Main Question or Discussion Point
Would they ace it? For those of you who don't know The Putnam is the hardest math test for undergrad students. The test has 120 points but most only score a few.
s2+c2=1 // for sin^2(a) + cos^2(a) = 1 1+t2=s2 // for 1 + tan^2(a) = sec^2(a) sab=sacb+casb // for sin(a+b) = sin(a)cos(b) + cos(a)sin(b) cab=cacb-sasb // cos(a+b) = cos(a)cos(b) - sin(a)sin(b)
Whereas I agree with the bit I put in bold I don't think the part it italics follows. You can be very good a "standard" math without being great at the type of math you sometimes find in the types of tests the OP is referring to; the reason is simply that these tests do not necessarily test knowledge but problem solving skills and whereas the former is something can learn by studying most of us will never be great at solving the kind of rather obscure problems you would e.g. find in the math Olympiad.While I can't answer your question, I realize it would probably depend on the math lecturer and what he taught regularly. As we progress in our math studies, the math we learn in grade school is child's play to us now. Following that extension if your job is to teach higher level math then that math will be child's play to you and you should easily be able to do the problems you routinely assign to your students. I'm sure this would be true of the Putnam.