Hate to be the devil's advocate, ask your professors if they're ok with a project with arduino.
I can't see why there should be an issue, but you are right that the OP should ask. If library usage isn't allowed, an Arduino (the hardware) could still be used, just as an AVR carrier board. You would likely have to use a regular AVR dev tool-chain, though, to satisfy any such requirements of not using external "third-party libraries" (beyond the core libraries in the AVR tool-chain).
Some may not like the idea that you can simply load a library to control servos or else. Made it too easy to do stuff. Don't learn as much etc.
I can understand and sympathize with this attitude in academia, but at the same time I wonder what, if any, issues in the future it causes when the students are employed? In the "real world", unless the company you work for is doing some extremely custom design work, or developing a product which needs an interface library, you are likely going to be required by the employer, or by your client/budget/timeline to use an off the shelf library solution. In fact, from a business perspective, you would be remiss in not checking out extant solutions to the problem you are trying to solve first
, before exploring a custom in-house developed solution. Only if those solutions don't exist or don't meet your requirements (time/licensing terms/cost/etc), should you explore an in-house solution which might need more expertise to develop.
Unfortunately, we see this hubristic "not invented here" attitude in more than a few manufacturing/development industries. Imagine if every mechanic insisted on fabricating their own nuts and bolts, or if every carpenter formulated their own glue? At one time, this was case, but over time standardization and specialization in the manufacturing process occurred to largely eliminate this. We are seeing the same occurring with computers and software systems, as well as embedded devices. In a way, the Arduino is (or should be considered) an example of this winnowing process.
While I agree that from an educational standpoint, an embedded-design student should know and understand how to implement say, a servo driver library, I also think it may be a disservice to the student to not allow the use of third-party libraries when appropriate. The education should be on when and where to use the libraries, and to understand how they work (and how they are developed) at the lower-level, but they shouldn't be considered verboten to use.