@ ColinsMum — I agree with the criteria that you list for the suitability of choices of enrichment topics. My thought was that more mainstream math meets them better than mathematical logic. But you're right about mathematical logic showing up more in computer science – this is an important point that hadn't occurred to me, thanks.
@ HowlerKarma — I agree with your general point.
• For the most part, the material in the books that I listed doesn't show up in the standard undergraduate curriculum, and many mathematicians aren't exposed to it until graduate school, and also falls under the "exploring widely" heading (e.g. many mathematicians don't know knot theory).
• Being exposed to mainstream math helps students decide whether or not to pursue math further.
• Most children who are interested in math won't go on to math graduate school.
• Deep mathematical subjects take a long time to absorb, often including returning to them multiple times before one assimilates them, so it's not necessarily bad to study them before taking courses on them.
• For those children who will go on to math graduate school and who have already mastered the relevant material before graduate school, such that they don't want to take the coursework, acceleration won't be problematic from the point of view of age, and graduate schools are more flexible about students skipping courses than high schools (for example).
Last edited by JonahSinick; 02/19/14 10:47 AM.
