<p>I've come to realize that the AMC tests, specifically the AMC12, and further tests such as the AIME, cover quite a bit of material that is not normally taught in high school pre-calculus courses. My question is, do these material belong in a specific field of mathematics? (Like, perhaps, abstract algebra?) And what sort of books should I read or courses should I take to actually cover this material? Thanks in advance.</p>
<p>The mathematics itself is all precalculus level or more elementary, so Abstract Algebra and more advanced math won't help you much (although it will enhance your problem-solving skills, the more important facet of contest math).</p>
<p>The specific techniques and ideas that tend to be neglected in math courses, but appear on contest math, tend to be found in problem-solving books. The most prominent books I know of are the "Art of Problem Solving" books by Rusczyk and Lehoczky. You can order them on artofproblemsolving.com. It is unlikely you will ever need any concepts that are not mentioned in these books.</p>
<p>Then it's a good thing I ordered those books. Unfortunately they came a week after I took the AMC12B, lol...</p>
<p>Anyway, thanks for the information. I thought these tests might include some really advanced concepts, but if not, then it's better. What about the essay/proof tests? Which areas of math do they cover and what skills would be needed?</p>
<p>They cover the same material, but to a more difficult degree. The AMC series of math competitions does not test calculus, so everything is pre-calc, though those proof tests (such as USAMO) are already very tough without calculus.</p>
<p>Just know up to Precalculus, very very well. I think that's the only suggestion. =P</p>