#serious-discussion

1 messages · Page 20 of 1

river moon
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because the interpolation problem only considers values that are in between the data points and completely ignores what happens after your data ends or what happens before the data starts

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interpolation tries to come up with a function that more or less looks the same as some unknown function on a given interval, it doesn't try to learn general behaviour of the data

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that's why you have hard limits in interpolation like $f(x_1) = y_1$ for some known $x_1, y_1$

fathom swallowBOT
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Transparent_Elemental

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next dew
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But the interpolation could span multiple points and run off the end of the dataset?

river moon
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it certainly does make a function that exists outside the data set region, but I'm saying that it's behaviour is up to chance and can have huge errors

next dew
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But it might be a good fit

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I mean like if you have overlap between splines

river moon
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chance of getting a good fit for prediction purposes is much higher in approximation methods than interpolation, you'll likely end up with a polynomial that goes straight up or straight down after your data ends

next dew
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And you calculate a spline based on the first few points instead of all points

river moon
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yes and you get a function that lies inside the data segment

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everything that's outside of that segment is basically up to random noise

next dew
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That's what I meant earlier

river moon
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I guess I don't understand what that has to do with predicting something then

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by definition to predict something you have to use current data to tell something about future time periods

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so you go outside your data set

next dew
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Like calculating part of a spline outside of the dataset

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Or finding a pattern in the splines

river moon
ancient flame
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opinions on computers?

deep mango
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dumb.

dense belfry
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🪨

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This emote of a rock is a computer

mint canopy
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Computers are just rocks we tricked into thinking, and if they can be tricked so easily, they must be morons.

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QED

zealous garden
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LMFAO

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that's what calculators are

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computers are rocks we taught how to think

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and if they can be taught, they must be pretty smart

mint canopy
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Nooooo nooo they're bad and I don't need to use them nooooooooo

bright hill
zealous garden
bright hill
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I think japanese people still use abacuses?

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I remember watching a documentary about how they use abacuses so much that they get literally engraved in their mind

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so like, they wouldn't need a physical abacus anymore

mint canopy
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Yes, there are japanese abacus (soroban) classes sometimes in japan

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Pretty impressive stuff

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I tried to learn the soroban a while ago, but it is simply so much practice for not terribly much reward

rare vortex
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Hey guys, this years i'm going to study to get a degree on general engineering, does someone knows where i can find maths/physic lessons to study them alone ?

manic ginkgo
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Khan academy or mit open courseware

rare vortex
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ty, does khan academy have specific course for each engineering branch or i must be careful while studying

manic ginkgo
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Yeah you should pick and choose the topics there. It had some good stuff for most pre-university maths and also for computer science

rare vortex
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Thanks a lot !

timid portal
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Would you all think it's reasonable to denote a finite sequence like this?: ${a_k}_{k=0}^n = a_0, a_1,\ldots,a_n$

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,texlisten

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word

manic ginkgo
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The bot is on strike

timid portal
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{a_k}, with subscript k=1 and superscript n

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I think I've seen sequences that don't terminate like this with infty in place of the n I want to put in the superscript

storm sage
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sure

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seems fine to me

frail lagoon
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Only minor thing is I'd use () instead of {}

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The former makes it more clear we're talking about tuples rather than just a set of elements and I'd say is more standard

storm sage
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wait we're talking about tuples?

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I thought we were talking about a function from {0,1,..,n} to some set

timid portal
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I don't necessarily want them to form a tuple since there aren't any other sequences in my setup, really just this one

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I'm looking for an excuse to be lazy is all

zealous garden
timid portal
zealous garden
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,, ( a \wedge b ) * = a \cdot (B*)

timid portal
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@fathom swallow $hello$

fathom swallowBOT
timid portal
# zealous garden ,, ( a \wedge b ) * = a \cdot (B*)

"Unfortunately we are still in the process of applying for message content intent for Paradøx and TeXit, so the bots are temporarily unable to read messages automatically. For now, you will have to mention the bots instead of using the prefix. This means that many features like automatic LaTeX compilation are broken for the time being."

zealous garden
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thank you!

fathom swallowBOT
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Couldn't find a member matching ryc @fathom swallow!

bright hill
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:/

neat lintel
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What do you guys think of taking graduate level courses as an upperclassman?

pure sun
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pretty common

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just do it

neat lintel
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I'm working on a project with a prof in the computer science project and he was talking to me about this being a viable option, but I don't know what the practical difficulty difference would be when I get to that point

neat lintel
pure sun
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if you have all the undergrad prereqs

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there's no reason not to

neat lintel
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I wasn't aware this was commonly done, that makes me feel a lot better about the idea

deep mango
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It's a good idea

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Take advantage of any drop deadlines / shopping periods you have

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To feel that stuff out

neat lintel
deep mango
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Yea for sure

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Well

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Depends on the exact circumstances but having a few grad classes is a great idea

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Bit easier to make connections with faculty in them for recs, too

pure sun
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i would say so

deep mango
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Dont take ur semester to do it tho

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Tank*

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Balance is important

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Some people throw on way too much at a time for no benefit

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Your instinct is better than any input we can give

solid blade
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how long do moderators usually take to respond to modmail?

ancient flame
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depends

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sometimes it's quick, sometimes it's longer

deep mango
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Schwarz: one syllable

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Bunyakovsky: four syllables

long epoch
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Lmao

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Just start giving things random names

deep mango
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naming things after people is dumb

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sure

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"inner product is 1-bilipschitz"

ember fog
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Would a laptop or tablet be more useful in uni as a physics (maybe statistics) student? I'm debating between the two and I've heard of the convenience in doing math problems on a tablet. However I'd also like to learn python and R. I have a pc already but would like something to take to uni.

shadow cloud
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i mean if you're going to be taking any classes where u write a lot i would recommend a laptop

