<p>Thanks for the honest replies, jars. On a side note, how does Caltech’s Math 1abc compare to the standards of a real analysis course? I’ve heard people say that Apostol is around half-way between a standard calculus course and one of real analysis. Although Math 1abc is more specific on the calculus part of real analysis, which is quite a broad area. Interesting considering that the next Caltech analysis course is a grad level course (although many undergrads take grad level courses pretty soon).</p>
<p>According to <a href=“http://www.math.caltech.edu/classes/ma_9/index1.html[/url]”>http://www.math.caltech.edu/classes/ma_9/index1.html</a>, there really are only 5 homework problems per week. So I can see how an IMO person would be able to do them very quickly. And I like how certain Caltech courses are posting their stuff online, although it’s not MIT OCW.</p>
<p>But yes, one of the things is that Math 1abc is the first time that some students have to do serious proofs on their own, so it can be quite a challenge for those to even get the starting steps of a proof.</p>