The first class Milan's decided to audit is a half-hour before Odette's first class, but she can get up early and show him the way, if he wants.
There is a lot about focus and pressure and from context he can probably glean the background detail that the common metaphor is that how magically powerful you are with respect to a branch of magic (there's some spillover, but generally the three accumulate power separately) is sort of like pressure, and how well you apply your mindset tot it is like how open a valve is, in response to how much magical power goes through.
There is a lot of speculation; no one knows for sure why exactly the three branches of magic hurt the way they do; there is a general categorization of each branch's "oddity," despite the fact that they're pretty sure the three are unrelated (conquest is instantaneous where the other two are not; sympathy hurts in a wide variety of ways where the other two do not; effort can theoretically be pushed beyond your practical power level in a way the other two can't). A lot of theoreticians think the three must be connected somehow, but mostly because a connection would be so tidy; there's no empirical evidence for it.
If he ever meets her he'll be sure to find out. Sure, she appears to be dead, but Milan does not plan to allow that to be an insurmountable obstacle indefinitely.
And that's the last class in his afternoon block. Time to go look up all the things that intrigued him over the course of the day!