@Danu by looking at conjugacy classes in SL(2,C) and how their representatives behave as Mobius transformations, we see that every transformation has one of the following cycle types: (i) every point is fixed, (ii) one fixed point and uncountably many ∞-cycles, (iii) two fixed points and uncountably many ∞-cycles, (iv) two fixed points and uncountably many k-cycles for some k>1. If such a transformation stabilizes a finite set, that finite set must be a union of orbits.
Therefore, the permutation of the set of punctures must have one of the following cycle types: 0,1 or 2 fixed points and a bunch of k-cycles for some k. I suspect every such permutation group arises from my aforementioned recipe as the symmetry group of some polyhedron under SU(2) acting on the Riemann sphere by isometries.
Yes, you're right. But I was thinking something complimentary while in school. I'm pretty sure the multivariable textbook used is James Stewart in second year, I believe.
Hi I have a graphing question and I'm not sure what method I should start with to solve it: The math department needs to schedule 6 classes. 10 students have indicated the courses that they plan to take. What is the minimum number of time periods per week that are needed to offer these courses so that every two classes having a student in common are taught at different times during a day. Two classes having no student in common can be taught at the same time. Each class has 1 lecture per week.
@TedShifrin I thought we solved it! But it must have to do with the lowest digit losing a number and the second highest digit gaining a number. The lowest number with the property of the sum of the digtis being equal to 18 is 99. Every other number, due to the properties of 9 will be divisible by 9. Since the number is divisible by 9, it cannot be divisible by 3 prime numbers.
So, in my class we proved Lagrange multipliers specifically when $f:\mathbb{R}^n\to\mathbb{R}$ and $M = f^{-1}(0)$. Is there some way to extend this to manifolds more generally?
How do you solve: "Kayla adds the same number to both the numerator and denominator of the fraction $1/10$. Her resultingfraction equals $2/3$ What number did she add to both the numerator and denominator of her original fraction?"
@Dodsy Typically always ever try to do the algebra when you have something unknown in the problem that you have to compute.
what a meh essay
@Daminark Anyway, if that was what you wanted to do; sure, if write $N$ locally as level set of some $g$, then you can do the Lagrange multipliers on a coordinate chart. I am not sure if that's what you want.
@Balarka in the standard way of doing it, you'd have some known function that you could look at Lagrange multipliers with. Hypothetically, though, on a more general manifold you could have the problem that you could have various charts near the point
Five workers together can build a road in 20 days. Suppose every worker works at the same rate. If three workers work on the road for 10 days before eleven more workers join them, then how long total will it take to build the road?
I could be emailing a best friend of a decade and a half and feel just as out of place. I just have trouble peopling, but I like to leave my comfort zone now and again.
@TedShifrin Very true. It's very easy if you don't know the person, I've found. For some reason, the graph of discomfort vs. closeness is a bell curve for me.
@Zee Funnily enough, people said that computers are "just adding machines" a long time ago. I think the fact that it's advanced so far is a demonstration of the power of computing.
@Daminark you see, I lied, I don't care what society needs, but the issue is still there, why do you want to do topos theory? couse it's cool right now?
I'll need to learn more math before deciding which direction I want to take it, if I had to make as good a guess as I could now, probably something in the direction of algebra, likely enough trying to mash it (and logic) into complexity theory
Nate: I think Zach's question is rather hard, unless you interpret it loosely. You might try to give a function from $\Bbb Z$ onto $\Bbb Q$ without insisting it's one-to-one, or you might try to give a one-to-one function from $\Bbb Q$ into $\Bbb Z$.
@Zee using those terms precisely are a bit lewd for me, one time one of those professors subbed in a class I was doing on algorithms in finite groups, and he talked about it some. I liked that a whole lot
This is all a projection (linear algebra intensifies), when I take those classes I'll get back to you on whether they're my thing or not, but right now I'm starting to lean the general direction of algebra and theoretical compsci over, say, analysis
"Nate: I think Zach's question is rather hard, unless you interpret it loosely. You might try to give a function from ZZ onto QQ without insisting it's one-to-one, or you might try to give a one-to-one function from QQ into ZZ."
$\frac{1}{1}$ is the starting point, then given $\frac{r}{s}$, the left subtree starts with $\frac{r}{r+s}$ and the right subtree starts with $\frac{r+s}{s}$
