In EE, however, it shows as http://www.university.edu/financialaid/index.php/contact
How do I get just http://www.university.edu/financialaid/contact ???
If I understand your setting correctly, the directory /financialaid/ would be given by administration and you want EE not to handle all content of all departments but (in this case) just for the financial aids?
In your (perhaps simplified) example, it would be more or less easy to setup EE in the document root, serving the content for all departments: every department would get its own template group, contact would be one template in the template group financialaid. That would result in http://domain/index.php/financialaid/contact ... and removing the index.php would give you the result you sketched.
However, that would need at least control over the web document root, if not all departments would be switched to EE.
In addition, your example of a typical EE URL is a bit reduced:
index.php/contact would most likely really be index.php/contact/index where contact is the template group and index the replacement for the missing template. Most URLs in EE have the form
(domain)/index.php/templategroup/template/url_title/additional/segments/following
Of course, most of this is optional (most of the time). While you have full control about the templategroup/template part and can specify the url_title for single entry pages, some additional segments will be used by EE automatically in some circumstances (for example when using pagination).
You now would have to think about your URLs and how they best fit into an EE structure.
In addition to removing index.php, outside of EE you can use .htaccess to rewrite the URLs even further. Again, you would have to make sure they will end in a structure that fits into EEs sceme. You could - for example - rewrite
(domain)/financialaid/contact
to
(domain)/financialaid/index.php/financialaid/contact (calling the templategroup financialaid of an EE installation inside the directory financialaid and there the template contact)
or even
(domain)/financialaid/index.php/financialaid/static/contact (calling the templategroup financialaid of an EE installation inside the directory financialaid and there the template static serving an entry named contact)
The possibilities using mod rewrite are endless, however the usage isn’t always easy. Its a feature of the Apache web server, so things might be different on IIS.
So, while I’d agree with Lisa, in case it is really needed, clever naming of templategroups, templates and entries (URL titles) together with .htaccess/rewrite would be the way to go.
-Markus