Wow I really like this document. As someone who really like mathematics but didn't get to do this as my major in undergrad, I'm missing out on so much, but also there is not enough time to start with undergrad books and do three years of basics... This document with all the clear statements at least allows me to see what is there to learn. Yes it's long, but compare that to dozens of the other books I would have to read to encounter these theorems, it's actually very short!
There is some useful "about this document" info near the end:
> The motivation to try such a project came through teaching a course called Math E 320 at the
Harvard extension school. This math-multi-disciplinary course is part of the “math for teaching
program”, and tries to map out the major parts of mathematics and visit some selected placed
on 12 continents. [...] A goal of this project is also to get back up to speed up to the level of a first year grad student (one forgets a lot of things over the years) and maybe pass the quals (with some luck). via http://people.math.harvard.edu/~knill/graphgeometry/papers/f...
Thanks. Same as the poster. But some “horrible” memory did meet me as I did math stat. Within 1/2 hour the lecturer tried to do a proof of central limit theory using an assumption that one can draw sphere to fill up a 3D space. Reading this does frighten me to a great extent at the same time appreciate what humanity have reached for doing such apparent “useless” things. Public goods are hard as it might look useless but unlike private goods it can be consumed and reuse many times. And some may find use of matrix in AI, number theory and geometry in encryption ... all because it is a public good that can be shared.
The trick whoonearth waste their life to create the first and develop later such “useless” things.
There is some useful "about this document" info near the end:
> The motivation to try such a project came through teaching a course called Math E 320 at the Harvard extension school. This math-multi-disciplinary course is part of the “math for teaching program”, and tries to map out the major parts of mathematics and visit some selected placed on 12 continents. [...] A goal of this project is also to get back up to speed up to the level of a first year grad student (one forgets a lot of things over the years) and maybe pass the quals (with some luck). via http://people.math.harvard.edu/~knill/graphgeometry/papers/f...