@Daminark So I'm finishing up Analysis 2, and I'm trying to decide if its a good idea to take a graduate intro to manifolds, or just move on to other topics
So for an intro to manifolds, you need to have a good grip on multivariable calculus, and depending on how the course is done, possibly point-set topology
So I'd say to find out what book they're using and what the professor for manifolds is going to be assuming as prereq knowledge. If it's something you could self-study, consider whether you want to wait until you get other classes down first and handle CS for now, or make the jump
Like, given sufficient self-studying of integration I'd think it's totally reasonable to do a G&P class
reminds me of the two-line horror story I once read- "You can look ahead, left, right or back. But wherever you look, don't look above, she hates people looking at her when she's watching them"
Lol I mean, it's easier when you don't immediately associate a word with a concept. Right now the only thing I know that's in the neighborhood of algebraic geometry is that Zariski topology is a thing
does anyone by chance know the opposite expression for a quadratic scale? I am just using square root to calculate my scale value... just wondering if there is a specific expression for such a scale
Take the following ordinary differential equations.
$$y'(x^2) + y(x) = x$$
$$y''(y'(y(x))) = x^{x^x}$$
$$y''(5) + y(x) = x$$
Is there anything wrong with any of these as differential equations? I know that nonlinear equations can result from terms consisting of various derivatives of $y$ mult...
Alright, I'll look into that. C* algebras are connected with operator theory, right? Because I felt that the part of functional I liked the most was the stuff on spectra at the end, so that'd be fantastic
Apparently my topology puzzle from a while back (two disjoint compact sets that each have simply-connected complement even though their union doesn't) is already well-known
Hey guys, quick question. Suppose I have an overdetermined (n > m) system of polynomial equations f_1(x_1, x_2, ..., x_m) = 0 f_2(x_1, x_2, ..., x_m) = 0 ... f_n(x_1, x_2, ..., x_m) = 0
I've used numerical methods to find an approximate common root of (f_1, f_2, ..., f_n). Is there some way I can check if there is an actual root somewhere near this approximate root?
Now that Rotman is going all Galois mode it'll be tricky to follow but it's been damn helpful. Just need to pick up all the series stuff and then I'll prob revert soon to analysis
If we get some good problems in (geometric) measure theory I'll be sure to pass them along
One thing that I know works in the case of a single equation is interval arithmetic. If I let y_i = [x_i - epsilon, x_i + epsilon] for some suitable small epsilon > 0, then I can use interval arithmetic to determine if 0 \in f_j(y_1, y_2, ..., y_m)
But in the case of multiple equations it's possible that each of them is satisfied at some different nearby point
@Astyx oh yea I wrote that out: So we have two open subsets $U_1$ and $U_2$ that satisfy the following conditions: $(I\cap U_1)\cup(I\cap U_2)=I$, $(I\cap U_1)\cap(I\cap U_2)=\emptyset$, and $I\cap U_1\neq\emptyset$, $I\cap U_2\neq\emptyset$.
Just a quick question, we know that $B = A^{-1}(I - A^{-1}CD)$ can be expressed in $B = (A - CD)^{-1}$
Because distributive, but how come we can't do this:
$B = A^{-1}BC^{-1}(I-C^{-1}BA^{-1}D)^{-1}$ ?
It's just a friend's notes, I'm failing to see how this is not valid. Trying to help out some underclassmen by helping them make some linear algebra notes (for statistics) :)
Substitution doesn't seem like there's any wrong steps
Hi :) I have a tiny question: We know that given a subespace S with dim(S) = n-1, of R^n, we can extend S basis to a basis of R^n with a good choice of a vector. Can we do the other way around? Take a basis for R^n and reduce it to get a basis for S? I'm not sure, I think it's not true...
But there are so many possibilities, so if you imagine two subspaces with different bases, you can translate either of them up, but given a basis, you can't take any random subspace and say "We got our basis by extending this", you might've gotten it from somewhere else
Hi :) I'm stuck on a convergence in probability question and have read that there's a specialised form of Chebyshev’s Inequality for counting random variables: $P(X=0)\leq Var(X)/E(X)^2$. I can't find any other references for this online though?
So Laci asked Boller to forward the message to the math list host, with a description of his "Algorithms in Finite Groups" class and everything. The prereq is first quarter of algebra, and we apparently have to get a permission form from the department head
Take the following ordinary differential equations.
$$y'(x^2) + y(x) = x$$
$$y''(y'(y(x))) = x^{x^x}$$
$$y''(5) + y(x) = x$$
Is there anything wrong with any of these as differential equations? I know that nonlinear equations can result from terms consisting of various derivatives of $y$ mult...