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it comes down to personal preference ofc

near mango
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6÷2(1+2)

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What do you all think

pure sun
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i think it's 13

open aspen
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naming things after people does indeed suck but when you let people name things however they want you get whatever the physicists think is okay

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and that is just pure choas

iron osprey
brittle socket
bright hill
zealous garden
alpine kindle
zealous garden
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William K. Clifford developed something he called his Geometric Algebras; these have been given the name Clifford Algebras by the wider community, while a special subset of them have been re-endowed with the name Geometric Algebra

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Then you and I shall maybe get along

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where are you on that journey

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I'm currently reading Intro to GA and GC by MD Taylor

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It's a good intro if you're already familiar with linear algebra and vector calculus

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Ah yes, GA4CS

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I have it downloaded but I haven't really read through it yet, supposedly it's the best resource on CGA atm

stray kite
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how does one number corollaries? i list them immediately after a theorem right

alpine kindle
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yes

lavish kayak
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Laptops are nice for the convience of working out of your home.
You can get (sort of) the best of both worlds by buying a tablet with a keyboard and a stand

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You will maybe need to fiddle a bit to make it run your coding environments, or you can ssh back to your home computer and run everything there

manic ginkgo
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@lavish kayak hey, did you manage to solve that spherical tetrahedron problem?

lavish kayak
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I got a bit further but I'm still working on it

manic ginkgo
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Cool, it was a pretty nice problem and just curious what the solution’s going to look like 😁

vapid sentinel
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Can you tell me a beautiful quote by any mathematician which gives a lesson for life?

wispy dune
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"Point set topology is a disease from which the human race will soon recover."

delicate panther
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"This theorem will take quite a bit of effort to prove, and many of the steps will be left as exercises." Truly one of the quotes of all time, teaches us to exercise regularly using steps

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Tao, analysis, page 118.

unknown.png
neat frost
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This is a fun type of proof

lavish kayak
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Feels like I'm missing a final piece

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I sent you a friend request, I'll send you the answer when I have it

bright hill
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ma brothaa

neat frost
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I like these though

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Yes brudda flonshed

deep mango
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We had a proof for my probability class like this where it was split into 10 steps

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Like 2 of the steps were easy and the rest were all super confusing

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And then in the end I didn't understand why the theorem was true at all even though I understood why every step was true

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😵‍💫

bright hill
open aspen
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Honestly yeah

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In that case I feel there should be some exposition outside the proof giving intuition for how the pieces fit together to get to the big statement

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Or give all the pieces fully proven, leave nothing as exercise, but then leave as exercise how they fit together

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I actually like that sort of "exercise to the reader"

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Though leaving stuff as exercise is way more based than people give credit to

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(For learning textbooks, not for reference textbooks)

bright hill
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like, trying to develop your own intuition for why the proof (and the theorem) works

open aspen
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Idk, 10 pieces is a little too much to expect I think

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If it's like a 3 step proof fine

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Depending on how large the leaps are I guess

bright hill
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that's fair

open aspen
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If it's like, I give you a map and prove it's kernel is something, and leave you to figure out how that induces an isomorphism to something else, that's fine

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But at some point it stops being "I've given you the proof, essentially, you just need to put the pieces together" and starts being "I gave you a Lemma you need, the rest of the proof is 4 pages, go nuts"

deep mango
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I completely agree ofc

open aspen
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The French style stereotype is so funny to me

alpine kindle
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have you all heard the song "finite simple group (of order two)"

open aspen
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Yes, I love it

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The cleanest of bops the math world has produced

alpine kindle
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there are so many golden lines

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and really funny combinations of lines

storm sage
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omg

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this is great

dense belfry
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That song is almost as bad as the Bolzano Weierstrass rap

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Which is saying something

storm sage
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the bolzano weierstrass rap is great

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I need someone to write down the full lyrics to this finite simple group song though lol

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omg it's on genius LOL

manic ginkgo
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What about Lobachevsky?

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It’s been stuck in my head recently

wild shard
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what do you call the proccess that for GPS, where 4 sattelites transmit their location and time of sending and your phone uses that information to figure out where it is?

manic ginkgo
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Triangulation?

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No clue tbh

storm sage
wild shard
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it might be, but when I look up triangulation it works slightly diff-

wild shard
storm sage
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np!

wild shard
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I was looking for that word everywhere lmao

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and you just know what it is

storm sage
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Triangulation involves angle measurements instead of distance measurements

wild shard
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7ye

storm sage
manic ginkgo
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Ah cool, first time I heard about it

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Thanks

wild shard
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I thought it was triangulation and I was looking it up but it showed using angles when I knew the GPS doesn't use angles so I was thinking it was slightly different and wasn't sure

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thanks

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btw how did you know what it was called??

storm sage
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Haha

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Magic :-)

wild shard
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is that like a commonly used term in math

wild shard
storm sage
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Nah

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But in geology yes

wild shard
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u a geologist?

storm sage
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Nah

wild shard
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oh

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I guess you just know because you're very special ;>

alpine kindle
storm sage
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down with.. that

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we're down with that

alpine kindle
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the Bolzano Weierstrass rap is so bad it's good

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but finite simple group of order 2 is unironically amazing

bright hill
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oog found in the wild

unknown.png
dense belfry
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Nice

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Usopp based af

burnt dune
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post a problem that can be solved in an elementary way ( in context of its theory ) and an extremely overkill solution

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i always find those cool

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like for example sqrt(2) is irrational by fermats last theorem

storm sage
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wait how?

wooden flax
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i thought sqrt(2) being irrat was usied in the proof

alpine kindle
burnt dune
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yea i get it but i was just using it to give an example to what i mean

wooden flax
fathom swallowBOT
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In Vick's Tusk

714316705303625818.png
alpine kindle
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i don't think irrationality of sqrt 2 would be of much use to a result in langlands

wooden flax
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this works if n>3

