Would you care to visit?

Spivak publishes his own book and also the solutions manual. They're available on amazon but information is here: http://www.mathpop.com/mainhtms/bip.htm I don't know of any solutions manual to Apostol, but a student who wanted help on a specific problem could post a scan of their work here or on a website and probably get help. As a matter of fact (especially if you're working off the edition I have) I'd be happy to take my best shot at a critique, and I'm sure others would as well. It wouldn't be as useful if you needed help on every problem though. When I say maturity I do not mean prior exposure to calculus. What I mean is: 1) Patience at working through problems that are not immediately obvious 2) Understanding of what is and is not a proof and a reasonable degree of facility with constructing them Actually I started typing more and then I decided that I'd just go with someone else's (good) definition -- http://en.wikipedia.org/wiki/Mathematical_maturity Some students are ready for this after a good algebra and trigonometry course. Others (quite honestly) will never be ready. This is a level of math that many people would find challenging even if well-prepared. The prior calculus course is often a good idea so that the student is familiar with the concepts and doesn't become lost in the formalism, able to manipulate symbols with facility but not really understanding what an integral is. But I have known other people who paired a really rigorous book like the above with either a physics book that applied the calculus or a 'concepts of calculus'-type book who did quite well.

Art of Problem solving or Elements of Mathematics at elementsofmathematics.com. EM is more self-paced whereas AOPS moves at a breakneck pace, but AOPS is more aligned with scope of a standard classroom (so it's easier to transfer in and out). They are both extremely challenging and rigorous programs.

How long has it been dead? If it's just thawed or thawing, cancel school and cook everything NOW.

You are totally correct that GA tech's calculus is accelerated beyond most standard calculus courses. This is why they say on their website that you can't transfer in calc 2 unless you've also taken linear algebra. This is non-standard. I keep editing this because I can't get it to sound right. I'm just intending it as a general guideline -- not as a 'covers everything in every class everywhere'. Clearly there's going to be some differences in coverage and this is exactly why I believe I said early on (unless someone else had said it earlier and better) that at a large research university with a talented student body it would be beneficial to repeat calculus because the coverage would probably be deeper and more thorough. But it will cover everything in an average calc 2 class.

Anton: You've listed level: challenging and linked to the AOPS book -- was this a mistake? I'd consider it more of a standard university-level textbook. Stewart: Ditto, very standard university-level textbook. Chalkdust: Uses Edwards and Larson, another standard university-level textbook. Spivak: Extremely challenging in a slightly different way from AOPS. Very heavily oriented to theory and proof. Apostol: Same as Spivak. Math-lovers often find it very difficult to choose between these two texts. The last two are going to require a significant amount of mathematical maturity and a fair background in proofs. I'd especially recommend work with inequalities.

Taking a year and a half off causes you to lose a lot of skill. BTW, I'm not saying that a student shouldn't repeat a level -- just that BC covers calc 1 + 2.

Careful about outdoor burning, the legality varies by state. (although a Viking funeral pyre would be a great way to send off a ram).

If you can get him out, there should be someone who hauls away dead animals for a fee. We have done that. When the ground is soft enough to dig we bury them with the skidsteer.

They haven't been able to find one yet although research is ongoing. http://www.cfri.ca/news/news/2013/10/11/immune-system-discovery-could-lead-to-ebv-vaccine-to-prevent-mono-some-cancers http://www.healthtalk.umn.edu/2013/02/26/u-of-m-studies-may-hold-key-for-mono-vaccine/

Oh, I had assumed that that had already been checked and the bulbs were actually different. Changing bulbs to different bases is easy-peasy once you have done one and with a little care.

Other people have discussed the probability question, but I'm going to discuss again. The problem with attempting to calculate the probability post hoc and conclude just how improbable it is to produce the world we live in is that the events have already happened. All of the worlds where life never arose at all, or life died out due to something like a bigger, badder dinosaur killer, well, they aren't here to calculate a probability. So this has already introduced bias. Sorry for the gruesome example, but picture that you take 1,000 men. And you line them up and you walk down and you shoot 90% of them, rolling a ten-sided die to select which one lives. Then you line up the 100 survivors and go down and shoot 90% of them again, choosing them the same way. Now 10 survive of the original 1,000. Do those men feel lucky? I sure would! They had a very small chance of surviving both selections. But the problem with this is that given this selection process, ten men were always going to survive. The only choice was which ten.

(shhh but I sometimes pick problems for calculus exams this way :D)

I agree with Eagle. Then just step back and pray for her. :grouphug:

I'm horrible at finding threads but I'm 99% sure it was lewelma. The title was something like "this unscientific american watches a fish walk out of the water" or something like that.

Calc BC = Calc 1 + 2. Calc AB = roughly 2/3 of Calc 1 + 2.

Designate that strand as a source for spare bulbs for the others and use one less strand :P

I'd prefer 1 or 2. Can you start AOPS and if she can't hack it, switch to Jacobs? For Jacobs, I'd skim/assign mostly the challenging problem set until I reached new material. Jacobs is a very good book and your option 1 is just fine as well, but I think the challenge is good for a child who can handle it.

The thing is that you're thinking of evolution as something the animal directs. It's not (imagine if it were, we would have such awesome super powers now). Something like this would probably have begin as a single bump -- a single proto-tooth of the gear, if you will, that caught just slightly and gave just a slight advantage. Even though it's a slight advantage, it adds up over generations -- look at how rapidly lactose persistence has spread through humans, and our generations are so much longer. Once something has evolved in the first place (such as limbs, eyes), adaptation occurs much more quickly. Once there's a gene that says, roughly, 'put a bump HERE', it's pretty easy for a mutation to say 'put two bumps HERE like so', or more so. Of course, there are going to be deleterious mutations as well -- for example, two bumps that actually lock the legs from moving at all. But those creatures would die out very rapidly, so those mutations would not persist in the gene pool.

I wouldn't use Saxon for a kid who needs extra challenge. Other than AOPS, you might also consider the IMACS Elements of Mathematics program -- he's just at a perfect age -- and it's online and totally self-paced. This and AOPS would be my first choices for a really mathy kid. Jousting Armadillos might be another option.

Interesting side note -- although on a flat surface the sum of the angles in a triangle is 180 degrees, this is not necessarily true on a curved surface. For example, if you draw a triangle on a sphere, with one point at the "north pole", and two points on the "equator" separated by 90 degrees, this triangle will have 3 right angles, and yet undeniably have 3 straight sides.

Put it on the table after dinner :P

Yes. I also have a specific (good) password that I use as the response to security questions. I don't care what they're asking.

I use pretty much the same password everywhere that I don't really care if it gets hacked. For example, wtm, myfitnesspal, and the like all have the same password -- because the consequences are low. When I need to change one of them I change them all. that frees up my brain to remember the passwords for important things that I DO care about hacking.

I think repeating precalc in summer school could also be a good idea if the school offers it.