Weirdly, my Advanced Calculus class didn't really deal with multi-variable calculus. I think that would be more the "practical" side of things, e.g., Differential Equations. Advanced Calculus was more abstract, concentrating on proofs. Which I loved. I guess my "hitting the wall" moment was trying Mathematical Topology. That was really abstract and, despite being all proofs, was a real struggle for me. I think it also depends on the teacher. When I had a different teacher (Hazel Jo Reed) for Abstract Algebra, I really loved it. It would be better if there were no prerequisites for any course. I mean, I would never have been able to take Advanced Calculus (Hans Guttman was the one that suggested it) without first taking Calculus if I hadn't gone to Evergreen. The bottom line is that trying everything everywhere all at once is the best approach to education. > From: Noelle <noelle> > Date: Sun, 5 Feb 2023 08:09:19 -0800 (PST) > > about AP classes & calculus & MIT > > B.J. in Arlington, MA, writes: This isn't about politics, but since > we're talking about AP courses, I thought I'd share my perspective. > > I'm a STEM kind of guy. In high school in the 80s, I loved math and > felt I was really good at it. I took all the math and science AP > courses my school offered. That included AP Calculus, on which I got > a 5 (highest score) on the "BC" (harder) variant of the test. > > Then I went to MIT, thinking I might major in math. With my AP > Calculus test score, I placed out of the first freshman calculus > course, skipping instead to the second, "multi-variable" calculus > course (think "Div, Grad, Curl, and All That"). It was a MISTAKE. I > was not ready for college level calculus. I realized that despite > aceing my AP class, I did not really understand the concepts. I fell > behind in math and never recovered, struggling through the remaining > required math courses and never taking another one. > > I majored in computer science instead, which I loved, and I've had a > great career and life. However, when my kids are making similar > decisions, I will certainly encourage them to take the hard/AP > courses in high school, but I will not encourage them to skip > college classes as a result. There is enough time to learn the > material you want in college, and if going further makes sense, > there is always grad school. Why rush?