Oct 23rd, 2020

🧮 Digitizing My Maths Studies with TeX

For the past days, I've had the chance to catch up on the fundamentals of set theory, relations, and elementary functions in the context of a maths pre-course at my university. While this will prove itself useful in the months to come, I challenged myself to reach an additional goal: Get all of this done, digitally.

I don't want to have multiple sources of information spread around, collections of pages of repetitions that just get stale, or anything else that's not searchable, and always available, for that matter. And since I'm already processing the contents of the studies into my personal knowledge base, maths should end up there as well.

It's also way easier to share my progress with fellow students or faculty staff this way, as I can just share my screen in meetings or send a link to some public Notion page.

So getting back to digital maths, there's only one way, really: Getting to know TeX, the gold standard in typesetting widely used for mathematics and other academic subjects. Using TeX, you can go from simple things like A={1,2,3}A = \{ 1,2,3 \} to full-blown equations

f(x)=i=0201i2g(x)=i=030i+2i3{{f(x)=\sum_{i=0}^{20}{\frac{1}{i^2}}}\atop{g(x)=\prod_{i=0}^{30}{\frac{i+2}{\sqrt[3]{i}}}}}

Like any system, it takes some time to get adjusted, memorize what you'll need most often, such as common symbols and formatting properties.

Having the experience of learning new programming languages and getting into different systems when working in computer science and software engineering felt like a benefit at this point.

So here I am, four to five days in, getting a fair share of daily training in TeX, and I'm quite happy. Instant learning feedback, seeing your formulas appear on screen after checking out the reference feels quite rewarding.

Of course, writing down maths isn't everything, and there are some tasks I still need to solve: Calculating actual results, visualizing and plotting (WolframAlpha seems like a potential candidate here), and probably countless things I haven't thought of yet. For starting out, though, this experiment has succeeded, and I'll continue to expand my muscle memory of TeX symbols and formatting in the time to come.