serious-discussion

[velvet dagger]

You're jumping back and forth a lot

Putting things at the end feels like it enables you a bit more to be like, okay here you don't need to think much about the underlying field, okay now we're talking R and C

[vast surge]

This geometric interpretation I feel can honestly be skipped. I never really found it especially illuminating, and it always felt like it was just done as an obligatory thing.

[velvet dagger]

Clear partition

[velvet dagger]

This is fair. Truly that might belong in a measure theory class

[vast surge]

It's not even really a R^n thing, it's just a R^2 or R^3 thing specifically. There's no geometric intuition for parallelipieds in R^37 or whatever because we can't visualize that

It formally still works if we have a notion of measure, but that's formalism that linear algebra students can't be expected to have and developing it is a bit of a diversion

I feel like very clearly stating assumptions in theorem statements can be helpful here by the way. If we have

Theorem 1.3.7. Let V be an arbitrary vector space over some field F. Then...

Corollary 1.3.8. In the case V=R^n, we see that...

[velvet dagger]

Oh wait a second I think I found a way to make the R and C case not an interlude

[vast surge]

It might get annoying, but at least when I learn a math subject that's basically how I do it anyway. Big theorem in a general case, then apply it to my toy examples and see how it behaves.

[velvet dagger]

Previously it felt like a random interlude in an otherwise smooth story

Buuuuuuuuuuuuuut

The first thing I'm gonna talk about in multilinear algebra is bilinear and quadratic forms

🙃

So the flow from here can be

• Bilinear and quadratic forms
• (R) Inner product spaces

So okay the way it's setting up is, let's say if it's in book form for simplicity (though I don't anticipate writing a book anytime soon, this is my mental model for teaching a class)

• Chapter 0 is preliminaries, the first bullet point
• Chapter 1 is generalities, so the next 3 bullet points
• Chapter 2 is coordinatization, so the last 3 bullet points
• Chapter 3 is bilinearity, so bilinear/quadratic forms and then inner product spaces (so the geometry kicks in)
• Chapter 4 is multilinearity (esp determinants)
• Chapter 5 is structure theory (eigenstuff, char/min poly, canonical forms, spectral theorem)
• Chapter 6 is analysis
• Chapter 7 is cool applications (SVD giving low rank approximation to matrices, maybe orthogonal polynomials, maybe a bit of error correction via LA over finite fields, stochastic matrices/Perron Frobenius/Markov chains?)

How does that sound Zorn?

Also @storm sage you I think would be interested/have good thoughts

[vast surge]

I still feel a little bit weird pedagogically about the placement of first iso and rank-nullity relative to eachother, but I understand the logic.

Also @JohnDS and @bronze pelican

[vast surge]

Where are norms? They don't really fit the idea of bilinearity, so probably not there. Are they being saved for structure theory? If students get well-acquainted with inner products first then "norm generated by an inner product" is a nice example to have.

[raven plaza]

Multilinearity in char 2

[velvet dagger]

Structure theory? How do they fit in there?

If anything I almost think maybe I should insert chapter 6 = analysis now that I think about it

And chapter 7 is cool applications

[vast surge]

Not structure theory, I think I was thinking they were originally chapter 4 but they weren't multilinear so I guess the next one

[inner wyvern]

got a silly question, if someone can please clarify

[velvet dagger]

I guess in principle there can be some talk about norms throughout but a full systematic treatment of norms might come later

Stuff like equivalence of norms in finite dimension, matrix norms, probably matrix exponential in fact

[vast surge]

If we do chapter 6 analysis, then norms would definitely fit there

[inner wyvern]

https://cdn.discordapp.com/attachments/880616249283973140/1245951048695152710/image.png?ex=665a9dd6&is=66594c56&hm=9723d5b287a19f61f12f28c0e63f2b5fea5aae916f038ccb312b54e3d8350d09&

[vast surge]

You might want to check out #❓how-to-get-help

[inner wyvern]

answer should be 3

sounds good

[vast surge]

If a book, I think a good absolutely batshit crazy idea would be to include a chapter on TVS. The goal isn't to use that for a standard course, but to have it there as reference material or for those kids who like the course to read the chapter over the summer or maybe for a project or... you know, whatever

[inner wyvern]

boom posted

[velvet dagger]

HAH maybe. Tbh this was mostly a thought experiment since Higher was interested in what I had in mind but it kept getting put off due to time

That itself came about since at some point I whipped up some quick ideas on how I wanted to present a first year calc class

[vast surge]

(TVS by the way stands for Tmean Value Stheorem)

[velvet dagger]

#discussion message that message, for reference

[vast surge]

Every time I do this I wind up reinventing baby rudin.

[velvet dagger]

Not in a ton of detail but yea

[velvet dagger]

This one I was a bit more conservative on than Baby Rudin wrt the topology, but I did more algebra

[fresh comet]

(I'm still here!)

just lurking this conversation very hard lol

[velvet dagger]

Oh I figured

I was just giving the context, like no I'm not quite writing a book this is just an interesting thought experiment you proposed

[vast surge]

Also because like aside from Bourbaki I don't really know of a good source on TVS specifically, the theorems are just all around the place in other chapters of FA texts

[vast surge]

We're not writing a book yet. Once we publish this thing, we'll put Axler and Hoffman-Kunze and all the rest out of business.

