<p>Worriemom,
I won't post my son's grades, but you'll have to trust me that he handles many AP and post-AP classes just fine. (He will have taken more post-AP courses (11) than APs (9) by the time he graduates.) One of his coolest research projects popped into his head during an English final. (doodle, doodle) He got an A on the final and did extremely well on the AP. He doesn't have a perfect GPA, but he has PLENTY to show for what he's done with his time. </p>
<p>I find scraps of proofs and programs in his pockets all the time when I do the laundry. Kind of cool to see where his mind takes him!</p>
<p>For these proofs, don't you need knowledge? I find that our school doesn't give enough knowledge. my son says it's easy, but work.
The science faculty is so bad in my son's school. For instance, when he was a sophomore, he didn't learn anything productive in Chemistry Honors. The course was so easy that he didn't do anything, but still got an A.</p>
<p>To be able to think about various proofs, you need knowledge. Where to find them?</p>
<p>you have to take initiative to learn about proofs etc. Go pick up Hatcher's Algebraic Topology on your own to learn what's in it; that's what i did. If your son did not learn anything in his Chemistry class in school, he could have picked up Zumdahl or something and learned the material himself. It's all about being proactive. Don't blame the school, their objectives are a bit different (getting everyone to just graduate)</p>
<p>Yeah, one thing I think that gets a lot of people is the idea of being good. You don't have to be really good at all your classes. You just need to do well enough. Then you need to specialize in 1-2 things. And these 1-2 things should be hard, and complicated, and you should go deep enough in these fields to be at the level of a sophomore or junior in college.</p>
<p>Also I think research and playing the safe game are orthogonal. Having gone to many of the top most science competitions and having met many other students there, I can honestly say that all of the best projects were done by students who took risks in investing mammoth amounts of time (and in turn disregarding their studies to some extent) for a low chance of success. I have never met a student who just went into a lab to "see what it is like" and came out to win big in these competitions. If you're going in for the big money, go all in.</p>
<p>Mollie: Yeah, it's not so pure for students to do research just to win these competitions. But at the time, for the sake of practicality, placing very high in these competitions open up so many doors its worth spending a month just to prepare for them (and the large sums of money don't hurt either).</p>
<p>Differential,
"Going deep" is exactly what my son did. He's always had an intense focus on one/two areas, and as he's gotten older, that came together with Olympiad, research stuff, and leadership opportunities. The depth that comes with pursuing an interest for a long time is a big contributor to successful HS (and later) research, IMHO.</p>
<p>Worriemom,
Yes, DS knows how to do proofs. He went to a non-Olympiad/non-competition-oriented summer program where he learned the finer points, though he'd had experience prior to that. From there, he got a college analysis book or two and played around. Was a lot more fun than DiffEq and MV, as far as he's concerned! He never lets teachers set the boundaries to his learning.</p>
<p>why are so many parents on CC? Let your child decide his/her path by his/herself</p>
<p>Mathwiz,
My S steers his own ship, trust me. We just hang on for dear life and enjoy the ride! :)</p>
<p>mathwiz90: Yeah i know what you mean. Im totally surprised. my first choice has been caltech for over a year and my dad still has to ask what the name of it is lol its really surprsiing to see so many parents take a real interest in their kids education
im not complaining though. in fact, i really like the fact that my parents dont pay attentino. itd be really annoying</p>
<p>as for the proofs, if youre just reading from a HS textbook, it most likely contains the theorems, but not proofs to many. I used wikipedia a lot, and mathworld sometimes too. They're pretty good for finding proofs, or at least explanations, on a certain random topic. As for whole subjects, if your hcild is interested in proofs, most upperlevel and graduate math texts are pretty rigorous so they could purchase an uupper level undergrad or grad textbook in the area theyre interested in. Or tell them to look trhough the book first to see how much rigor it has before they purchase it.</p>
<p>To learn how to write proofs well, you take courses such as real analysis, discrete mathematics, etc. Foundational classes that are rigorous. And no, it's very hard to learn how to write "just proofs." It's a skill picked up as you study other things.</p>
<p>^agreed- even though a lot of math immediately beyond single variable calc is proof based (i.e. in my multivar and diff eq class, we prove everything) you really don't learn HOW to do the proofs (beyond very simple ones such as dot and cross product properties etc)</p>
<p>Well I was talkin more along the lines of looking up prooofs as opposed to learning how to write them.</p>
<p>Multivariable Calc proofs are somewhat trivial compared to USAMO. If you want to learn real proofs, do USAMO problems.</p>
<p>if you want to learn real proofs pick up rudin or apostle or hatcher or munkres</p>
<p>...or artin :-) though that's abstract algebra, not analysis or anything. nice book though</p>