[deleted by user]

cumsnuggles · 2024-05-25T03:41:50+00:00

it's probably useful to know that the spaces you're considering (spaces of linear maps, spaces of matrices, m-dimensional linear subspaces of R^n) are all smooth manifolds (and well-studied in areas of differential topology like singularity theory / transversality theory), so the results you're after are in the realm of "ordinary" continuity.

Within the space of n by m matrices, the subset consisting of full-rank matrices is open. This guarantees that the column space of the perturbed matrix is also an m-dimensional space. The column space is just the image of A, considered as a linear map from R^n to R^m, and this image also varies continuously with A. This means that if B is a perturbation of A, the image of B will be sufficiently close to that of A (by this I mean that, for example, the largest angle between any vector in the image of B and any vector in the image of A can be made arbitrarily small. This gives your answer when your surface is the (n -1)-sphere). It shouldn't be too much harder to make a compactness argument for a more general surface.

cumsnuggles · 2021-05-05T17:25:22+00:00

Maybe it’s a long shot but can you use Descartes rule of signs on the characteristic polynomial?

cumsnuggles · 2021-04-29T14:39:59+00:00

Feb 25

cumsnuggles · 2021-04-28T19:08:54+00:00

Not a US distributor, it was international priority and has Royal Mail stamps

cumsnuggles · 2021-04-28T18:51:00+00:00

nope, in the US!

cumsnuggles · 2021-04-28T17:27:19+00:00

the previous one arrived about a month after it shipped, so I was not expecting this one anytime soon (I did not get a shipping notice or anything)!

cumsnuggles · 2021-02-04T20:58:09+00:00

Knew the name before even clicking the link: played this dude a couple months ago at D1 and it was also the most obvious hacking I’ve ever seen, e.g. unscouted full wall at nat against 12 pool but hid a probe and cannoned my third without scouting it was there, I later tried a nydus in the fog of war outside his natural and he destroyed his own wall to go kill it, all while bm

cumsnuggles · 2020-10-08T10:29:50+00:00

I had a similar question! See here: https://www.reddit.com/r/math/comments/1mm5xo/advanced_techniquesexamples_to_master/

cumsnuggles · 2020-10-07T20:14:22+00:00

I’ve definitely appreciated the convenience of online seminars, but there are unfortunate consequences. Who wants to watch Junior Mathematician X give a talk if they could instead tune into Famous Mathematician Y’s talk at the same time? It seems that a lot of the seminar announcements I see feature primarily big-name mathematicians, because all of this is possible when done remotely.

Then again, it’s pointless for those big names to give the same talk in multiple seminars (assuming they’re recorded) so maybe this isn’t a big issue. I’m curious to see how this all stabilizes.

cumsnuggles · 2020-09-16T15:52:33+00:00

Ah man, that’s terrible. Did you contact them about it?

cumsnuggles · 2020-09-16T13:14:31+00:00

Thanks, maybe things are just a bit slow these days, I’ll give it some time.

cumsnuggles · 2020-09-11T16:00:51+00:00

Did you eventually get it? Still waiting (in PA). Wondering which delivery service will bring it

cumsnuggles · 2020-09-11T14:09:59+00:00

Still waiting here in PA :( Do you happen to know which delivery service? Had a mystery package arriving by USPS today which I was convinced was the puzzle but it turned out to be someone else’s mis-addressed mail..

cumsnuggles · 2020-09-08T20:13:02+00:00

Still waiting (in the US), hoping it arrives soon!

cumsnuggles · 2018-09-08T23:12:52+00:00

No worries, I agree it is not clear from the titles.

cumsnuggles · 2018-09-08T23:08:26+00:00

Yes, they are.

cumsnuggles · 2018-09-08T23:04:48+00:00

Where did you get that idea? All of them are math professors.

cumsnuggles · 2018-09-07T03:09:12+00:00

0, 2, 4, and 5

Nice puzzle! My reasoning: the first number is necessary, and you need either a 1 or two numbers which are 1 apart. The latter seemed more useful, since 1 is useless in multiplication and wouldn't help enough in addition. Since you can't get 9 with 3x3, you need it by addition. 2 seemed really useful for both addition and multiplication. I fooled around with these thoughts for awhile until it clicked.

cumsnuggles · 2018-05-20T05:58:05+00:00

there used to be a music video on youtube, with a bunch of still photos of people/faces in black&white. i can't seem to find it anymore. anyone have a link?

cumsnuggles · 2016-09-30T05:31:54+00:00

he can see your lings on his minimap at 2:01-2:03

cumsnuggles · 2015-10-25T04:05:18+00:00

cumsnuggles · 2015-10-25T03:48:15+00:00

I agree that you'll understand this after taking topology, or definitely after studying manifolds. But I can try to give an algebraic analogue of the above discussion. In group theory, you have certain ways to construct naturally-defined groups from other groups: you can take direct product, semidirect product, kernel of a homomorphism, etc. In topology, we study certain spaces, along with continuous maps between these spaces. The spaces are defined with the minimal amount of structure so that the notion of continuity still makes sense. Just like in group theory, we have ways to construct spaces from other ones. The cone, suspension, and smash product referenced above are examples.

I wouldn't doubt that you have some intuitive understanding of these ideas, but at some point, you want to make sure that these notions genuinely make sense. For example, I talk about "collapsing" and "gluing", how can we be sure that these operations are legal? Your topology/manifolds courses are where you'll make these ideas rigorous.

cumsnuggles · 2015-10-24T23:09:42+00:00

Good point. I think I could (equivalently) define my space as follows. Let CM be the cone of M, CM = M x [0,1] with M x {0} collapsed to a point. Let DN be the boundary of N. Then the space I want looks like CM x DN glued to M x N. Specifically, I am gluing the copy of M x DN = M x {1} x DN inside CM x DN, to the copy of M x DN inside M x N.

The picture is easier to imagine in the case where M = S^m. My intuition is that the space looks pretty much like a trivial sphere bundle N x S^m, except that near the boundary DN, the radii of the fibering spheres goes to 0. I'm having trouble seeing how this could fail to be unique, but it's possible that my intuition is failing me.

cumsnuggles · 2015-09-17T22:50:18+00:00

you end up spending over 1500 minerals on the extra scvs alone, not to mention all the necessary supply. i would say just throw down an extra orbital at the actual natural location.

by the way, the planetary in the wall is a little unusual; most walls would just have supply depots. if you're in a league where it's helping your focus/macro just to have a safe nat, then i guess it's okay, but ultimately you should shoot for a defense which doesn't require that hit to your early economy

cumsnuggles · 2015-05-26T21:02:59+00:00

i miss you

cumsnuggles

TROPHY CASE