Have you learned linear algebra yet? Is topology harder than Calc BC? Is abstract algebra harder than Calc BC?
How many proofs do you write for your AP calculus BC class? What kinds of things do you prove? Have you proved all the field properties and definitions of operations for the complex number system starting from the Peano axioms?
No high school class comes anywhere close to a mid to high-level college course in the subject. Not only is Math 55 harder than BC Calc, but so is Math 25, Math 23, Math 21, Math 20, Math 19... Math 1 is similar, from what I've heard.
The actual workload in college is generally smaller than it is in high school, particularly when you consider how much more free time you have (fewer classes that meet fewer times a week), but the material is much, much harder almost universally. Don't assume that just because you're taking AP courses that you know how difficult a subject can get.
mbaboy- The difficulty of Calculus BC depends largely on the school- some go beyond the material required for the AP test, while others barely prepare their students at all. However, I can guarantee you this- if you want to find a challenging math course in college, you DEFINITELY will find one.
I've been at Harvard almost three months now, and one complaint I've never heard is "This class is too easy"- that's something we left back in high school. (Of course, there are some classes that are pretty easy, mostly a subset of classes meant to fill core requirements for people that don't specialize in the subject, but in general it's very, very easy to construct a challenging courseload.
>one complaint I've never heard is "This class is too easy"
That's true -- not because there are no easy classes, but because you know they're easy when you sign up and you've chosen an easy class for a reason (like...you're taking Math 55 the same semester!), so there's nothing to complain about.
totally agree. Like my BC Calc teacher is craaazzzyyyyy hard! She goes WAY beyond the AP test. Seriously, we took a sample AP test four months into the class, and only 2 people in my class (out of 30) did not get a 5. It's crazy.
I don't know what Math 55 is like these days but it was insane when I took it a few decades ago. I remember getting a 57 on one test -- and it was the highest grade in the class! Our professor, Konrad Osterwalder, was so disgusted that he gave us another test on the same material and I scored 55! Even this was charitable, as I mostly just moved symbols around on paper without much notion of what they meant. I never did succeed in understanding the calculus of manifolds. It was an early warning that I was not destined to be the next Euler.
Hmm, "I mostly just moved symbols around on paper without much notion of what they meant"
That testifies to the difficulty of math 55 but doesn't put the class in a good light.
Everybody learns something from a horribly hard situation, like a test that bad, but why is it that you were left "without much notion of what [the symbols] meant" if you were taking a class you were interested in, at a good university, where there must have been good teachers and advisors?
Though the class is paced for talented people, it sounds like you were egged on, not taught, through the material.
Well, I think that I hit the wall with the calculus of manifolds. Math had always come easily to me before that and I was unprepared with coping strategies (or alternative learning strategies) when it suddenly got damnably difficult. I also subscribe to the theory that I saw mentioned recently that some people think better discretely and others think better continuously. With the single exception of real analysis, which I did very well in, I did much better in the discrete courses (e.g, algebra,* logic) than the continuous courses (complex analysis). I also think the quality of undergraduate pedagogy in the Harvard math department was highly variable -- I may not have been particularly bright, but my Math 55 classmates were. And I read a lot outside class, token, and got far more from that than from many of my classes. To be fair, I was too stubborn and proud to ask for help, from classmates, TAs or professors; this was by far my biggest academic mistake.
* "Algebra" here is groups, rings, etc, not HS algebra.