[Outdated, please look at pinned post] Casual Conversation

Calculus

Taylor series approximations work because the derivatives of the taylor series expansion and the function it is approximating are the same (and the values at the given point). Likewise, the derivative of e^x is e^x because the taylor expansion of e^x is 1 + x/1! + x^2/2! + x^3/3!... which becomes 0 + 1 + x/1! + x^2/2! + x^3/3!... when the derivative is taken. So the derivative of the taylor expansion of e^x is itself.

Torts, which is to say the things in civil law that will get your ass sued, but aren't contracts. Mostly your basic personal injury stuff.

My Torts professor was a local legend, and basically left the teaching of the subject to an obsolete version of a non-mandatory text. He never asked about it, and he never built his exams around it, and only occasionally mentioned the damn thing. Instead, his exams were mostly based on recitations of facts from cases and he especially delighted in including questions based on his "tangents" in lectures, well practiced over decades of southern-fried paper-chase nonsense. I was told this about the exams, and took the second years at their word. Several old exams were also freely available for review in the law library. I spent the entire year terrified and confused, holding on for dear life to remember enough to pass. I guess I did okay, getting a B on the midterm and a C (C-minus? I honestly don't remember) overall in the class. Since it was graded on a curve, I was clearly not alone in how I approached the material, though in retrospect actually knowing anything about torts would have helped too.

It was two years later, almost time to graduate, that I was having discussions with classmates and realized, "Holy shit! Torts have elements!" That is to say, there are actions and criteria that have to be satisfied: e.g., there must be (1) an action X taken with (2) mindset Y, that (3) results in damages Z, (4) ameliorated by concept AA or defense AB. Things get squishier around the edges than criminal law, but it's basically the exact same analytical framework as that, a course that I (relatively speaking) enjoyed and did much better in. I mean, I guess I knew what most of the relevant concepts were, but the idea that they fit together in a logical way, not just as a mush of "whatever wins the case" was an epiphany.

Now, to be fair, if I'd done all the things that a properly motivated and earnest legal scholar is supposed to do, like heeding the cliched guidance to study two hours for every hour of class, to do all recommended reading, and to avail myself of office hours, I likely could have figured this out much earlier, but it happened how it happened, and in my defense, none of my other professors thought themselves too important and too bored to share the basic underpinnings of their subjects with their first-year students.

The one teaching Contracts totally fucked that second-year who rode a motorcycle, though.

Trigonometry. My high school math teacher was a literal math genius and would always go deep into proofs and theory, sometimes not even getting to our homework stuff until the last 5 minutes of our 50 minute class. As a result I went from the "gifted" math group to nearly failing.

When I went to college I had to take a math placement test and ended up in Math 99 (below college level math).

It was there I was finally taught SohCahToa and everything clicked. I actually use simple trig a lot in my job now.

How instances work.