Man. Java for math. What a bad idea: loads of developper time typing and casting stuff, less than extraordinary performance. Assuming you don't asbolutely have to use Java (i.e., it's not because he wants you to add some function to some framework): What's most important between performance and programming time? Are you going to be reprogramming an testing prototypes very often? If so, I'd go with python + LINPACK (etc.) bindings.
http://directory.google.com/Top/Computers/Programming/Languages/Python/Modules/Math_and_Calculations/has a lot of nice links.
If you're going for raw speed (at the expense of development speed), Fortran is pretty good for bottlenecks, but you'll probably have to use a commercial compiler if you want to have F90 (i think GCC's F90 frontend is coming along, and Intel might have a free version of their own). I believe the Boost library for C++ has some nice stuff (mostly matrix operations, though).
Of course, I can't let this pass without mentioning Common Lisp, which would let you develop rather quickly, and then add the declarations to make it go faster. There are several math packages and bindings for CL, since it's been used a lot for scientific computation. SBCL and CMUCL are both Free, optimising, implementations for *nix. Under windows, I've been told that GCL (Free, compiles to C) is pretty good. There are also several demo versions of commercial environments for Win32, all crippled in a different manner (memory usage, time limit, etc).
Whichever you choose, I'd first go with a nice book. "Dive Into Python" has received great reviews, and there should be tons of C++ books at your institution's library (don't get one of those Learn in 24h or for dummies books, though). I don't know shit about Fortran, so you'll have to ask someone else. Finally, for Common Lisp, I'd recommend two books which happen to be available free on the net:
http://www-2.cs.cmu.edu/~dst/LispBook/index.html (Common Lisp: A Gentle Introduction to Symbolic Computation, David S. Touretzky, can probably also be found at your library), and
http://www.gigamonkeys.com/book/ (Practical Common Lisp - more down to earth, assumes more programming knowledge, iirc. Not on bookshelves yet.)
