I am going to do an online exam next week. Since this will be done by students at home, there is no way to guarantee that they do not cheat. I am thinking of asking for a proof of work, i.e., photos of their sketch papers. It certainly cannot stop anyone from cheating, but maybe it can make it a bit harder.
On the other hand, this is an elective course. So students may not have too much incentives to cheat.
Update: I have decided to not to ask for this. Ultimately, there is no way in preventing cheating in home exams. It is better to save honest student the time.
As for the exam, I am teaching discrete mathematics, and I would like to ask students to apply theorems to solve problems. I don't really test computations because I allow them to use WolframAlpha to do the computation.
I also want to test their ability to discover mathematics, i.e., ask them to do a bit of counting, such as the number of binary trees, and discover a formula for these numbers, and prove it.