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=*

river moon
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@fathom swallow tex $\sqrt{2} + \pi = \pi + \sqrt{2}$

fathom swallowBOT
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Transparent_Elemental

268952088564727810.png
river moon
wooden flax
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idk how trustworthy

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anyways just use rational root theorem lol

bright hill
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@sinful mica A=>B means if A then B

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and A<=>B means if A then B AND if B then A

sinful mica
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okay

bright hill
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sry, didn't want to interrupt the story lel

sinful mica
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no worries i like this stuff

worldly fulcrum
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A<=>B can also be phrased as “if and only if”

sinful mica
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i came across a solution to finding the intercept on a straight* line but my notation is confusing because i used weird variables

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but basically if you have two points (x1, y1) and (x2, y2) and you wanna find the x intercept, if we let c = -y1/dy then c*(dx) + x1 gives us the intercept

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but

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I wasnt able to organize my thoughts very clearly and my equation originally had a typo

tender tulip
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does the latex bot here support matricies

storm sage
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Yes

unique reef
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Mathematics major is it worth the effort? Discussion lmao

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Just want to know the opinion of math majors

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As I'm considering doing it, despite the fear of ending poor bhappy

stone ferry
sinful mica
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my friend came in clutch and explained my logic though, went full qed

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this is what i had originally

river moon
sinful mica
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keep in mind that "c = y1/dy" has a typo

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its supposed to be c = -y1/dy

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but they gave me a proof that it works

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look at this

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its beautiful

unique reef
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Or to computer science lol

manic ginkgo
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Nah machine learning be where the buckz at these days

sinful mica
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i hear everyone talking abt compsci being a great field to get into, especially ai

unique reef
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Yeah it is where there are the most high income jobs

bright hill
unique reef
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Specially data science

sinful mica
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also, i didnt realize that points and intervals are different

manic ginkgo
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There’s good money for the financey maths folk as quants in hedge funds too, way more pressure though

zealous garden
sinful mica
# sinful mica

i heard about "interval notation" on khan academy irt coordinates and kinda jumped to conclusions when trying to write what i meant here

sinful mica
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like what level of maths should i learn in order to safely go job searching

manic ginkgo
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Linear algebra

sinful mica
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I'm at highschool alg rn, what next

manic ginkgo
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Probability and stats

unique reef
sinful mica
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calc -> statistics -> multivar calc -> linear alg ->?

unique reef
manic ginkgo
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Tbh you’ll be fine in any science or maths subject

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It’s pretty easy to switch over to a software eng family job

zealous garden
river moon
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you're probably not going to understand big part of multivariable calculus and statistics without linear algebra

sinful mica
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i dont know what level it is

river moon
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same for statistics without multivariable calculus

unique reef
sinful mica
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sounds complicated

zealous garden
river moon
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LA is taught together with calculus

zealous garden
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It's pretty standard to teach stats after 1 course of Calc

sinful mica
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oh ok

unique reef
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Yeah you can learn calc and linear algebra together

sinful mica
zealous garden
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Yeah LA together with calc is best

sinful mica
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excitingg

unique reef
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Though I recommend learning the high school math really well for proper understanding calculus

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Don't skip steps

sinful mica
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noted

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It's slowly getting easier

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kind of

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not easier

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but I understand the stuff that was hard for me before

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like solving for a variable

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my brain has probably atrophied a lot so these little things that yall probably learned in middle school feel like a huge achievement to me

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It is a huge achievement for me, compared to everything predicating these moments

manic ginkgo
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You got this, ain’t easy learning things on your own

tender tulip
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$\sum_{a=0}^{N}{\sum_{b=0}^{a}{f(a,b)}} = \sum_{b=0}^{N}{\sum_{a=b}^{N}{f(a,b)}}$?

fathom swallowBOT
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Mizalign

315847860400816129.png
sinful mica
odd narwhal
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Yes, you can show that both these sums represent the same set of pairs

sinful mica
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ik a lot of notation uses greek

tender tulip
odd narwhal
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Ok...

tender tulip
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and pairs

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not sure if it was true

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thought i fucked up somewhere

noble tundra
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right?

bright hill
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that was from yesterday....

sinful mica
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friend 7*3 is 21 isnt it

frail lagoon
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It is

sinful mica
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isnt this using implied mutiplication

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fuck

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8

bright hill
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@near mango you got any alts by any chance?

near mango
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No

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Why?

sinful mica
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i struggle with basic arithmatic lol 8*3 is 24 tho

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wait

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no

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6+2(1+2) is 36

frail lagoon
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No

sinful mica
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3rd times the charm

frail lagoon
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Well I'd intepret that as 2 + (2 * (1 + 2))

bright hill
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that's a division sign lel

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not addition

frail lagoon
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Bruh

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Well then there's no point wasting time on it

sinful mica
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i need glasses whoops

bright hill
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2/2(1+2)

frail lagoon
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Deciphering badly formed collections of symbols is just a monumental waste of time

bright hill
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people should just use wolfram more

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,w 2/2(1+2)

fathom swallowBOT
bright hill
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there you go

frail lagoon
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Or just realise nobody uses division signs lol

bright hill
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lmao

sinful mica
#

1/2 is 0.5, 2*0.5 is 1, 6/1 = 6?

frail lagoon
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Ye

sinful mica
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good

bright hill
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yes

sinful mica
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i got* it

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oh

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wait

gray snow
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halo

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bro I just got ban from physik server

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imagine that

zealous garden
#

what for

sinful mica
zealous garden
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you can't ask me to imagine something with insufficient information

sinful mica
#

parenthases have priority

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1+2 = 3

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6/2(3)

gray snow
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not specified bro

chilly hull
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do not argue over this question guys

