Recent content by Saint Medici

Maybe I'm just being dense, but I've been having issues with the multiplying non-disjoint permutation cycles (as you may have guessed from the topic title). Simple products like (1, 4, 5, 6)(2, 1, 5) [an example from my textbook], as well as in the opposite order. Mayhap that I'm tired...

Intrinsic critical points of a function... I have a problem that's giving me a bit of trouble. The solution is not vital to my existence, but it's been eluding me long enough that it's grown to be a pest. I've figured out the easy part by hand, and I have the less obvious solutions by way of...

Solving for x? Solving for y? Solving for Q? I don't understand how that solves anything. Not being a smart-alec; I just don't understand.

Can anyone point me in the right direction for this problem? I can't seem to approach it from the right angle: Let A, B, C be real numbers such that A>0, B>0, AC-B^2>0. a. Prove that a number Q>0 exists such that Ax^2+2Bxy+Cy^2 \geq Q(x^2+y^2) b. Find the largest possible Q. I...

I was flipping through "Surely you're joking, Mr. Feynman" and I came across something he said that I'm curious about. I'll go ahead and quote it: "The book showed how to differentiate parameters under the integral sign - it's a certain operation. It turns out that's not taught very much in...

During a conversation I had yesterday, a math professor I occasionally meet with mentioned in passing, "and you might want to try to graph f(z)=e^z on the complex plane...hm...yes...anyway..." (where "z" is complex). So I sat down at Taco Bell yesterday to think about it, and, for a few minutes...

I think the title describes my question fairly well. Could someone please explain to me the difference between a field and a ring? While you're at it, feel free to explain the concept of "mod." I see these all the time when I'm reading, but I've never had anyone to tell me what they actually...

Oops, I knew I forgot something. I'm in the US, so anywhere in this country would be preferable, but I'm still open to overseas options.

I'm slightly confused...are you asking why 0!=1, or are you asking what the solution for "x" is in the problem ln(ln(ln(ln [x+4])))=e? In the case of the former, use that link. In the case of the latter, all I did was eliminate logarithms by using each side as a power of "e." ln(ln(ln(ln...

This doesn't really classify as a homework question, but this is the best place I could think of to post this. My apologies if I am in the wrong. I'm planning on continuing my math education all the way through the doctorate level. However, at the moment, I have only the barest of ideas as to...

Here's an interesting problem (interesting to me, at least) that my professor gave me last year (outside of class...it had nearly nothing to do with the subject we were studying). It's of two parts: The first part is fairly simple. Suppose you have the graph f(x)=x^2. What is the radius of...