I am currently doing a master’s thesis in probability theory with a French supervisor. He gave me some M2 lecture notes, and my goal is to learn the material, fill in necessary details, and try to explain it in my own words. Q1: I am not sure if this is a common practice for math students in probability theory. To me, the notes are quite condensed and have small flaws or inaccuracies, but there are no major gaps.

In addition to proofs, there are some very technical estimations and calculations for bounds. For example, after bounding a fancy sequence five times, one can show that it converges to 0 or 1. My question is: should I focus on understanding these technical details, or is it better to focus more on the underlying theory and main ideas, while letting go of some of the heavy calculations?