ca47, this is custom code modification.
I guess that all students have email addresses in studentname@universityname.com format? (like jane@auca.com, bill@auca.com, bob@auca.com).Where the part after @ is always one and the same for all addresses?
If this is the case you can just add a new check/validator to the "Email" field, so that only emails that end with @auca.com, for example, will be able to register. All other emails will result in "Incorrect email format" error.
Search for "email pattern", "email validation php" or "regular expressions for email validation" keywords in google to find the solution.