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this question was made intentionally vague

sinful mica
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but division and mutiplication have equal priority, and should be solved for from left -> right

zealous garden
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implicit multiplication is based though

chilly hull
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heres the thing though

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hang on i cant latex

zealous garden
#

lmfao

sinful mica
#

6/2(3) = 3(3) = 9

zealous garden
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disagree

gray snow
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its so bad

sinful mica
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or

zealous garden
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I subscribe to the convention that implicit multiplication (multiplication by juxtaposition) trumps multiplication and division

sinful mica
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6/2(3) = 6/6 = 1

zealous garden
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under this convention, the latter is the answer I am compelled to choose

sinful mica
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bc its hard to tell

noble tundra
chilly hull
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is it \frac{6}{2(1+2))}\ or \frac{6}{2}(1+2))

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i cant latex

zealous garden
gray snow
zealous garden
#

imo juxtaposition is a very strong indication of grouping

chilly hull
#

@gray snow dm modmail

zealous garden
#

and it's more efficient than parens

chilly hull
#

and ask for role

sinful mica
#

hmm

gray snow
chilly hull
#

is it $\frac{6}{2(1+2))}\ or $\frac{6}{2(1+2)}$

fathom swallowBOT
#

Cat Bread
Compile Error! Click the errors reaction for more information.
(You may edit your message to recompile.)

249995298632368128.png
chilly hull
#

help

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i cannot latex

gray snow
sinful mica
#

me neither

zealous garden
#

so I read 6/2(1+2) as $\frac{6}{2(1+2)}$

but 6/2*(1+2) as $\frac{6}{2} (1 + 2)$

fathom swallowBOT
#

wraithlord_koto

311328389351079936.png
chilly hull
#

why are we

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even arguing this tbh

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this question was obviously built to be ambiguous to troll people

zealous garden
#

obviously

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that doesn't mean we can't have a discussion

sinful mica
#

valid

zealous garden
#

it just means don't take it too seriously

chilly hull
#

true

sinful mica
#

vague notatation is

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hisss

zealous garden
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vague notation is the worst in the first place

sinful mica
zealous garden
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I'm looking at you tensors

sinful mica
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lol

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idek what a tensor is

gray snow
#

ye bro explain what is

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that diff geo shit?

sinful mica
#

i just remember it has something to do with vectors

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and matrices maybe?

zealous garden
#

A tensor is an object who can be described by a set of numbers with respect to a basis, these numbers changing according to the tensor transformation law under a change of basis

neat lintel
#

Careful

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The basis is the rich part

gray snow
zealous garden
sinful mica
odd narwhal
#

A rank (n,m) tensor is just a multilinear map with domain V^n x (V*)^m

chilly hull
#

i am kinda curious

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why is hammack putting what i think is combinatorics? idk

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in an intro proofs book

sinful mica
#

yes

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kind of

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i still like advanced maths tho :<

neat lintel
# zealous garden I still fear bases (to some degree)

I spent half an hour defining tensors for my problem seminar before the professor let me start the proof to Spivak’s DG exercise on the tensor product rule for derivatives and at some point I got tired and said a tensor is an element of a tensor space

zealous garden
#

the easy part to remember is that vectors are tensors, covectors are tensors, square matrices are also tensors

sinful mica
#

valid

gray snow
#

where exblain

zealous garden
chilly hull
#

is there a

odd narwhal
#

$\kappa$

chilly hull
#

super super super tensor

sinful mica
#

i really did not

fathom swallowBOT
zealous garden
#

a multivector is an element of a geometric algebra

chilly hull
sinful mica
#

but thank u

frail lagoon
#

Pain

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Pain

neat lintel
#

It makes more sense to define it the same way we did vectors

sinful mica
#

its just tensors all the way down innit

zealous garden
#

a k-vector is an element of an exterior algebra

frail lagoon
#

There are different senses in which different people use the word tensor

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Even if they are heavily related when it comes down to it

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Physicists seem mostly to focus on tensor fields in this connection

odd narwhal
#

Heh

frail lagoon
#

Hi

odd narwhal
#

Connection

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Nice one

frail lagoon
#

Ay

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thanks

odd narwhal
#

No I wasn't saying hi

frail lagoon
#

I know now aha

zealous garden
frail lagoon
#

Yes

neat lintel
zealous garden
#

I agree

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disgusting

frail lagoon
#

As someone who has had part of a degree doing physics and part maths this hurts lol

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And also when stuff is all in coordinates and no mention is made of coordinate free stuff

zealous garden
#

coordinate free is the best

gray snow
#

ye bro

frail lagoon
#

Ye

zealous garden
#

lolwhat

frail lagoon
#

That is a physicsy anachronism adaik

neat lintel
#

I have never heard that before

zealous garden
#

never heard of that

frail lagoon
#

I have only ever seen dyads and shit via physics

frozen merlin
#

mfw when "free" means no basis in geometry, and basis in algebra starebleak

neat lintel
#

The prefixes don’t even make sense for that

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There’s nothing 3 and 4 about tensors

frail lagoon
zealous garden
#

lmfao

frail lagoon
#

What sort of context are you saying free in in geometry?

neat lintel
#

Smh

zealous garden
#

that's lame

frozen merlin
frail lagoon
#

Oh fair lol

zealous garden
frail lagoon
#

The base field here

neat lintel
odd narwhal
#

Ground field

frail lagoon
#

Or ground field fair lol

zealous garden
#

I see

#

a multilinear map to the base field

#

are there any special properties about this map in general?

frail lagoon
#

But yes an important thing is that multilinear maps out of a direct sum of spaces correspond to linear maps out of the tensor product

frozen merlin
neat lintel
frail lagoon
#

So in this definition we're basically just working with elements of the dual of the tensor product

#

Makka pakka we stan

odd narwhal
sinful mica
#

angular momentum = rotation right? is it like the product of two vectors at right angles

