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There is a parallel in college physics. Typically, most colleges have two tracks: "Calc-based" and "non-calc-based" physics. Everybody finds the non-calc-based

There is a parallel in college physics. Typically, most colleges have two tracks: "Calc-based" and "non-calc-based" physics. Everybody finds the non-calc-based course to be an utterly bewildering exercise in memorizing formulas. Even the calc based students are baffled by it. The calc based course is widely regarded as easier and more intuitive -- if you also take calc. Stats is the same way. I was a math major, and my college had two stats tracks: "Math stats" and "stats for scientists." The first track was 2 semesters, and we had to prove everything. Of course we used calc. The second track was 1 semester, and was an utterly bewildering exercise in memorizing formulas. I took "math stats," but was then asked to run the discussion section for "stats for scientists." There were things that were utterly intuitive to me, but that I couldn't satisfactorily explain to the students, such as the need for different formulas and methods for discrete and continuous distributions. Freshman economics. The professor bent over backwards to make sense of the formulas related to things like the supply and demand curves, because he couldn't use derivatives. Also, it was 1982, and yes, the professor showed us the Laffer Curve.

munchbunny 4y ago
I had a similar experience, I took stats without calculus just because that was what was available/feasible in college, and eventually I took a more rigorous calculus based probability and stats course in my early 30s. Despite having to relearn my calculus, the difference in conceptual clarity was obvious from even the first lecture because the answer to “why does this work?” has a direct interpretation through calculus that you usually can’t get without calculus. Feels a lot like hiking: as you get more fit you also get access to more fun.
- analog31 4y ago
  Thinking more about this, my answer to "why learn calculus" is that so many ideas and tools of modern life are explained, and even relate to one another, through calculus. Without calculus, many simple things become unapproachable, or have to be approached by rote learning of formulas and rules. When in grad school, a friend of mine taught a freshman course on modern history, and in the first week he introduced a general outline of calculus. The students were surprised, but he explained that calculus is a thread woven through modern history thanks to the importance of science and technology.

munchbunny 4y ago

I had a similar experience, I took stats without calculus just because that was what was available/feasible in college, and eventually I took a more rigorous calculus based probability and stats course in my early 30s. Despite having to relearn my calculus, the difference in conceptual clarity was obvious from even the first lecture because the answer to “why does this work?” has a direct interpretation through calculus that you usually can’t get without calculus. Feels a lot like hiking: as you get more fit you also get access to more fun.

analog31 4y ago
Thinking more about this, my answer to "why learn calculus" is that so many ideas and tools of modern life are explained, and even relate to one another, through calculus. Without calculus, many simple things become unapproachable, or have to be approached by rote learning of formulas and rules. When in grad school, a friend of mine taught a freshman course on modern history, and in the first week he introduced a general outline of calculus. The students were surprised, but he explained that calculus is a thread woven through modern history thanks to the importance of science and technology.