I'm still not 100% sure what your lecturers would like you to be working on, but there's a lot you can do with an Arduinio. One suggestion would be to use a microphone (about $5 from Sparkfun
https://www.sparkfun.com/products/12758) and a MSGEQ7 specturm analyzer (also about $4 from Sparkfun
https://www.sparkfun.com/products/10468) and a handful of LEDs, and then do a project based on the algorithms used to display the sound on the LEDs -- for example, look at the Muzio Kickstarter project -- I think that's Arduino (or similar) based -- I love the way they have implemented the peak hold effect.Another idea would be to create some simple system like a heater heating water in a container where water is slowly flowing in and out and use the Arduino to implement a PID controller function.Another idea would be to take a cheap-and-cheerful 9DOG breakout board (like Adafruit's LSM9DS1 which is about $15) and use the Arduino to read the data coming out of it -- process it into something useful, and display the results on a PC screen.Maybe some other members of the EEWeb community can suggest additional ideas.