[velvet dagger]

Yeah tbh I don't think much about TVS other than Banach spaces and maybe their weak topologies

And in the latter I just say hmmm okay some of the theorems probably hold if you replace "Banach space" with "locally convex TVS" I think/hope

Though really I do need ot do more functional

[velvet dagger]

We have a crew on here that I think just has a good mind for the cognitive model for math

I'm not gonna say I have a mind for pedagogy because tbh I probably don't. My pedagogy is trial by fire

[vast surge]

I keep saying that I feel like in 5-10 years, with the people that we have here, I reckon this server is going to become a real powerhouse in the math world

[velvet dagger]

But the cognitive model for how pieces fit together?

I think yeah I'm decent at that for sure

[velvet dagger]

Polish cafe round 2 lez go

[vast surge]

Like we're not all there yet, but "yeah all these mathematicians met on a discord server as students" might just become the future textbook's version of

Yeah basically Polish cafe 2 electric boogaloo

[raven plaza]

New OpenStax?

[velvet dagger]

Honestly we have a nice spread researchwise too

[vast surge]

Or like Bourbaki group 2.0

[storm sage]

Yeah, it's quite unfortunate. Everyone should study what I'm studying.

[raven plaza]

We should be studying four majors

[storm sage]

Brain off right now

[velvet dagger]

Actually speaking of what people are studying

[raven plaza]

Is this an analysis oriented course

[storm sage]

Would be fun to include Lotka Volterra model

And also least squares regression

[velvet dagger]

John will be ecstatic to know that at this Philly conference I'm at, my talk is listed as "Geometric Group Theory/Dynamics"

[vast surge]

Right now qual prep and FA on the side. I should also probably try to teach myself AT and manifolds or ODE/PDE for one of those quals but

[velvet dagger]

Idk Lotka Volterra but least squares is a good inclusion yeah. I guess I forgot about it since idk much and my impression was that it's just

Oh

Distance is L^2

Minimize that

Geometry

gg

[storm sage]

Lotka Volterra is predator prey dynamics haha

Linear system of ODEs and all

[velvet dagger]

It doesn't stick out super strongly in my mind

Oh, I didn't quite wanna include ODEs in here, I assume people don't necessarily know that

[vast surge]

I think it's worth including an aside on just in case

[velvet dagger]

Damn I should call her to say RIP

[vast surge]

Sorry hold on one sec

Nevermind you already saw I don't need to mod ping

[solid yarrow]

hello

[vast surge]

Maybe don't make fun of people with aids though? That's just a douchey thing to do

[velvet dagger]

Ugh he didn't respond in time before I got bored

So I just whacked him

[solid yarrow]

I wanna do math. But have to do physics instead :(

hml

[velvet dagger]

Born to do math
Forced to do physics

[velvet dagger]

Also not necessarily

[raven plaza]

Study the parts of physics that turns into math

[vast surge]

I reckon like, we could write a book with a fairly large number of optional sections. There's going to be LA classes where everyone in the room has taken calculus, and so introducing basic ideas of systems of ODEs - even if just for a lecture or as optional side reading - wouldn't hurt

[fresh comet]

then we can start recommending our lin alg book in #book-recommendations

[vast surge]

Just linear algebra

[velvet dagger]

It's kinda "I like almost everything so I want to include almost everything" lol

[solid yarrow]

Study all the math to understand physics

[velvet dagger]

The chapter stuff I gave was an outline but I wanna include as many points of view as possible

[vast surge]

Born to do math
Forced to do bio
The @native oriole story

[storm sage]

there's already too many linear algebra books

[velvet dagger]

Gram-Schmidt is taking a basis and turning it into an orthonormal basis
It's also a deformation retraction of GL(n) to O(n)
It's also QR decomposition

Also if this is a class I am definitely gonna have people do stuff on computers

Maybe compute a few examples by hand to make sure they get the point

But they're learning numpy

Or matlab or whatever else

[vast surge]

Introduce fourier series in the section on change of basis as an optional section

[velvet dagger]

I was gonna include it in the inner products section

Which comes after

[wild lantern]

This is incredibly based

[vast surge]

Ah yeah that also makes sense

[velvet dagger]

But yeah I won't just do R^n with dot product

I want to talk a bit about Fourier series and about orthogonal polynomials

[solid yarrow]

Physics is a subset of Math

[velvet dagger]

Nah

Physics is empirical fundamentally

No mathematical statement's validity depends on the results of an experiment

Truth in physics relies very crucially on experimental evidence

[solid yarrow]

So... no concrete evidence.

Handwaving moment

Yay!

[vast surge]

Counterargument: String theory

[velvet dagger]

I mean

If string theory turns out to make a concrete prediction that's disproven

It becomes dogshit physics

With no value

So it'll have mathematical value alone and cease to be physics

[solid yarrow]

It proves... that Dami is a physicist and not a mathmetician

[velvet dagger]

If turns out to be correct

Then it'll be a claim that a mathematical model correctly overlays onto a physical system

[velvet dagger]

Wha

[vast surge]

Ha you're a physicist

[velvet dagger]

If anything I'm being an armchair epistemologist right now smh

[vast surge]

That doesn't make you not a physicist.