#

or the sum,

zealous garden
#

angular momentum is the product of two vectors yes

sinful mica
#

okay

frail lagoon
#

Yeah fair I mean we are usually working w finite shit here anyway but ye

sinful mica
#

gotcha

frail lagoon
#

Mb

odd narwhal
#

No potatoI mean

zealous garden
#

it's the same kind of thing as torque/forque

odd narwhal
#

You consider the Cartesian product without a Vector space structure

frail lagoon
#

Oh yes mb ye

sinful mica
#

I just wanna make sure I understand what a vector is :3

frail lagoon
#

I don't really know why I even said direct sum

zealous garden
#

A vector is an element of a vectorspace (x2)

frail lagoon
#

Ye

sinful mica
#

could dx be defined as a vector or do we need 2 dimensions

zealous garden
frail lagoon
#

Not really anything to understand since it's just a definition

neat lintel
wooden flax
#

vectors can have any number of dimensions

#

*be apart of any dimensional vector space

zealous garden
#

dx works just fine in 1 dimension as an infinitesimal

sinful mica
#

that tedx guy was right math really do be a language

zealous garden
#

worse

#

it's multiple

neat lintel
#

dx dy are called tangent vectors of a manifold. They send you up into R^n with respect to the basis of partials d/dx and d/dy which allow you to get around the tangent plane to an abstract surface at a point

zealous garden
#

I don't disagree with this explanation

sinful mica
#

goes to google rq

neat lintel
#

It’s the intuitive version of why we can say they’re vectors

#

I’m not misleading you

zealous garden
#

it's right

#

there's just some deeper things to be discussed as well, and I don't want to take it there either

neat lintel
#

The tangent plane is a vector space there we go

#

Nothing much else to be said

zealous garden
#

yes it is

sinful mica
#

oh i believe you i just gotta figure out some definitions to really grasp it

zealous garden
#

and vectors are elements of vector spaces

#

the differential is a tangent vector in a vector space

#

therefore it is a vector

sinful mica
#

wait

neat lintel
#

All vectors of the tangent plane are called tangent vectors quigg

zealous garden
#

yep

neat lintel
#

This is bc the tangent plane is a vector subspace of whatever ambient space it’s in

zealous garden
#

just a vector, that is tangent

sinful mica
zealous garden
#

a subspace of the same dimension as the manifold, nuh

sinful mica
#

I'm so glad I binge pbs spacetime so some of this actually clicks

#

well, they go into qm and relativity from time to time and cover topics related to topology

zealous garden
#

you should watch an actual video/lecture series

neat lintel
#

Or open a book

zealous garden
#

book is ideal

neat lintel
#

The lectures are always worse than the book

zealous garden
#

but I'm staying in vein

#

everything is worse than the book

neat lintel
#

Unless that book is written by Hatcher

bright hill
#

what's wrong with hatcher's books?

neat lintel
#

He is the epitome of the “an introduction to this subject but for ppl who already know it” meme

#

My AG professor is literally introducing us to it before we get to read the book by Hatcher

zealous garden
sinful mica
neat lintel
#

Lee or Spivak

#

Those are my heros

zealous garden
#

for topology? nuh

neat lintel
#

Wdym

zealous garden
#

I don't have a lot of time with topology

#

I've read Mendelson

neat lintel
#

Lee is highly topological. Spivak is more geometry flavored but he will also introduce the topology to you

zealous garden
#

and I know what I've encountered in analysis and multivar settings

sinful mica
#

I've watched stuff by susskind if that counts

zealous garden
#

I know some topology stuff but I want more

sinful mica
#

do you recommend Calculus by Spivak

deep mango
zealous garden
neat lintel
#

Calculus on manifolds by Spivak is better left for after Rudin level analysis

deep mango
#

spivak's calculus is really good but it's probably better to just learn normal calculus and then analysis if you want to continue in math

#

what...

#

calculus on manifolds maybe

neat lintel
#

That’s what I meant

deep mango
#

yea

sinful mica
#

bear with me

neat lintel
#

If you want to do research read both

#

You gotta get used to the ideas

sinful mica
#

im basically this guy

#

like

#

I almost understand a lot of things

#

almost

#

it is in a lot of cases

neat lintel
#

I have approximate knowledge of three fields and I plan on keeping it that way

#

Any more fields will put a strain on what I can do

sinful mica
#

so I'll just have to work and ask questions

neat lintel
#

Diff geo/top, analysis, dynamics/PDEs

#

Anything else I speak about is just me treating it like a toolbox at this point

#

I don’t have enough time to learn how to prove the other fields from the ground up sadcat

ripe wasp
#

cocoomba what's your opinion on speedrunning rudin in about a month then reviewing all that material while doing other subjects like complex analysis and/or something like spivak com?

velvet dagger
#

Oh I only know three fields: STEM, Social Sciences, and Humanities

neat lintel
#

if you can’t do that you’re not ready

jovial ember
#

I only know three fields: Q, R, C

ripe wasp
neat lintel
#

Complex analysis will be a different flavor than real analysis too btw

velvet dagger
#

Hmm, chapters 5 and 6 will def go somewhat faster

ripe wasp
neat lintel
#

Honestly

jovial ember
#

You just aren’t committed to the grind

#

I don’t even use textbooks, I develop the theory myself

neat lintel
#

Sorry I’m not Tao

velvet dagger
#

Not forgiven tbh

zealous garden
sinful mica
#

math really does feel like witchcraft

jovial ember
#

What the fuck does that mean

ripe wasp
velvet dagger
#

Algebraic numbers?

