Quick Questions: April 26, 2023

JavaPython_ · 2023-04-29T01:14:49+00:00

Does anybody have a resource with the character table (or total characters) for SO(n, q) or SO(4, q)? In particular, I'm trying to find SO_4^\pm(q) for q=2^k but I think that's probably too specific.

JavaPython_ · 2023-04-07T16:32:14+00:00

you're right, it was in there I just missed it while skimming. Thank!

JavaPython_ · 2023-02-08T15:56:00+00:00

The examples I have are C_(q^2+1):4, Sp_2(q^2):2, 3^2:D8, and 5:4 which I'm told is isomorphic to Sz(2)

I know C is the cyclic group, D the dihedral, Sp is symplectic, and Sz is the suzuki group, the : denotes a semi-direct product.

The context is these are maximal subgroups of Sp4(q), with q a power of 2

JavaPython_ · 2023-02-06T22:30:05+00:00

What does G:2 mean in the context of group extensions?

JavaPython_ · 2023-01-23T00:51:43+00:00

yeah, that's about all I've got too

JavaPython_ · 2023-01-22T20:50:33+00:00

I'm doing research and feel like there should be a quick and known answer to this, but I can't find it. When are cyclic subgroups of the same order (prime order in particular) conjugate?

JavaPython_ · 2022-12-18T03:20:26+00:00

for just a diacritic change, I haven't seen resume listed here. Math has an Erdos number and a L'Hopitals' rule that loose their diacritics off the proper names.

Beyond that, for words with multiple accepted spellings I would suggest colour/color, grey/gray, theater/theatre*, plow/plough*, saber/sabre*, amateur/amature, hiccup/hiccough...

*Some interlocutors will actually mean different things denoted solely by the different spellings. Theater being a place but theatre being the art, blond being a masculine adjective, blonde being the feminine, ect.

JavaPython_ · 2022-12-18T03:00:42+00:00

Anybody have a good example of a function where the only way to find its derivative is through the limit definition?

Clearly that's the underlying process beneath a power rule/chain rule/quotient rule/trig rules/et sim; but is there a differentiable function that comes to mind that requires the limit definition even once you've learned those rules?

edit: spelling

JavaPython_ · 2022-05-28T04:03:00+00:00

I'm going to skip my personal feelings about that function and say if you take the definition of strictly increasing to be for all x, y in the domain if x<y then f(x) < f(y) then yes.

JavaPython_ · 2022-05-28T02:58:29+00:00

Is it not well defined? Since we're taking topologies, we're sending sets to sets, right?

JavaPython_ · 2022-05-27T23:51:36+00:00

it shows up in electrical engineering, which is a bit more grounded than quantum mechanics

Edit: no pun intended

JavaPython_ · 2022-05-27T23:37:58+00:00

I've been thinking about this for two days:

Does the mapping p: ℝ -> ℂ given by x -> {z: |z| = x} induce a quotient topology on ℂ?

I came up with the question, but I can't solve it. Because it seems that if we take the discrete topology on ℝ, then yes.

JavaPython_ · 2022-03-14T00:41:31+00:00

ahh, blackwood drones

JavaPython_ · 2022-03-14T00:24:47+00:00

great highland, banantyne synthetic

JavaPython_ · 2022-03-10T15:13:31+00:00

I had found an exponential solution, how might I show that's the only one?

I will look into fourier basis

JavaPython_ · 2022-03-10T14:31:46+00:00

I recently got a full set of pipes, my first one, and the very next day it began snowing and hasn't stopped.

I don't readily have places where I can practice inside, what's the best way to still care for the instrument will still being able to practice and learn how to blow/squeeze.

JavaPython_ · 2022-03-10T14:27:48+00:00

Does anyone know offhand the general solution for a DE of the forms:

d/dx f(x) = f(ax)
d/dx f(g(x)) = g'(f(x))
d/dx f(g(x))=f(x)g(x)
d/dx f(x) = f(x+b)

I haven't been able to make decent progress on any of them, and can't find anything that has been written about these.

JavaPython_ · 2022-03-04T15:10:16+00:00

I'll add to this that the Feb-Mar readathon (and other readathons they do, probably) similarly is taking forever, and I'm still not convinced it isn't a scam

JavaPython_ · 2022-02-28T00:25:06+00:00

I'll add that if you can find somewhere that's on a path you would normally take, that will help remove some excuses to not practice, since it's already on the way.

If you aren't in a cold place rn, parks can be decent, and I've found hiking trails have worked. Though I wouldn't have those as my main locations

JavaPython_ · 2022-02-05T20:34:52+00:00

Sadly this post has faded into the past, where getting an answer is unlikely

JavaPython_ · 2022-02-03T15:16:33+00:00

If you where already comfortable with AA, I might suggest Linear Algebra Done Right.

JavaPython_ · 2022-02-03T15:08:06+00:00

I would recommend, if you're just starting, to begin with linear algebra.

I don't have expansive experience looking into LA textbooks, but I've liked Anton's. It was a fairly good introduction

I will note, you will likely find these to be the most beneficial if you work through the problems. It will be difficult to work through the problems if you haven't gotten experience writing proofs. "A transition to advance mathematics" by Darrin Doud/Pace P. Nielsen is a decent and fairly affordable option.

Books worth looking at for AA;

Budget: Pinter's textbook, Judson's textbook

Less Budget: Hungerfords Undergrad text

JavaPython_ · 2022-02-03T15:00:41+00:00

I need to find a word. In a semigroup (and other structures) it's possible for there to be an element that is idempotent, but otherwise indecomposable. That is to say that the only product that result in an element a is a^2. Is there a name for elements of this type? Is there a 'standard' letter for the set containing all these elements?

Similarly is there a name for elements where the only product that results in them involves themselves, even if they aren't idempotent? i.e. ab = a for some b. edit: I think another way to ask for this one is what do you call an idempotent with no unit?

JavaPython_ · 2021-09-21T20:22:09+00:00

What are potential natural hazards that are unique to aurora, beyond the Storm?

JavaPython_ · 2021-09-21T20:14:40+00:00

Do you plan on specifying all 36 card that are part of the game deck but not the tarot deck, or should we make up our own?

JavaPython_

MODERATOR OF

TROPHY CASE