If anything that just confirms that you're a physicist.

[velvet dagger]

But epistemology is much more math than it is physics smh

You can't make me use bra-ket

I won't do it

[solid yarrow]

?

[bleak quartz]

May anyone suggest any books which discuss functions in the perspective of set theories and linear algebra? homomorphisms, linear maps, transformations and such please someone

[vast surge]

If you scroll up you'll see that me and amin are writing one now

[solid yarrow]

Have you tried searching in #book-recommendations ?

[solid yarrow]

A book?!

[raven plaza]

Imagine if the book is like 30% linear algebra and 70% applications

[velvet dagger]

It might be

[vast surge]

So... most LA textbooks?

[bleak quartz]

what branch ?

[solid yarrow]

Even better 20% linear algebra and the rest ist just plain analysis.

[velvet dagger]

Thing is there are too many cool linear algebra applications

I mean the actually cool stuff

Error correcting codes, orthogonal polynomials, Markov chains

Maidenful applications you feel me?

[solid yarrow]

Idk. Never really enjoyed linear algebra all too much till now.

[velvet dagger]

Until I started talking about it?

Dam I am a good salesman aren't I

[vast surge]

Book title: "Introducton to Linear Algebra"
Table of contents:
Chapter 1. Linear Algebra
Chapter 2. Banach and Hilbert Spaces
Chapter 3. Bounded Operators
Chapter 4. Spectral Theory
Chapter 5. C* and von Neumann Algebras
Chapter 6. Unbounded Operators

[solid yarrow]

No. I mean like the lectures and stuff were like meh

So I didn't really activate my self study interest mode

[solid yarrow]

Yes!

I want a signed copy though

._.

[fresh comet]

calling this "Introduction" is so hilarious. I approve!

[vast surge]

This also feels like the wrong order

[velvet dagger]

Yeah unbounded should come first

[solid yarrow]

Put the riemann hypothesis in the exercises

As an appendix problem of some sort

[vast surge]

Every problem will be a cleverly disguised open problem

Arbitrary exercises will be starred to indicate that they're harder.

They're all hard.

[solid yarrow]

lol

From the contents I know like 40-50 %

I guess

Don't know if I just translated them wrong

Might be more

[vast surge]

Dami's is real. Mine's a shitty joke; the idea is that it's actually a functional analysis textbook

[solid yarrow]

I was wondering what Neumann algebras were

lol

Never heard of it

[fresh comet]

Dami is actually going to write this book?

[vast surge]

Would it be a crazy idea to try and shoehorn some representation theory into an intro linear algebra course?

[vast surge]

No.

[solid yarrow]

:(

[vast surge]

But it's a serious proposal for what he'd do if he ever teaches LA

[velvet dagger]

Probably a bit crazy

I mean the thing is how you'd do things depends a bit on the surrounding classes

[fresh comet]

yes, I asked him to make this proposal

[solid yarrow]

We definitely need a math book from Mathcord

[velvet dagger]

My kinda hot take is that if I were designing stuff from the ground up

I'd actually want a fair bit more algebra in first year than is typical

[jolly linden]

Huge sale on Springer right now‼️

It ends in like 8 hours or less

Quick question guys - does Springer let you print out the Ebooks i buy from them??? Or it doesn’t offer pdfs, so I have to read them from their site???

Huge thank you if you know and can answer🙏

[vast surge]

Don't pay money for ebooks

That's just getting ripped off

[solid yarrow]

piracy

[vast surge]

🏴‍☠️

[solid yarrow]

true

That's the point where you ask zorns

[vast surge]

Yeah I don't understand why algebra is often introduced so late. Especially something like an intro algebra course at the Pinter level or so could easily be a first year course at the level of calculus or LA, and yet it's often taught in the 3rd year of an undergrad degree

[velvet dagger]

So what I would probably do if you really gave me full control ground up is this

I would want the group theory surrounding permutations and arithmetic, and then enough ring theory to show that if corporate wants you to find the difference between Z and k[t], the answer is "They're the same picture"

[raven plaza]

Wait why are Z and k[t] the same

[velvet dagger]

Really what I mean is the fact that they're both Euclidean domains

And the story that ED => PID => UFD

[vast surge]

All euclidean domains are isomorphic.

This is a famous result called "Daminark's Theorem"

[vast surge]

Oh yeah dami have you seen my proof of the largest composite number

#discussion message

[velvet dagger]

[raven plaza]

I wonder if you can do addition on N^N in a way that coincides with the addition (Z^+, +) on N^⊕N = (Z^+, ×)

[vivid halo]

they obviously give you pdf access but it's a waste of money

literally just download them for free like everyone else does

[solid yarrow]

But @vivid halo what if you don't find the book you're looking for?

[vivid halo]

this basically never happens to me

[solid yarrow]

Can't agree on that part.

[vivid halo]

skill issue

[solid yarrow]

[vast surge]

This only happens if you're trying to get a book that's been out of print since the 1970s, or if you're trying to get the brand new edition of a pearson book that came out several weeks ago.