zealous garden
#

Q^2 with a complex product

velvet dagger
#

Oh

jovial ember
#

It’s Q(i) lol

zealous garden
#

not how I think about it

velvet dagger
#

Huh

jovial ember
#

Okay

velvet dagger
#

C = R(i) so Q(i)... is pretty analogous

neat lintel
zealous garden
#

You're taking the Rationals and adjoining i to extend it right

jovial ember
#

…

velvet dagger
#

This is correct yes

zealous garden
#

I'm taking a 2 dimensional vector space of rationals, and endowing them with a product

velvet dagger
#

My guy

#

Those are the same thing

zealous garden
#

I know

#

that's my point

jovial ember
#

What the hell are you talking about

velvet dagger
#

"not how I think about it"
"that's my point"

Sound like conflicting statements

zealous garden
#

My point is that they are the same thing, but that the first (your) way was not how I think about it

ripe wasp
modest coral
#

is there anyone available to help me who has passed like 9th grade math cuz this is some bull right here man im in help-10

sinful mica
neat lintel
jovial ember
#

Lmfao

#

Stielijsdfis

#

I feel that

neat lintel
#

Stieltjes

ripe wasp
#

no idea how t spell it

neat lintel
#

I’ve typed it so much by now that my phone recognizes what I’m trying to do

velvet dagger
#

That's an actual mood

jovial ember
#

Me with Chmonkey

#

Lmao

ripe wasp
#

there are way too many consonants in that word

jovial ember
#

Using the Darboux integral when teaching analysis because idk how to pronounce Stieltjes

zealous garden
#

pog

velvet dagger
#

Why does all water I have in Europe taste so bad

neat lintel
jovial ember
#

Are you in Europe rn?

velvet dagger
#

Yea

wooden flax
#

Copenhagen

jovial ember
#

Where

wooden flax
velvet dagger
#

Now Budapest

wooden flax
#

ooh hungary

jovial ember
#

COPE

#

enhagen

#

Are you at conferences?

wooden flax
#

LOL

velvet dagger
#

I mean different waters kinda taste different because of the minerals and all. Kirkland is best water

#

Yeah automorphic forms summer school and conference

wooden flax
#

dami you should still try that kirkland alkaline water i showed you

#

its bussin bussin

jovial ember
#

You should try MB

wooden flax
#

MB?

jovial ember
#

My balls

velvet dagger
#

You walked right into that

jovial ember
#

Okay no more

wooden flax
#

:((

neat lintel
jovial ember
#

I can’t start the civil war again

wooden flax
#

im the DN king

velvet dagger
#

And: maybe Invictus, tbh I'm a bit worried about screwing too much with a good thing

jovial ember
#

Have u ever gotten Dami Invictus?

velvet dagger
#

But we shall see

neat lintel
#

Anyone remember 2010 arrowhead water

wooden flax
#

its just kirkland premium

wooden flax
velvet dagger
#

I'll def try it and get back to you

wooden flax
#

aight

velvet dagger
#

An attempt was made

wooden flax
#

and it was a success

jovial ember
#

No

velvet dagger
#

Actually Invictus you'd be surprised about something

wooden flax
#

hm?

velvet dagger
#

Guess where I had the best tap water ever

#

3 tries you won't guess

wooden flax
#

hungary?

jovial ember
#

Your mom’s bedroom

wooden flax
#

flint, michigan?

velvet dagger
#

I just said the water in Europe is bad lol

wooden flax
#

oh lol

#

michigan is in the US

#

fyi

velvet dagger
#

yeah but we know Flint lol

#

3 real guesses

wooden flax
#

hmmmm

#

do you want cities or like more specific

jovial ember
#

Morocco

wooden flax
#

LOL nice

velvet dagger
#

Not Morocco

#

But you can do cities or states

jovial ember
#

New Yahk

wooden flax
#

ill go new jersey

velvet dagger
#

NY is #2

#

NJ similar to NY so not quite

wooden flax
#

maybe oregon #1?

jovial ember
#

Oregon water sucks, WA water stays winning

wooden flax
#

theyre water is probably contaminated with marijuna so you will probably like it more

velvet dagger
#

Oregon no

#

Last guess

wooden flax
#

ok its gotta count

jovial ember
#

It’s gonna be a dumbass pun

#

Or he’ll say your mom’s bathroom

wooden flax
#

KANSAS

velvet dagger
#

That's correct actually

wooden flax
velvet dagger
#

Kansas dick fit in yo mouth

jovial ember
#

Kansas L fit on your plate

wooden flax
#

knew it

velvet dagger
#

Invictus is smart

wooden flax
#

ye

velvet dagger
#

I knew when you caps locked it

#

You knew where I was going

wooden flax
#

yup

jovial ember
#

TFW hard read the Kansas but fell for MB

velvet dagger
#

But yeah nah it's actually NY

neat lintel
#

Kansas water?

#

It has a lot of corn

velvet dagger
#

Kansas water taste good?

#

No it cannot 😦

#

Honestly even in Texas the tap water was like, fine

wooden flax
#

chmonkey have you met ryc irl yet

velvet dagger
#

But my mom hated it lol

#

In NY when we wanted to have water we just go to the sink

jovial ember
wooden flax
#

nice

jovial ember
#

When I visited NY for a visit

wooden flax
#

oo

jovial ember
#

Err

velvet dagger
#

But in Texas, we had this really fancy fridge from the previous owners where you could like

neat lintel
#

The tap water in Arizona is something that’s really really hit or miss

jovial ember
#

For a like school visit

velvet dagger
#

Get water and ice from the fridge

jovial ember
#

visited for a visit

velvet dagger
#

Which is kinda wild

wooden flax
#

Lol

velvet dagger
#

But that broke and we never fixed it lol

jovial ember
velvet dagger
#

Just started getting bottled water

wooden flax
#

i have that kind of fridge!

