You mean something more than the registration you have in a vanilla WordPress install. Registration Plus is a plugin that you might look at.
Might need to give users FTP access to upload files if you don’t want then writing posts.
hardinal,
Do the students need access to the PDF after it’s uploaded, or are they just sending it to you through the website? If you need them to just upload a PDF, I recommend the cforms plugin (http://wordpress.org/extend/plugins/cforms/). With this plugin, you can create an upload form that records students’ names, email addresses, and allows for PDF uploads. It will store the PDFs on WP and also email them to you.
If this isn’t what you’re looking for, could you please provide some more information about exactly what you’re trying to do? Maybe explain the process a student will go through in the registration and upload setups.