Math Software
depends on how far into numerical science/simulations science you want to go...
maple/matlab/mathematica all are good depending on the type of syntax you want to be bothered with. In cdn matlab/maple are more dominate for undergrads i think...matlab is beautiful i think because its syntax is easier but if you can write scripts for maple that'd be cool to. Personally i prefer matlab because it was more dominate with teh simulations people at MAC.
Maple was more for people who didn't really code as part of their research.
However applied mathematicians used maple...where as numericals used matlab....
so talk to your profs, because you should decide based on the 4 years you spend at school..industry i hear uses matlab more, but thats based on a friends opinion
however because you doing an undegrad might I suggest learning C/C++ and building the stuff from scratch, since alot of fastperformance simulations are still based in c/C++ and its better to be a person of 2 trades for the same field i think, that is to say applying both math/code to physics(theorist+coder)
look for the books
[0] numerical recipes in C or C++ or fortran and
[1]the COmputational Physics book by Landau,
[2]David Eberly's Code that comes with his 3D graphics book.
[3]Chris Hecker's Code for 3D rigid body Dynamics...its open src i believe
if not your outta luck.
[4]MillionBody book can't remmeber the exact title but there are a whole bunch.
THis way as you go through your undergraduate
you can code the simulatoins alongside/or shortly after learning the concepts...something I regret not doing especially for class/analy mech and astrophysics.
Might I suggest further into looking at the packages STL/SDL/OpenGL to go along with the numerical recipes and eberly
also perhaps pick up gary flake's book, to understand terms about simulations, i rather enjoyed this book but picked it up abit to late when i was in university.
If you want to look for inspirations or set goals...looks towards working for IBM just to use their clusters...the fastest in the world when the IBM "name" did a talk. BlueBrain was one of the projects that interested me.
