>>10013132>>10013160>>10013174>>10013179Thanks for the foxes
>>10013193I'm not
>>10013189 so I don't know if it's a meme or not but maybe try to look up the papers and presentations by the course lecturer on youtube and the like to get a better feel for what she's presenting. I think her results would probably be condensed into some talk somewhere.
https://www.youtube.com/watch?v=vd2dtkMINIwThe way I study is by doing every problem and if they lay out a proof to a theorem first try to prove it myself before looking at the proof they presented. It's kind of tedious but you get faster as you start seeing the tricks of how to proceed. It also makes learning the later chapters easier since you don't have to keep looking back to remember past results, so in some sense, taking a long time to deeply and thoroughly understand the basics can save you time in the long run. Efficiency is good and all
but you should aim for understanding. Hope that helps a little.
>>10013201Rather than "take on faith" it's more that there are prerequisite material that in the interest of time they aren't able to cover. That's kind of why you're supposed to cover things like set theory before taking abstract algebra, so nothing is taken on "faith". It is possible to start from the ground up to build the foundations of a subject from scratch, but this is usually kind of tedious and the added value is dubious at best. Take this example
http://www.geometry.org/tex/conc/dgchaps.htmlwhich goes very in depth to cover all the prerequisite material, unfortunately that means you have to go through over 1400 pages until the DG. This is kind of why you have separate classes to cover material that then build on one another. Also you shouldn't consider any class "complete". Every field of mathematics is not only growing, but constantly intersecting with other fields of math, blurring the lines between fields. Every textbook and class you've encountered are mere slices of the grand picture.