Blue Collection Intro

The way I do math has its advantages and disadvantages. I often run interesting topics in parallel, watch a few lectures, do some problems, take notes, and condense. However, I don't organise the things I collect, and I leave it in the messy (and often very compacted) state I first write it in, after working through it in a notebook. I also don't do any lecture series or course covering exactly what they do and doing all of the exercises they suggest. My ADHD makes me jump between books, topics, problems, and lectures. The advantage of this has been that I see mathematics more holistically now, and I can pick up new ideas and run with them somewhat smoothly.

For example, I just started learning category theory from this book "Basic Category Theory." And a problem in the first chapter uses homotopy theory for topological spaces. I had covered more or less of an undergrad point set topology course, but had no idea about homotopy or any notions from algebraic topology. But I was able to pick up the definition of homotopy, construct the fundamental group of a topological space, and show that this construction induces a functor from the "category of topological spaces with base-points" to the category of "groups" in the span of a few hours, which was fun.

The disadvantage is BIG. I don't do nearly enough exercises as I should, and I don't really have FULL UNDERGRADUATE COVERAGE of any text/course. I have more coverage on point set topology, abstract algebra, and linear algebra than I do with analysis. I've also done a decent (elementary) amount of graph theory, combinatorics, algorithms, and Ramsey Theory.

But I feel a little shame (and guilt and resentment) by not seeing most topics through to its entirety. The need to fill holes in my mathematical knowledge, polish and collect stuff that I've left in notebooks, and do more exercises, almost always arises whenever I see any math at all. And I intend to do it eventually.

However, right now my north star problem takes precedence. Whenever I feel lazy to work on the main stuff, I'll at least try to polish things I've collected a little and put them here in the Blue Collection. And when I feel like I've got more time, I'll definitely fill holes in my knowledge.

But it is what it is, I'm not too bothered with the way I carried out doing math so far, it's really fun!! For now, Blue Collection is just where I dump my notes, with a little polish on them. More notes are coming :)