What connection does this person have with the university?
Have you done business with this person in the past and how did this person know about you?
This deal is not a normal deal and there are deficiencies in it that work against you.
Have you asked the person or the university how they intend to use the product that you are providing for them? Is it going to be used as a television commercial to attract new students or a video that is posted on their website? Maybe you could suggest that they allow you to include a mention at the end of the video that shows "Video Prepared by Your Company Name" that might lead to future business to you from viewers who like the video?
Ask them to provide the names of at least 2 business references of companies they have done business with in the past and then ask if payment was prompt or on time and is there any reasons for dissatisfaction when dealing with this institution?
Is being paid one-half upfront going to bel enough to pay for materials/supplies you have already used and also be enough for you to profit on your labor (just in case they decide to not pay the other half), or shouldn't you be asking for 3/4ths of an upfront payment? That stipulation about an upfront payment should actually be in the contract and not be part of a later communication that appears to be outside of the contract.
There is no way you should be waiting 30 days to receive final payment for your work. If this is a large university they should be able to be financially stable enough to pay you within 3 days of your delivering the final product to them and that is what you should also stipulate in the contract.
Bottom line is that to protect your own financial interest and other concerns, you should be consulting with your business law attorney to negotiate this contract to a successful resolution.