[visual breach]

Wdym, you mean when you cannot find pdf?

[fresh comet]

fwiw, there have been cases where I have been unable to find biology textbooks to download on my friend's behalf

mostly because biology books tend to get a new edition every couple of years, and the newest editions simply haven't been... freely distributed across the internet yet

[visual breach]

Yeah it sucks when that happens

[steep mountain]

its a specific C*-algebra, specifically the ones with a predual

[dreamy ore]

fascinating

this is the worlds oldest sundial, from ancient egypt

and u can see daytime is split into 12 hours

what reasoning could they have had for this

the babylonians used the a unit of time which was about 2 hours (thus daytime having 6 units)
this makes sense because the 12 zodiacal signs rotate once per day
so u have 12 signs per day, 12 units of time ("hours") per day

12 being from... their sexagesimal system i guess?

they split the year into 12 equal segments of 30 days each (ignoring the last 5 days) and then that naturally gives you 12 zodiac signs based on which constellation the sun resides in

i wonder why the egyptians decided to split daytime into 12 hours

especially since their zodiac system had 36 signs "decans"

maybe it was arbitrary

These predictable heliacal re-appearances by the decans were eventually used by the Egyptians to mark the divisions of their annual solar calendar. Thus the heliacal rising of Sirius marked the annual flooding of the Nile.

This method led to a system of 12 daytime hours and 12 nighttime hours, varying in length according to the season. Later,[when?] a system of 24 "equinoctial" hours was used.

hm

doesnt explain how the 36 decans gave rise to 24 hours

but apparently they did

[solid yarrow]

Sometimes I search for a book and I don't find a free pdf for it.

[dreamy ore]

you try harder

[solid yarrow]

It's not like I don't try ._.

[dreamy ore]

also fascinating

the first decan according to the egyptians was called sopdet

which is their word for sirius

this is apparently equivalent to the first 1/3 of cancer

but sirius is just.. so far from cancer

strange

[bronze pelican]

Intimately related

[solar hawk]

Hello.

[vast wraith]

[visual breach]

nG might help you overcome this skill issue.

[lofty mango]

I can't live life without free PDFs

[pure hollow]

Hello

[novel pebble]

hello

[novel pebble]

are you talking about zlib?

[zealous tendon]

#help-31 message please help!!!

[lofty mango]

Yeahh and few more

[novel pebble]

few more? are there another things?

[zealous tendon]

What that bruv

[lofty mango]

Yeahh there are

Honestly internet is vast

[wintry heart]

can anyone teach me matrices?

[dreamy ore]

helo

jens

[vast wraith]

hi hi

[vast wraith]

one nice thing about this figure is that it is quite easy to draw freehand, by first dividing into four and then each section into three

i’ve no idea how they would have done it though

oop but i promised myself i would go to uni today so i have to get going right about now

[north topaz]

bai

[vast wraith]

i have officially left for uni mwahaha, but will take my sweet time getting there

[vast wraith]

i have officially reached uni mwahahaha

time to sit around doing nothing

[north topaz]

cool

why did you leave for uni btw

[vast wraith]

as an experiment

[north topaz]

lol wut

[vast wraith]

to see if i could

[north topaz]

I mean like to study at uni

or what

[vast wraith]

no, i set realistic goals

and occasionally overshoot

[north topaz]

oh

[lime pawn]

you good? I need you.

[north topaz]

what the hell man

[acoustic rivet]

bat man

[lime pawn]

srry, ⁠#help-45 needs help. I'm stupid and don't understand it

If you don't, I can get north

[stark thistle]

lol

[tulip void]

what tablet should i buy for math surface ipad or samsung

[twilit monolith]

i used a samsung

[sterile juniper]

Today minecraft is unplayable thats make me leave video games related

I think I should continue my scientific work

[bitter ember]

yea we have had issues and there is a huge power outage close to where i live

something is up

[sterile juniper]

Character development

Haha

[bitter ember]

what kinda work you got?

[sterile juniper]

Students

[sterile juniper]

Owh sorry

Hmm

Derivative influence for science

Its simple

[bitter ember]

i barely know derivatives

just finished algebre I

algebra*

isnt deravitive d/dx?

[sterile juniper]

In college?

[sterile juniper]

Yup

[bitter ember]

me smart

[sterile juniper]

In physics known as velocity and acceleration

Derivative application

[bitter ember]

cool

I am going into physics next year

atleast half of it what I heard is about quadratics

and I actually liked quadratics

so im excited

[sterile juniper]

Quadratic is foundation

[bitter ember]

fr

[sterile juniper]

You learn trigometry?

[bitter ember]

thats also next year

[sterile juniper]

I assume you are grade 9

[bitter ember]

im taking tons of stem + math classes

yea

so next year is

Accelerated Geometry
Accelerated Algebra II
Accelerated Trigonometry
Intro to Probability & Statistics
Accelerated Chemistry
Astronomy
Electronics II: Physics

so im just planning to take alot of stem

[sterile juniper]

Seems college

Hold on

Owh no doesn't matter

I learn above grade 11 too

[neat lintel]

just looking for some general advice but would it be best for me to study algebra 1 or geometry over the summer?

