This page will show how to configure your gmail account to cooperate with your university mail. These instructions should work for any student email account at this university.
Log in to your university email. Click on Settings->Options in the top right corner.
Now click on the organize email tab on the left, and then the inbox rules at the top. Then create a new rule for arriving messages. on the new inbox rule page click the more options link and use the following rules
Now save the rule. This rule will move all messages received from university mail to your gmail folder and redirect the message to your gmail account. You should not need to check this mail account anymore.
Log into your gmail account. Under Settings->Accounts and Import -> Send mail as click on Add another email address you own
Save these settings and you should be able to send mail from your university mail with the dropdown in the gmail compose new message window