All right, so much for the competition, I goofed off so much in the past few weeks that I’ve barely made a scratch in it.

Still, I want to explore UMAP a little bit further as it touches upon both topology and category theory.

Still, I never took a formal class in either topology so it’s a good idea to start with the broad lines of said fields and motivate why I decided to dedicate one article on it.

Topology is math where the notion of distance is not taken into account. e.g. A world where the distance between your nose and your keyboard is “the same” as that between the moon and the sun. A tennis court is the same as a ping pong table. And so on and so forth.

Category theory is math where you study the relations between things instead of what they are. It was meant as an alternative to the set theory.

But most importantly: it provides a common language for most (all?) of mathematics. [note to self: link to interesting example here]

My motivation is that I took a second course in Complex analysis without taking either topology or category theory, and really wish I did as the language of the instructor had to deviate from schedule to create mini-courses in both.

Since I am a lowly BA holder from a no-name university doing stuff on my own dime, I do not have the luxury to go in any great depth into any one mathematical topic lest I starve to death. I believe that gaining some knowledge will help me have an easier time in learning more math.

Will time prove me wrong? No clue and I have to admit my decision is made mostly on the basis of RUMINT, but I did promise that I would share all the mistakes.

The second motivation is eminently practical, it is… oh,and who am I kidding?I imagine there might be an application somewhere down the line but mostly, It’s fun to learn about this stuff.

In any case, if journalism is the first draft of history, this blog will represent my first draft of notes. I will revisit as time permits.

My posts will differ greatly from math textbooks. In my experience, intuition is most important but often glossed over in math textbooks.

It will be extremely informal and there won’t be a ton of proofs of formulas. I won’t dig into the details unless I believe that there is some new twists, the details of the implementation are really important or it differs enough from undergrad math that I should take a second look.

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