[north topaz]

are you at a STEM magnet school?

[bitter ember]

no

just a regular high school

[north topaz]

intereesting

[north topaz]

you can choose either, but algebra 1 is better if you want to study calculus in the future

Euclidean geometry is beautiful though
I mean you didn't specify, Cartesian geometry also definitely helps with calculus also

otherwise called coordinate geometry (but that's a bit of a dumb name cause there are many different types of coordinate systems)

[north topaz]

oh wait so what are you going to do in physics, cause it's called electronics lol

also astronomy is pretty cool
not everywhere is like the US where they offer so many course options

cause your high schools can have like 2000 students or something, so there's that economy of scale

[bitter ember]

Physics in Electronics correlates with Amperage, Volts, and how they travel quickest as possible

[north topaz]

that would be unthinkable in other places to have so many

[bitter ember]

it also reveals the thermodynamics behind it

[neat lintel]

Maybe I'll try a bit of both I will need it and I plan on taking Calculus sometime later I'm probably going to focus on algebra for now tho, thanks.

[north topaz]

ah okay so electricity

I mean I thought you were doing Raspberry Pi and stuff

lol

[bitter ember]

technically im going to be in Pre calc next year

[north topaz]

no worries

[bitter ember]

since Accelerated Algebra II explains integrals

[north topaz]

cool

that's unexpected

most classes start with differentiation first

[bitter ember]

Integrals - Differention - Limits - something

thats how it goes

[neat lintel]

Any suggestions for like videos or websites for me to learn, I plan on doing virtual next year and I just wanna be able to find like notes and good explanations.

[north topaz]

isn't that just straight calculus then

[bitter ember]

yep

pre calc briefly explains the first 2

after sophmore year

junior year will be

uhhh

[north topaz]

https://www.youtube.com/watch?v=MHeirBPOI6w&list=PL0o_zxa4K1BUeF2o-MlNpbRiS-oE2Kn6J

org chem tutor and prof Leonard on YT for videos

Khan Academy for practice

[north topaz]

also from around video 110 they start covering algebra 2 content

[neat lintel]

oh cool good to know

how long do you think it would take for me to do algebra 1?

[bitter ember]

AP Probability & Statistics
AP Chemistry
AP Pre-Calculus
Accelerated Physics
Math Investigations I

my junior classes

stem

[north topaz]

it really depends

[bitter ember]

what grade you in?

[north topaz]

if you can keep up the practice I'd say 6 months, well it always takes longer than you think

[neat lintel]

I'll be starting 8th next year i just wanna try and skip some classes if I can

[bitter ember]

It will definately take you 6 months

[north topaz]

basically assuming that the standard curriculum of 9 months in a school year is 3 months of bloat

but like it's important to learn this stuff well and thoroughly, like understand why things work like that

[neat lintel]

yeah thats what ive been doing outside of school

not what ive been taught

[north topaz]

not all of the topics will be carried on to further study but they're kind of good to know, it's a bit silly to justify it like that but yeah

[bitter ember]

Most of Physics relevate around Quadratics, Calculus, and Trigonometry

[north topaz]

also I like this playlist cause there's some revision on fractions

[bitter ember]

but Physics is a VERY complicated thing

[north topaz]

percentages, number problems before you start on linear functions

[north topaz]

exactly

yeah I mean all the physics you are learning will be an approximation of the truth

but as you learn more and more, the approximations get closer to reality

like a limit tending towards some value

but never reaching it

[bitter ember]

rate this AP Physics question

aw shoot

it wont let me send images

:c

[neat lintel]

This is not true

Wait oh it has calc

[surreal bison]

why do people think sending a image of the question verbatim is a good way to ask a question

[fresh comet]

a lot of the time, it's because they don't know how to properly ask a question

as in, they cannot figure out exactly what it is that they want to ask

[serene heron]

I think it's better than an hour of xy problem though

[fresh comet]

xy problems are awful

[surreal bison]

not just that but also

what's the misunderstanding?

[neat lintel]

what are xy problems?

[surreal bison]

what part did you struggle with?

instead it's like "ah! problem! do it for me!"

[serene heron]

person wants to do Y and ends up trying to use technique X but can't get it to work, so they ask about X

but don't mention Y

so you end up trying to help them with a really weird specific thing X, which might not even be the right thing to be doing in the first place, rather than actually helping with the problem Y

[fresh comet]

allow me to present this gem

(this was yesterday)

[neat lintel]

TIL theres a term for that, cool

[serene heron]

it's a term from tech support iirc

[fresh comet]

!xy

[quasi jetty]

Please show the original problem, exactly as it was stated to you, with the entire original context. A picture or screenshot is best. If the original problem is not in English, then post it anyway! The additional context might still be helpful. Do your best to provide a translation.

