By recommend, I mean content you actually find to be high quality, well done, and easy to absorb and follow. By relearn, I mean I have forgotten everything I ever learned in high school.
On a related note, what math should one know? Are there any upsides to go beyond everyday math? To brush up on lost math skills? I’ve forgotten most of my math classes, as I wager most have…
Math is one of those funny things that’s always all around you even if you’re ignorant of it. The ancient Greeks calculated the circumference of the world to an impressive degree of accuracy and they didn’t even have calculators - they just looked at some triangles and made some guesses.
Do you need to know the circumference of the world in your day-to-day life? Probably not. But it’s cool as heck knowing that you can figure that out by applying the right formulae.
If you know math and you’re faced with a problem that can be solved with math, then you can solve the problem. If you don’t know math and are faced with the same problem, you might not know how or if it can be solved.
Your specific question: “Are there any upsides to go beyond everyday math?” is an interesting question because of the implication of what ‘everyday math’ is. Depending on our professions or interests, your definition of everyday math might be radically different from someone else. Numeracy is enough to go on for a lot of people, which often implies arithmetic. But hey, fractions are always coming up in places, and if you add algebra to the mix you can start solving some interesting problems.
Some level of applied mathematics are used in all sorts of fields. Construction, Finance, Medicine, Software, Logistics, Conservation, Cooking, you name it. And the beautiful thing about a lot of these cases is that you don’t need to know very complex math in order to follow along an established procedure. For instance, I don’t need to know how to find the proof for compound interest, but I can easily look up a formula so I can make some projections of my investment plan.
Anyway, long story, but math is one of those ‘use it or lose it’ things. And if you’ve lost the math, then you start to be unable to see where math can be used. Keeping the math alive or rekindling it opens you up to possibilities that you might otherwise be ignorant of. Learning math for its own sake is fine, but finding ways to use the math you’ve learned is what helps keep it alive, and broadens your own horizons too.
I make my living doing pretty basic math that people are too lazy to learn or too afraid of. Financial simulations and shit like that. Pays to understand at least the most basic probability, statistics, calculus. I used to rely quite a bit on dynamical systems theory and linear algebra, but that was years ago now. To be fair, you also need to learn to code this shit up, but that’s not hard, either.
I feel like there are some interesting ideas in pure math topics like Real Analysis, Abstract Algebra, etc. Although I’m terrible at actually writing proofs and such.
Formalizing e.g. limit is quite interesting! Limit is related to tendency; sequence x_n converging to x means for large enough n, x_n is sufficiently close to x. That is, you can choose N such that | x_n - x | < eps for n >= N. In some sense, you are concretely defining what rough terms mean!
To look into these, you can read through books disregarding proofs. While proofs do hold ideas, they can be headache-inducing.
Personally speaking, I absolutely suck at math. It was and continues to be my worst subject. Likely to do with my adhd.
I was only able to really get up to and through basic algebra and some geometry in school. Past that, nothing else. I do fine. I’d say thats the minimum unless your in a field that requires a higher level of math.
