Math dilemma

Pre-College Topics High School Life
1

<p>I am in a very odd situation. I love math and have taught myself (authors in parentheses):
real analysis in one (Rudin) and several (Spivak) variables;
linear (Shilov) and abstract algebra (Artin);
complex analysis (Ahlfors);
topology (Gamelin/Greene);
and a little bit of number theory (Niven/Zuckerman).
[Not just reading of course. I can do the problems, too.]</p>

<p>Here's the issue. I just took the AMC 12 and got a horrible score (not nearly good enough to qualify for the AIME). I am very confused about all this. Does this mean that I've been "fooling myself" somehow about learning math? How is it that I do fine with more advanced subjects but can't even get an average score on something as concrete as the AMC?</p>

<p>Note: I hadn't prepared for the AMC beforehand. It was a last-minute request made by our math department chair. But isn't the AMC more indicative of innate creativity and problem-solving ability anyway?</p>

2

<p>Everything that you’ve taught yourself (although I’m sure, very useful) is irrelevant to the AMC.</p>

3

<p>The AMC has to do more with creative problem solving whereas school mathematics is more algorithmic and formulaic.</p>

4

<p>Don’t get me wrong–I know all of that stuff has nothing to do with the AMC. Those were simply out of my interest; I didn’t even know what the AMC was until recently. (Also, the algorithmic/formulaic mathematics of high school classes is nonexistent in these subjects).</p>

<p>That being said, does preparation make as much of a difference in the AMC as it seems? (I would hope so.)</p>