Hello friends. So, I have been searching many, many forums (most notably mathoverflow.net and MathStackexchange) and I think there is a certain type of thread which, in the post by Chris (which he was dictated by me) excludes. Namely, very eager undergraduate and graduate students often have a desire to aim their studies towards learning a particular subject that very much interests them. For example, I've had a member of this forum message me and ask "Do you know what the best route I could take if I wanted to learn algebraic K-theory?"--needless to say I did not. That said, the user's question was really not that unintelligent. Often times the road to some of these higher-level subjects seem to be shrouded in mystery, ambiguity, and straight out contradiction. For example, if someone wanted to learn algebraic geometry one 'must' learn commutative algebra, complex geometry, representation theory, homological algebra, etc. I put the 'must' there, for this is precisely the point of this thread. Some people insist that you really must learn all of these subjects and some say that "Homological algebra! Ha! That's not at all necessary to do algebraic geometry" while another source might say "Representation theory is entirely too much. That said, I'm glad to see homological algebra is on that list--it's a geometer's best friend". To make the matters more confusing is that when one finally looks up these prerequisite subjects they all seem to be interdependent: "So, before we start the commutative algebra we recall some basic facts from homological algebra" and even the hilarious "So, to make the commutative algebra a little more intuitive we'll assume you have some background in algebraic geometry". Put simply, learning things on one's own can be a mess.


So, I think that this forum should be opened up to such questions, things like "I want to learn about elliptic curves, how should I proceed?" These shouldn't be one answer, one question threads I don't think either. I think that it should be one big thread about, going with my previous examples, the struggles to learn ellipitic curves "You should definitely learn this first because it really is helpful there" or "You should definitely use this book over that book, because no one does it that way anymore" etc.


One note I'd like to make though. Please, do research before you post a question in one of these threads/make one of these threads--no "Hey, I want to learn differential geometry, do I need to know linear algebra???".



Feel free to comment on/about this.