@TedShifrin yes I was surprised. It would be nice if something like that happens. With the people around here in math.se there will be good talks. But it is as with the community blog I guess. That's all. Would be nice.
Yup. For fun with vectors, you should do the exercise of proving that the medians are all concurrent, the perp bisectors are all concurrent, and the angle bisectors are all concurrent. The three points you get are collinear and there's a 1:2 ratio in lengths :P
It sure didn't used to be, @badass, but in the US high school math education has gone to the dogs completely. I don't know what it is where you are. Geometry (with proofs) is more sophisticated, but I don't see the point of doing trig before you've thought about basic geometry.
I'd taken algebra at my previous school, and the next one had no high school to stick other students in. They weren't allowed (or something) to just have me not take a math class or just learn it myself, so they had the teacher assign me some problems from a book every class and work while he taught algebra.
Well, memorizing what someone else does for you is NOT the solution.
I was upset with my own students that when I gave them a linear algebra proof that was disguised from the ones I'd shown them how to do they were (except for the best students) at a loss to even start. I'm going to give them a talking-to about that when next semester starts. Studying does not mean memorizing past problems.
It's become clearer as I've taken more classes that, fundamentally, you should be studying the proof methods far more than the theorems. Because once you know the ideas, re-deriving the theorems (or doing similar exercises) is not very hard.
Brian Scott left in a huff the other day because I criticized his behavior, and a guy cursed me for rudeness because I lost patience with someone asking a homotopy question who needed multiple coaxings.
@Mike, en.wikipedia.org/wiki/Jensen's_inequality The most famous version of it is probably the one in probabilty theory, although what I quoted was merely the case when the measure space is finite with counting measure.
Well, I've been where people like Pomerance, Granville, and their students have been, along with combinatorial types of analysts (Magyar, Lyall), so they all know it. I've now read the question. I'm expecting $n_r$ can't be arbitrary.
@TedShifrin, did we overlap in graduate school? Schnirelmann density is easy to work with but heavily dependent on the first few values. natural and Dirichlet densities are more work but are what one really wants.
@TedShifrin, bit surprising that Pete got back to me, maybe September, I worked out a lot of minor questions, and he submitted the manuscript on Nov. 29, to Acta Arithmetica....Maybe I know your name as a recent (at the time, 1980) advisee of someone there.
@OldJohn, yes. There is a fellow named John Voight, now at Dartmouth, who lives for this stuff, helped with the Pete article. He says he is busy for a few weeks. Anyway, it is clear that lots of Hilbert quaternions are not the sum of two squares, 2-adic stuff. Much harder is to show that, allowing multiplication of such sums by a unit on the left, we recover all of them. Voight knows enough to do the hard part, I really do not. Oh, it turns out the actor's first name is Jon, no letter 'h'
@TedShifrin, saw Kirby on Friday but did not speak with him. Was hoping to run into Voight, on sabbatical here until March