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You can watch the progress during the summer at http://planet.sympy.org/
Introduction
SymPy is going to participate, the same way as in 2007 (see GSoC2007).
Now it's time to get involved in the project - sign up to the SymPy mailinglist, try to fix issues, send patches, simply let us know about yourself.
You don't have to be an expert in Python or other technologies. All we require is that you work on your project as your main job over the summer. If you work hard, we'll help you with everything, e.g. to improve your Python skills and to learn how to work with Mercurial, how to send patches, etc. We also require that you blog at least once a week about what you do.
We hope, that you will continue contributing to SymPy even after the summer ends - this is of course not a requirement, but if we had to choose between two applicants, one delivering excellent results for 2 months and then stops, the other one also working hard during the summer (maybe not being as good as the first one), but staying with SymPy after the summer, we prefer the latter, as this helps SymPy more in the end -- but as said before, this is not a requirement, just our wish (see also Google's goals and the Python Software Foundation's expectations wiki).
We encourage you to read the GSoC 2007 students reports (see the wiki link above) and feel free to ask them directly for their experience - either on the mailinglist, or privately.
Ideas list
On our public wiki: http://wiki.sympy.org/wiki/GSoC2008Ideas
How to apply
On March 24 Google opened applications for students as described on the official timeline, the deadline is April 7. Please apply directly to mentorship organizations, you can apply to anyone you want, last year it was Python Software Foundation, Portland State University and the Space Telescope Science Institute that students were successful at. The applications at each organization will be judged and the best ones will be selected (according to the number of slots that Google assigns to each organization).
Informally however, it's good to get involved with the SymPy project before, so that we can help you write a good application and select a good topic, that fits you and us well (and that has a good chance of succeeding).
Ondřej's note: if you want me to proof read your appliction (recommended:), send it to me before you send it to PSF or other orgs.
Links
Main GSoC2008 site: http://code.google.com/soc/2008/
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Hi, I am intrested to participate in google summer of code in python.As i know python is a powerful language & very intresting language,we can easily implement in mathematics and solve our problem. My email-id:jenaajitkumar718@gmail.com
Excellent, please write to our list what you want to implement and we'll discuss it and help you write a good application.