[surreal bison]

I disagree about picture or screenshot but I imagine that empirically it works better for people that are horrible at asking questions

but like i don't get how you don't gain this ability to ask the question

like

[fresh comet]

I want to see Xela go into the help channels for a day or two

[surreal bison]

surely one notices the place that one stops understanding

[fresh comet]

what would be the expected outcome

[surreal bison]

i did for like a very small period of time, less than a day

[fresh comet]

and what happened

[surreal bison]

took a long time to determine what the damn question was

[fresh comet]

yes, that happens a lot

one needs a good amount of patience to help people in those channels

[surreal bison]

but like how does one not know how to ask a question like this

it just seems automatic to me

like i should obviously provide enough information for the person answering to understand what's going on and for them to know where i got stuck

all i need to do for this is to state the question and then go "and i didn't understand [bla]"

Let's take something valley helped me with a while back.

Fulton and Harris at one point stated "thus, the representation is determined by the character on the cartan subgroup"

after writing down things on a board and looking again at the thing preceding that statement i managed to reduce this to a linear algebra problem

it hinged on "is the matrix you get from this invertible?"

[visual breach]

Oh good debate

[surreal bison]

i gave some details (not enough to in the end actually finish the proof, because i didn't forgot to mention an important restriction on these matrices and thought that the other restrictions i mentioned were sufficient) about the matrices in question

Valley suggest gershgorin, using the example matrix i provided, and i believe he also prodded me here about whether it actually was diagonally dominant so that gershgorin could finish it

upon reading this i realized that the restriction i forgot was important and finished it

Now, imagine that instead I just said

[visual breach]

It's an earned skill I think

Ah right. You are forgetting the most important factor

Laziness

[surreal bison]

pretend the underlining and writing isn't there

[fresh comet]

there's a lot of people who are either too lazy to ask properly

[surreal bison]

imagine i just posted this and said "halp"

[fresh comet]

or else they are so confused that they don't know what to ask

[fresh comet]

and they are just looking for someone to hold their hand

[surreal bison]

But I only started asking questions like this when I started discording on mathcord!

I know I am better at introspection than most

And I know the kind of things someone would need to answer the question

[visual breach]

Hmm, then I guess it hinges upon how much effort one will put.

Many just like to leave things out to someone else, being hopeless, wanting others to help them up to the end

[fresh comet]

to be honest, the users who ask proper questions are the ones who already have some idea of the problem at hand

[visual breach]

Also number of times people just asked for answers

[fresh comet]

the ones who just post a screenshot or picture and say "help" usually have no idea what's going on

[surreal bison]

Like generally I give the definitions of things and especially anything that I'm not sure is standard.

Like
"Suppose we have a semisimple finite dimensional lie algebra over an algebraically closed field of char 0. We can do the root space decomposition like [bla] where bla is bla.

Now, it is claimed that [statement]. But I have no clue why/I tried this and got stuck/isn't this literally false"

[solemn pawn]

are there vcs

[fresh comet]

that's usually how questions are asked in the advanced channels, from what I've seen

[surreal bison]

not anymore

[fresh comet]

that's the good way to ask

[solemn pawn]

why

what happened

[surreal bison]

moderation difficulties

[solemn pawn]

damn

[surreal bison]

i'm going to two parties tomorrow

[fresh comet]

the help channels, pre uni channels, and early uni channels have a lot of questions that just go "halp"

lol

[visual breach]

Now I feel guilty, I asked questions like

• how to even cohomology compute do

Or

• How even differentiate over ring

[surreal bison]

i imagine you probably asked it better than you think

[fresh comet]

there's also the people who say smth along the lines of "okay, I have a test tomorrow and I don't know ANY math AT ALL. SOMEONE PLEASE HELP ME OR I'LL FAIL OMGOMGOMG"

[visual breach]

(I am joking, hopefully I was better than that)

[surreal bison]

The most cryptic of my questions are when the author has made a cryptic statement.

[surreal bison]

yeah but the issue there is different lol

[visual breach]

It can be largely similar

[fresh comet]

mhm

[craggy parcel]

"0+0 =? hardest problem in all of math!"

[surreal bison]

a highschool graduation party of my highschool closest friend and a birthday party of someone i haven't met in meatspace yet!

[surreal bison]

me when nonunital monoid

[chilly hull]

i have a test on petting my cat tomorrow and i have NO IDEA how to get to him.

[surreal bison]

wait do monoids need an identity

[chilly hull]

please help me i need to find him otherwise i fail

[surreal bison]

fuck wait i can't remember...yes right

[neat lintel]

depends on the author

[visual breach]

Yes it does

[fresh comet]

the most frustrating people to help are the ones who refuse to cooperate, for whatever reason

[surreal bison]

oh right if they don't it's a monod

[visual breach]

But it's just a naming

[chilly hull]

monoids dont need inverses i believe

[surreal bison]

correct

[visual breach]

Semigroup denotes one without identity

[surreal bison]

if they did it would be called a monnnoid

[visual breach]

Tbh I wonder if semigroup is ever truly useful

[surreal bison]

a monnoid is just a group

[chilly hull]

and is magma non-closed?

[visual breach]

You can always adjoin identity

[fresh comet]

welcome to the help channels! we have:

trolls
ghosters
cheaters
people who want you to do their work for them

[surreal bison]

yes i "used" it

i think

[fresh comet]

I hope you enjoy your stay!

