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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.

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Do read Apostol's calculus books , both volumes . They are probably one of the best calculus book available . They include almost all topics in details and with rigour and applications , you've listed . Just go for those 2 books by TMA , you won't need any other math book . For graph theory , you can pick up Diestel , it is available for free on internet .

And you can never know all the math , you'll require for these topics. Just read these books and work out their exercises . And then if you need to learn anything else , then you will have to pick it up along the way from internet or buy another book . I don't think , any one can give you a complete list of all the math books you should read . However , I am sure after Apostol's books , you are good to go . They will teach linear algebra, calculus,vector calculus and differential equations and probability and statistics as well , also you get an introduction to modern mathematics .

You will have to balance between both MIT OCW and books , like there is a separate OCW course called advanced calculus available that specifically uses apostol's books . You can do that , Nothing is ever learnt in all depth from just a single source .

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Thanks a lot for your response. I looked at the synopsis of both volumes of Apostol's books on Amazon. They seem like they cover many areas of math which is a good thing. –  user1772959 May 24 '13 at 4:54
    
FYI: You can buy international editions of Apostol for FAR cheaper than the hardback original prints. Check abebooks. I likewise greatly recommend his two volumes. –  5space May 24 '13 at 4:56
    
Continuation of last comment after I hit enter by accident...I guess I would say my goal is just to learn a lot of different kinds of math and build intuition so I can apply certain mathematical techniques or ideas to soft matter systems. There is so much information out there that I will never be able to know it all, but being exposed to many things seems to be what learning really is. Being able to think about a problem from many different perspectives and link ideas. Thanks again. –  user1772959 May 24 '13 at 5:01

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