#

its super fancy

jovial ember
#

Yeah I do, and all my friends do too

wooden flax
#

like you can push up your glass and it gets ice

#

and water

jovial ember
#

I’m actually surprised that like nobody in NY has it

#

Maybe it’s region dependent

velvet dagger
#

Yeah I never heard of it in NY

#

Which is why when I saw it in Texas I was like

#

broooooooooooooooo

jovial ember
#

New tech

#

Dude Dami did you see the new Melee tech that Tafo was talking about?

velvet dagger
#

Like this is the beginning, eventually self-flying electric cars

#

I'm scared you're trying to get me with something here Chmonkey

deep mango
#

we also visited for a visit to the beach

jovial ember
#

And for the zoo

deep mango
#

that was very nice

jovial ember
#

Oh wait no, we didn’t

deep mango
jovial ember
#

Because you weren’t in NYC

deep mango
#

don't remind me

wooden flax
#

is columbia far from nyu

jovial ember
#

Tech this dick in yo mouth 😂😂

jovial ember
deep mango
#

i mean

jovial ember
#

Like 30 mins on the subway

deep mango
#

they're as far as you can get in manhattan, almost

#

without being ridiculous

jovial ember
#

Yeah that’s true

#

But like

deep mango
#

but manhattan is smol

jovial ember
#

They’re both in Manhattan

#

It’s real close

deep mango
#

it's about a 4 mile walk from nyu's campus to columbia's or something

jovial ember
#

Compared to most other unis

deep mango
#

and the subway is easy

jovial ember
#

Yeah

velvet dagger
#

Yeah I knew you were going for something

jovial ember
#

Does the red stop close to NYU?

deep mango
#

oh actually 5.8 miles

#

the red

#

yes

#

the red stops close to nyu

#

the 123

jovial ember
#

Cool

#

Yeah

deep mango
#

i wish people just called them by their colors if they didn't care which one you pick

#

i do want to do the walk up there at some point

#

sounds fun

jovial ember
#

I would’ve said red line if I remembered to

#

Sounds like an hour and a half walk maybe?

deep mango
#

could walk up the hudson maybe, i haven't been up past like 50th street on the hudson

jovial ember
#

2 hours

deep mango
#

where the intrepid is

#

i wonder if the intrepid has any free days coming up

#

that's a fun thing to go see

jovial ember
#

What’s the intrepid

deep mango
#

it's a big battleship

#

there's also a space shuttle on it

jovial ember
#

Oh

#

Whacky

deep mango
#

it's a whole museum

#

if ur into the american militaristic mindset

#

top notch stuff

#

but it's also pretty cool if you aren't

jovial ember
#

Ah yes, noted US military supporter Chmonkey

zealous garden
#

If it has a cool story I'm down

hallow blade
#

oh the 1 stops at christopher

#

never go to the west village forgot that existed lol

#

the only time i've been that way is when i walked from les creperie only to find out the 9th st path is closed past 11:50

wooden flax
deep mango
odd narwhal
#

Chmonkry supports the military industrial chain complex

peak tide
#

ascending chain or descending chain?

deep mango
#

Sideways

odd narwhal
#

Unbounded

#

Because it's unnatural

deep mango
#

😵‍💫

neat lintel
#

Semibounded

bronze wedge
#

Locally bounded

deep bridge
#

if you know how visual polynomial division/multiplication works pls dm me

brittle socket
#

"Visual polynomial division" hmmCat

tawdry radish
#

as opposed to invisible polynomial division

open aspen
#

as opposed to partially translucent polynomial division

hollow sundial
#

as opposed to stained glass polynomial division

brittle socket
#

Lol

velvet dagger
#

I feel like the proper "opposite" here is closer to audial polynomial division

open aspen
#

now here's the question

#

what is "opposite" when there is more than one descriptor

#

Is the opposite of "old nephew" "young nephew"? or "young niece"?

hollow sundial
#

neither. the answer's clearly turtle

open aspen
#

is the opposite of "visual polynomial division" "auditory nonpolynomial multiplication"?

#

and whats the opposite of a polynomial anyway

devout nacelle
#

The opposite is "not (visual polynomial division)"

potent plume
#

Why people asking what's the question and problems

stone ferry
#

"visual polynomial division" sounds like the kind of term that gets used in a school district to talk about a whole collection of topics that aren't connected really, but the curriculum wasn't written by a math prof.

velvet dagger
#

I'd say here that context should suggest which part of the descriptor is best considered as defining the ambient setting

#

And ideally that should leave more or less just one attribute which you can, if not negate then have another one which "principally contrasts"

#

Hence why I put opposite in scare quotes

storm sage
#

the ambient space here is visual polynomial division

#

the opposite is just the empty set

tender tulip
#

For any two lattices with a heterogeneous relation, we can consider two different functions between them that map any set to the set of elements in a lattice that are related to that set element-wise in the other (it’s also reverses the order & turns meets to joins and vice versa)

For group actions, a relation can be defined between the power set of the set being acted on and the lattice of subgroups by saying a group element fixes a set element. The group stabilizer of a subset and fixed set of a subgroup are these relations.

Naturally with any field F, automorphisms of F form a group action on the set of F, and we can consider the aforementioned lattices. I’m probably going to see how seperability, algebraicity, and galois-ity impact this structure

(Sorry for the terrible wording, once again, i did this mostly symbolically so it’s hard to translate into known terms)

#

also afaik every field automorphism is just a ring automorphism of the field, which is a commutative division integral domain

#

idk if the rule that any intermediate ring of an algebraic field extension is a field has anything to do with this

#

algebraicity causes finite orbits as well, finite extensions causes finite intermediate automorphism subgroups, but seperability seems, weird

untold sapphire
#

for the purpose of this joke i'm pretending your surname is R-module

burnt dune
#

when a non binary person decides to make a diet for themselves

#

when calculating their TDEE

#

what do they choose? male or female

woven whale
#

their biological sex

#

just like trans people

burnt dune
#

so does the trans thing "preserve" BMR

woven whale
#

not sure if you actually do biological modifications such as taking testosterone

burnt dune
#

yea thats why i asked

#

seems weird

#

500mg test is such a good first cycle

#

xd

deep bridge
#

if u know stuff about circle geometry and chords and central angles go to help 21

bright hill
#

sigh

echo tundra
#

bruh

dense belfry
#

@burnt dune if hormones are what matter than you use the associated sex to your hormone level

burnt dune
#

Okayyy

#

Makes sense

tender bobcat
#

1/3(1+2)4/5

#

Evaluate 🥺

woven whale
#

4/5

bright hill
deep bridge
#

-2x^2 + 4x + 5 is 3 term and degree 2 right?

woven whale
neat frost
bright hill
#

doesn't mean the joke is any less bad!

