science. I would like to go to graduate school and focus on theory and computation of synthetic polymer and biopolymer systems. So I'm planning of studying things such as Hamiltonian mechanics, statistical mechanics, molecular dynamics and monte carlo simulations.
I feel like college doesn't teach math that good. I want to study more topics and go over topics I studied in classes before and hopefully build my mathematical intuition. The areas I was thinking about were: single and multivariable calculus, linear algebra, ODEs and PDEs and statistics and probability. I also saw that some researchers use topology and graph theory to study protein structures. Are there any other areas I should include?
Besides what area to study, my other question is which books to study in a particular area? I took Courant's book "Introduction to Calculus and Analysis" out of the library today. I'm trying to find the "best" or most recommended books because I would like to go through all the topics this summer, thus I don't have a ton of time. Good thing is a lot of it will be things I already know but just analyzed in more detail.
Would I be better off reading textbooks or doing MIT OpenCourseWare courses? I appreciate any responses or recommendations.