I’m an alum of the program from the first year it started (2010), so bear in mind that it’s completely possible that my advice concerning this is outdated. However, here are my thoughts on it now looking back:
1) The level of required preparation beforehand will obviously depend on the structure of the exam. For our EM class (Prof. Pohl), the list of possible topics was given to us ahead of time, but the material we could bring was limited (could be wrong on that…feel free to correct me, older folks). For our QM class (Prof. Blondel), the topics were not given, but we could bring any material we wanted to prepare. We were given 20-30 min prep time for both classes (don’t remember precisely). In any case, obviously use what you’re allowed to your advantage.
2) You don’t need to memorize the book. Give a “spark notes” style outline. You don’t need to provide anything fancy. The professor wants to see how well YOU know the material, not how much the author of the book knows the material. I would suggest first to imagine you are explaining it to your parents (assuming they aren’t experts in the fields themselves) and build up the level of detail for your personal understanding from there. Use further detail to answer questions that the professor asks. You don’t need to give an all-inclusive lecture!
3) In your oral exam, I recommend you maintain composure and go at a slow and comfortable pace. It’s a very informal setting; you will get interrupted and asked questions in the middle of your presentation! They likely will not try to intentionally derail you (at least they didn’t to me). The questions will likely be more of a clarification than anything else. In any case, if you proceed at too fast of a pace, you will likely lose yourself when you are interrupted. This was a mistake I personally made. Stay relaxed, you’ll think more clearly.
4) We all passed! I know I personally tripped up a little bit like I said before, but none of us failed and most did very well. I promise you will survive. We were all nervous and scared of it too.
I hope that helps some. Good luck!
P.S. If you have more questions, feel free to email me at firstname.lastname@example.org Just keep in mind that the time change is 12 hours, so I probably won’t get back to you until the next day.