#

it's similar

willow patio
#

anybody ever noticed how Cannon-Thurston maps almost look like they have particles?

terse flax
#

No

#

Space group cm2

oak silo
#

Do you guys feel like a numerical methods class is needed for physics? Its not included in my curriculum, wondering if its worth taking up

limber thunder
#

I know of a physics program that does have a numerical methods class

#

especially numerical methods for ODE and PDE

#

but from what I've seen some physics majors learn these things on the fly

#

when it's needed for research and stuff

#

and often some library already does it

#

so you don't need to implement the algorithms yourself

oak silo
#

Okey cool ty! How i understand it rn is thats it basically about approximation methods right?

limber thunder
#

yep

#

things like Euler's method etc

oak silo
#

Ohh okey, thank you!

sick burrow
alpine kindle
chilly hull
#

same

tender tulip
#

For any cancellative monoid, the group of units (elements with an inverse) form a group.

Well, Z/nZ remove 0 under multiplication form a cancellative monoid, and have a group of units (coprime to n). Can this group be cyclic?

#

it works for odd prime powers but only 2^k where k = 1 or 2

brittle socket
#

How is that funny

chilly coral
#

It's not funny, it's just a fact

brittle socket
#

Well he put "Counterexample" so I thought he meant for it to be funny

bright hill
#

but also

#

very very dumb

#

lel

tender tulip
#

If we have a field of characteristic q

#

In it’s poly ring

#

are x^q - x and 0 the same poly in the ring or are they different polynomials element-wise in the ring

dapper badge
#

they are different as elements of the polynomial ring

#

namely, one of these is the additive identity and the other is not

#

elements in the polynomial ring are not characterized by the map they induce on the underlying ring

cobalt star
#

should i learn multivariable calculus before vector calculus

deep mango
#

Yes

cobalt star
#

ok

deep mango
#

Vector calculus depends strongly on other topics in multivariable calculus

#

You do plenty of partial differentiation and higher dimensional integrals

storm sage
deep mango
#

Yes

#

It's not the same polynomial

#

It's the same polynomial function

#

i.e. it is indistinguishable from 0 under evaluation homs

#

But these are different elements of F[x]

#

(does fermats little theorem work for all fields of char p? ive never thought about this)

storm sage
#

lol I was wondering the same

deep mango
#

Surely either the proof goes through or it doesnt

#

But i dont remember the proof monkey

storm sage
#

well if the proof doesn't go through it could still be true

velvet dagger
#

Fermat little theorem says that a^p is a mod p?

#

How do you translate that exactly to a general char p field?

#

It's not true that if k has char p, then x^p = x for x in k

#

Because over a field degree p polynomial has p roots

deep mango
#

Hmm

velvet dagger
#

And if k is a field you don't really want to think of elements of k "mod p", F_p is a subfield not a quotient here

#

So basically the answer is no

deep mango
#

Ok

#

So what I said is true for F_p[x]

#

And the premise is false for k[x] apparently, though i do not understand dami's argument

velvet dagger
#

Well, if you swap the polynomial now we can be talking

#

I'm saying it isn't true that "a^p = a"

#

But if you say "a^{p^k} = a" now we're talking

deep mango
#

Hmm

storm sage
#

what is the k in p^k...?

neat lintel
timid portal
#

This may be a silly question, but is a sequence thought of as a set?

brittle socket
#

Yes

deep mango
#

Well

#

Its ordered

timid portal
#

@fathom swallow Ok, so I should write ${a_n}_{n=0}^{\infty}={a_0,a_1,\ldots,a_k,\ldots}$ or something to that effect?

fathom swallowBOT
deep mango
#

No

#

A sequence is a function from N to a set

#

The function tells you what the nth term is

#

A set isnt ordered

timid portal
#

I see, so it would require more writing than what I want

deep mango
#

But a sequence is

#

Yeah

timid portal
#

Yeah

#

I wanted to just write a sequence in curly-bracket form and then just write out terms to keep it grounded

deep mango
#

You can use parenthesis to denote ordered tuples though if you want

#

Like

timid portal
#

Literally talking about the sequence 1, 11, 111, 1111, ...

deep mango
#

(a1, a2, a3, ..., ak, ...)

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Is what I would write

timid portal
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Interesting

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I didn't know people would want to write sequences as tuples, this is the second time I've had that recommended

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Unless if you're the same person lol

brittle socket
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Well, a sequence is a function (from N to another set), and (hence) a set of ordered pairs

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So that notation makes sense

timid portal
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Yeah but if it's a function from N U {0} to whatever, wouldn't it make more sense to write it as (1, a1), (2, a2), ..., (k, ak), ...?

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It's not nearly as appealing

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But that's what I thought of first lol

open aspen
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the subscript already holds that information...

brittle socket
timid portal
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Ok I see, didn't know that

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Thanky

brittle socket
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Oh and also, there is an equivalence / isomorphism from the "regular" definition of n-tuples and the function definition of n-tuples (for n>2 ) iirc
[the function def works for n>2 only cos you still need to define ordered pairs first]

timid portal
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The regular definition being (a,b,c,...) is an element of A x B x C x ... ?

brittle socket
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No