You can use the Raspberry Pi as you would use any other Linux-running computer, notably the PC.
The main difference between a PC and the RPi is that PCs run on x86 or x86_64 (AMD64) architectures, and the RPi uses a ARMv6 processor.
So if you have a pre-compiled application for the PC, you will have to try to emulate a PC somehow on the Pi to try to make it work. And this is far from being simple, not to mention efficient. You will not have commercial scientific applications like Mathematica, MatLab, LabView with versions compatible, for example. On the other hand, you have open source alternatives that are pre-compiled for the Raspberry Pi and can be installed with a simple command like GNU R, GNU Octave, SciLab and other great software.
A special mention to Python, as I can presume by your tag on the question: being an interpreted language and working perfectly on the Raspberry Pi, you should be able to run your python-programs without any change.
Also if you have the source code, you most likely just need to compile it on the RPi, or Cross-Compile it on the PC targeting the ARMv6 architecture, to have it running, just as you would on the PC.
Resouces of the RPi are, obviously, very limited comparing to what you have on a PC, in every term conceivable.