[surreal bison]

might have been something else

[visual breach]

Hm

[surreal bison]

semi group of units of the octonions or something

[craggy parcel]

as a green name this is bad pr for the server

[visual breach]

Isn't this monoid?

[craggy parcel]

only a matter of time till the mods censor you

[fresh comet]

my bad

[surreal bison]

uhhhhhhhhh

[visual breach]

Well it would also have inverse

[surreal bison]

not associative

[fresh comet]

I think most of the green names (and the mods who work in the help channels) would agree with me though!

[visual breach]

I thought Octonions are associative algebra

[surreal bison]

no!

[visual breach]

,w octonion

[surreal bison]

(right?)

[craggy parcel]

the mods make ad revenue off server activity didnt you know

[fathom swallow]

Results provided by WolframAlpha

Click here to refine your query online
Upgrade to WolframAlpha Pro!

Requested by abstia

[fresh comet]

[visual breach]

Tf

[fresh comet]

when will I be paid to put up with the helpees

[surreal bison]

the point is that g2 is to octonions as su2 is to quaternions

[visual breach]

Nonassociative multiplication

[craggy parcel]

[surreal bison]

that is, lie algebra is to lie group as malcev algebra is to moufang loop

don't ask me about those two i have no clue about them

[visual breach]

How do people even deal with Octonion

Its unit would be magma just with inverse

[surreal bison]

so you can take e1 e2 = e4 and get the kther multiplications by uhhh a certain set of operations like cyckically permuting

or soemthing

[serene heron]

it's "divisibility" since there's no identity

[surreal bison]

oh fano plane

octs have id!

[serene heron]

and it's a quasigroup iirc for just magma + divisibility

[visual breach]

Why no identity?

[craggy parcel]

the algebra nerds are at it again

[surreal bison]

tbey certainly have id

[serene heron]

I mean a magma with only inverse

[surreal bison]

ah

[serene heron]

not octonians

[visual breach]

Nonassociative algebra is just so

[serene heron]

lie algebras are nice

[visual breach]

Ah btw @fresh comet what are you working on nowadays?

[fresh comet]

nothing new

[visual breach]

Ah, are you in summer vacation now

I thought classes would be around

[fresh comet]

I've been on summer break for the last month

my fall/winter semesters ended a month ago

[visual breach]

Woah, pretty early summer break

Fall semester?

[fresh comet]

The semester from September to December is called the Fall semester, and the one from January to April is called the Winter semester.

May to August is the Summer semester

I have a couple of courses rn, that run from May to June

so half semester courses

kinda

[visual breach]

Ah interesting, I would imagine there would be Spring semester

[fresh comet]

tbh, calling the semester that runs from January to April the "winter" semester is kind of stupid

idk

I would call it the Spring semester

but eh

what've you been up to, Absta?

[visual breach]

Yeah me too but i guess it is decided

Hmm I've been just following coursework, some alg geo and differential topology

Tbh also learned class field theory but it seems to become unholy mess

What kind of courses you taking, higher?

[fresh comet]

not math, at the moment

I'm finishing up my "breadth requirements"; I think one would call them "gen eds" in the US

so I'm doing a philosophy of science course + a very very basic geology course

[visual breach]

Ah, gen eds. Bane of university students

[visual breach]

Do you like it?

I guess it depends on person

[fresh comet]

yes

I like both, but they are eating my time a bit

[visual breach]

Yeahh

It feels difficult to self-learn math in these periods, right?

[fresh comet]

yes

I'm also taking driving lessons rn

and some other stuff is going on in life

so I feel super unproductive with maths atm

[visual breach]

Ahh fair

I was even more unproductive in my early age

[fresh comet]

I hit... 1.02k messages in the last 24hrs

yikes, could've spent that doing smth productive

oh yeah Absta, did you see this
#discussion message

[visual breach]

Being productive by avoiding such might be overrated tho

[visual breach]

Oh wow

[fresh comet]

I live in #bots, what can I say

[visual breach]

Bots channel can be fun!

[fresh comet]

so much waves

Absta is rank 16 in the past 30 days

[visual breach]

Yeah I do discord too much

[fresh comet]

if you do discord too much, what does that say about me

I'm nearing my 30 day message peak now...

only a couple dozen more messages to go

[visual breach]

Xela could be insurmountable tho

Also some of your messages is just typing t!top in #bots so

[fresh comet]

I'll get top 3 again for sure

[fresh comet]

a lot of them are

[visual breach]

Time in discord may seem inflated for you

[fresh comet]

last time I was rank 3 with this many messages

almost rank 2

but rank 1 was more than both of us combined

[visual breach]

O, that's an improvement!

[fresh comet]

more messages is improvement?

[fresh comet]

don't forget my GIF spam in #chill, or my keyboard smash posts

[visual breach]

You are lower in rank now

[visual breach]

Yeah you are not dedicating too much time in discord!

[fresh comet]

not for long

top 3 soon!

[fresh comet]

even discounting those posts, that's like 9.5k messages at least

which is a lot still

[atomic furnace]

is differential equations that hard?

[fresh comet]

depends

[atomic furnace]

wdym like does it depend much on integral calculus or something?

