I am on a school computer (Ubuntu Lucid Lynx) and I would like to run some code that has dependencies on certain libraries. I would like to install those libraries into my user account using apt instead of having to compile them source, as I don't want to deal with dependency hell. Is this possible?
The next best thing you can do is to download the packages manually, then use is
dpkg-deb -x to extract their contents to your home directory. Obviously, there won't be any automatic dependency resolution, and you'll have to use
$LD_LIBRARY_PATH or other tricks to make things work with non-standard paths.
You could be sneaky and set up a private RPM repository, but that's more trouble than it's worth and probably easier to add another system to the network, get permission, or have a virtual machine set up for you with a few additional privileges granted. Make friends with an authorized admin, being up front, and maybe they can open other doors for you.