b@r!um

quicksilver: a lot of Putnam questions look not too hard, but there's almost always a "twist" involved (e.g. one fairly obvious solution and then a second one that hardly anyone finds; or a question that could be easily solved with a calculator but requires some creativity to solve without one). Of course you might just be one of the 100 most mathematically gifted college students in this country...

Some other personal and highly subjective experience and by no means general:

Math was considered one of the hardest majors offered at the university I was taking math courses during high school. About 300 students each year started as math majors, and only about 40 of them passed the intro courses (linear algebra and analysis). The other ~260 students changed their majors, mostly to computer science, physics, engineering, econ and business and most of them are quite successful in their second majors.

Maybe most of these students just declared the wrong major to begin with, but I think that math (axiomatic math and not the crap taught at most colleges -- yes, I admit that most math major programs are not too challenging) is one of the harder subjects of human inquiry.

quicksilver40133

Well, I had old exams online and solutions, I worked maybe 1/5-1/4 of the problems on about 1/4 the exams and got them right, exactly. I only did the ones that looked doable. They included game theory, logic, and optimization problems. Problems asking about abstract algebra, real analysis, topology and other math-intensive subjects were nearly indecipherable to me. That being said, I am still doing better on these tests than the best math majors at my school, which is what irks me. I don't think the problems I solve are hard problems. Then again, most solvable problems aren't hard.

And I agree that how the subject is taught has a lot to do with how hard it ends up being. But that's true of any subject; anything can be taught in such a way that it's arbitrarily hard. IMO, that is.

b@r!um

Kudos for doing so well on the Putnam exam. Maybe you should talk to the math department and see if they let you take it next year (if you have not graduated by then, that is).

I agree that any subject can be taught arbitrarily hard. But math, by definition, is axiomatic - that's just not how most colleges teach it. It seems that most colleges make it easier than it is on purpose by omitting the very essence (and imo beauty) of the subject.

quicksilver40133

Thanks, barium. I've already looked into it, but the sponsor is all about math majors... and I'm just out of luck. That's fine, it's their loss.
As for the other, I can concede that. I do love math.