To start with, see
http://www.tex.ac.uk/cgi-bin/texfaq2html?label=filesusedUse the \listfiles command to produce a list of all the packages you are using on both systems and compare them. It should show you what versions they are.
At a wild guess, your school package versions may be out of date. But if LaTeX can read them, you can certainly look at them: examine the log file and you will see each package listed with the full filename as it is loaded. You can open these in Kile and look at the top few lines where the version number is given.
What you can't do at school, of course, is change the actual installed files: you need to email your system administrators and ask them to update the version of TeX they are using.
In the meantime, you can install your own updated versions of any package you want, in your own private TeX directory tree (path) at ~/texmf (that is, a subdirectory called texmf in your
main login directory (
not in ~/Documents or wherever it is you put your files).
Check that at least one of the local symbols $TEXMFLOCAL or $TEXMFHOME includes your private path by typing the two commands in a shell window:
$ kpsewhich --expand-var '$LOCALTEXMF'
$ kpsewhich --expand-var '$TEXMFHOME'
If one or other of them includes ~/texmf (in full, perhaps /home/yourname/texmf), then create the subdirectory path in it to the right directory name
for each updated package you want to install, download the fresh package from CTAN, and install it there.
For example, if you find that (mythical example) package foobar is out of date, create the directory following the example of the path used for the existing (system) version shown in your log file:
$ mkdir -p ~/texmf/tex/latex/foobarChange to that directory and download foobar.dtx and foobar.ins from CTAN:
$ cd ~/texmf/tex/latex/foobar
$ wget http://www.ctan.org/tex-archive/macros/latex/contrib/snapshot/foobar.dtx
$ wget http://www.ctan.org/tex-archive/macros/latex/contrib/snapshot/foobar.ins
Install the package:
$ latex foobar.ins$ pdflatex foobar.dtx; pdflatex foobar.dtx
That will create foobar.sty (the package file, and maybe others), and foobar.pdf (documentation).
You don't need to run texhash on a private tree, although you can if you wish: LaTeX should look in there first,
before it tries to use any other version of a package. You can test that by reprocessing your document and checking the versions used in the log file as before.
If all else fails, as an extreme solution, you can always put new .sty files in the same directory as your .tex documents. LaTeX always looks there first before anywhere else.
///Peter