I am a PhD student in several complex variables. My advisor wants me to study Forstneric's "Stein manifold and holomorphic mappings" from page 100 to page 250; I have one month. I have never attended a differential geometry class. I have never been into such a situation; I was always used to prepare exams in a very detailed way, which is clearly impossible in this situation.
Do you have any advice?
Thanks.
Ravi Vakil has made some interesting comments about learning math:
"...mathematics is so rich and infinite that it is impossible to learn it systematically, and if you wait to master one topic before moving on to the next, you’ll never get anywhere. Instead, you’ll have tendrils of knowledge extending far from your comfort zone. Then you can later backfill from these tendrils, and extend your comfort zone; this is much easier to do than learning 'forwards'."
Later, Ravi states:
"A subtle leap is required from undergraduate thinking to active research (even if you have done undergraduate research). Think explicitly about the process, and talk about it (with me, and with others). For example, in an undergraduate class any Ph.D. student at Stanford will have tried to learn absolutely all the material flawlessly. But in order to know everything needed to tackle an important problem on the frontier of human knowledge, one would have to spend years reading many books and articles. So you’ll have to learn differently. But how?"