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What math should you learn if you want to get the most ROI out of “skill stacking” it with another applied domain you’re interested in?
Where’s the line between math being a true power-up vs a fascinating distraction?
Personally, just off the top of my head, I think most of the value comes from the following:
- Being rock-solid on the applied math that shows up all the time across all fields of engineering: linear algebra, calculus-based probability & statistics, algorithms, etc.
- Having broad knowledge of advanced approaches to mathematical modeling: differential equations, machine learning, etc. This includes not just conceptual understanding but also procedural fluency with foundational techniques.
- Knowing the basics of proofs. It’s less about knowing particular theorems and more about being able to follow lengthy logical manipulations and carry them out yourself in general. (However, the way you build up your general skills here is by practicing on particular instances – there’s no escaping the particulars.)
- Going deep into mathematical modeling supporting the particular domain(s) you’re interested in. Here, it’s not just about learning and developing modeling techniques, but also building domain expertise. Your models will only be as good as their data, and most data isn’t available in machine-readable or even human-readable formats – it’s siloed in the heads of domain experts who have extracted a massive amount of learning from a massive amount of hands-on experience.
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