Goals: Deeper understanding of mathematics as a discipline, learning of useful formal concepts in mathematics, preferably with day-to-day applications such as probability theory.
Request: If possible, find a good balance between overly technical and overly practical presentation. Probability theory introduction usually suffer from the latter, more abstract concepts more from the former.
My expertise happens to be largely concentrated in general abstract nonsense (which I think has a bad rap it doesn’t deserve; to me it’s the analogue of using a high-level programming language instead of a low-level one) but I’ll see what I can do. It’s worth mentioning that I gave the title as “(pure) mathematics...” instead of “mathematics...” because I don’t have any particular expertise in applied mathematics.
Well, try this: Show how general abstract nonsense could be relevant to a rationalist in his day to day life or in his general understanding of the world. Or try an introduction to general abstract nonsense that does not leave the reader with the feeling that it is, well, general abstract nonsense.
So, in mathematics general abstract nonsense has a more specific meaning than this. It specifically refers to certain kinds of arguments in category theory.
Goals: Deeper understanding of mathematics as a discipline, learning of useful formal concepts in mathematics, preferably with day-to-day applications such as probability theory.
Request: If possible, find a good balance between overly technical and overly practical presentation. Probability theory introduction usually suffer from the latter, more abstract concepts more from the former.
Useful for what purposes?
Well, I was thinking practically useful, e.g. geometry. Not general abstract nonsense.
My expertise happens to be largely concentrated in general abstract nonsense (which I think has a bad rap it doesn’t deserve; to me it’s the analogue of using a high-level programming language instead of a low-level one) but I’ll see what I can do. It’s worth mentioning that I gave the title as “(pure) mathematics...” instead of “mathematics...” because I don’t have any particular expertise in applied mathematics.
Well, try this: Show how general abstract nonsense could be relevant to a rationalist in his day to day life or in his general understanding of the world. Or try an introduction to general abstract nonsense that does not leave the reader with the feeling that it is, well, general abstract nonsense.
I’m not sure about “day-to-day life”, but this application of general abstract nonsense certainly did make my day better when I read it: link
So, in mathematics general abstract nonsense has a more specific meaning than this. It specifically refers to certain kinds of arguments in category theory.
That is quite amusing. Of course mathematicians have defined “general abstract nonsense” to mean something specific. :P