I am literally flabbergasted with the amount of scientific software packages available nowadays for Python.

Dealing with vectors/matrices, linear algebra, signal analysis? Use SciPy. Introduction here. Just have a look at how many different modules it has.

Need to plot that data? in a LaTeX friendly format? Use Matplotlib. Introduction here

Symbolic math? No problem, use Sympy. Introduction here

3D computer graphics? VTK plus its Python bindings will do the job.

Image processing: The Python Imaging Library + SciPy's ndimage module will fit the bill. ndimage has even stuff like watershed transform, and mathematical morphology operations!

Machine learning/data mining: pyML (mostly SVM), pybrain, pyevolve (genetic algorithms), and Orange (data mining).

Natural language processing: NLTK. Also, a plethora of parsing tools.

Hell, I even made a typo in google, and found a library for simulations! simpy.

Most of these can also be easily used from the Python prompt, but you should use IPython whenever you want to play with any of the libraries mentioned above. The same recommendation applies for any scenario where you want to use the Python prompt; features provided by IPython like reloading a .py file without restarting the Python prompt, defining ad-hoc reusable scripts by merely enumerating previous commands, or firing up the debugger whenever you get an exception, from the place that provoked it are simply amazing.

One can only wish to have enough time and a proper excuse to play with all this stuff.

(Jeez, what a dork! I'll pretend not knowing you in a party if you feel too embarrassed :P )