[visual breach]

What was it, the PDE for aerodynamics

[fresh comet]

PDEs

[visual breach]

It is a Millenium problem, so I'd say it can be pretty difficult.

[fresh comet]

integration is a must for diff eqs

[fresh comet]

Navier-Stokes

[atomic furnace]

im about to study DE in my next sem I hope I survive

[fresh comet]

good luck

[oblique flicker]

hellour

[exotic wyvern]

You got this I believe!

[exotic wyvern]

I love me some Navi stokes

[jagged forge]

<@&268886789983436800>

also the guy above them

why am i here at 4am

[delicate mulch]

go to sleep

[lofty mango]

You should not use discord after waking up early 🙃

[jagged forge]

i'm not

[winter pelican]

You should help me with yr11 trig!

[jagged forge]

i have not gone to sleep yet

[visual breach]

Have good night!

[winter pelican]

Help with my trig forum pls

[visual breach]

If you need help, help channels are better bets.

Sadly forum gets less attention

[ebon pelican]

when you, for the purposes of being tidy, need to remove the negative sign of the leading coefficient of a polynomial equation P(x)=0, do you generally think of it as multiplying by -1 or dividing by -1

[static loom]

idk

[pure hollow]

Prolly multiply but idk

[neat lintel]

The former but they're equivalent so your choice doesn't matter

[light olive]

is 'mathematician' a profession or is it just a title for people that do mathematics?

[pastel tusk]

why are exponentiation and roots so weirdly defined for complex numbers

is there a rigorous definition of the "principal root"

[neat lintel]

If someone has an answer to this please also ping me

[neat lintel]

This might help I have no idea https://en.m.wiktionary.org/wiki/principal_root

Here it’s defined in C as a root which has the highest real part and positive imaginary part

[neat lintel]

It's an actual profession

[vast wraith]

it is both

[icy void]

Do i major in math, statistics or cybersecurity?

[old oak]

that settles it, definitely a bot

[robust brook]

major in all 3

[fresh comet]

cybersecurity

maybe then you can figure out how to stop this hacker from occupying your account

clearly, your privacy is compromised here

[old oak]

history of late antiquity is a fascinating area and worth studying

[vast wraith]

real

[gentle stone]

I need all your thoughts. I’ve done my google search and stuff but I don’t know, I don’t somewhat find it helpful. I need all your help for this.

Im a mechanical engineering student. And currently I’m hating it. I wanted to do computer science but unfortunately due to my lack of hard work mechanical engineering was the degree I could get due to less competition. But I’m considering change my major through internal transfer.

But my choice is Mathematics. When it comes to mathematics I find it almost like computer science. It’s problem solving on the most part. U have a formula in maths, u have a code in cs and basically the more u practice on how to code like how to solve a math problem you learn through it. Like there is active learning in mathematics and computer science and I like that. But I hate engineering because of how much I need to remember and I’ve always disliked physics too. So I was hoping well could y’all suggest whether if you guys think it’s a good choice to move to mathematics from mechanical engineering?

[river moon]

you can (and tbh should) learn math while doing mechanical engineering

and consider that you're not going to be solving math problems as a job most likely

[latent edge]

Political science

[river moon]

much like knowing how to code in some language as a cs student isn't enough to get a job

there's still an engineering aspect in cs in that you need to know how some specific technology works

[latent edge]

Getting a job in programming is pretty much an act of shooting yourself in the foot

[gentle stone]

True. I was leaning toward banking with mathematics. Unfortunately my university does not allow me to take a Math Minor while I do mechanical engineering and plus I’m already struggling with the physics part. I’m doing great on the math side although I’ve only done easiest courses like Calculus I, II, III Linear Algebra, Statistics and PDE (including Fourier Series). Though I struggled in some of them I was able to take it as a motivating challenge unlike other engineering courses which is a lot of reading with physics along with memorization.

I also planned on maybe directing my career path towards Banking as a trader with mathematics. But from what you are saying, it’s made me indecisive.

May I ask, with your Postgraduate in Mathematics or with any lower tier degree in Mathematics, what do you do for living? Assuming u did Postgrad in Maths from your roles.

[river moon]

I didn't, I'm just running c++ saying hello world

idk why would you need anything more in terms of math than what you know to do something outside math research

[sturdy gulch]

i may be stupid but isnt there a simpler way to prove l'hopitals rule that doesnt use cauchy MVT

cant i just do

[neat lintel]

Prove it by linear approximation, although that's much more work than using cauchy's MVT

[sturdy gulch]

$\frac{\frac{(f(x+h) - f(x)}{h}}{\frac{g(x+h) - g(x)}{h}}$

[fathom swallow]

Serphic

[sturdy gulch]

=

$\frac{f(x+h) - f(x)}{g(x+h)-g(x)}$

[fathom swallow]

Serphic

[sturdy gulch]

i mean it'd be a huge pain in the ass to prove this with functions that have different variables huh

like w chain rule

[crimson crest]

is/are there any "complete" mathematics tutorials? Like that guides a person from high school level to preuni to uni to advanced/olypiads

I am a uni student but I feel like I have some extreme gaps in my knowledge

[vast wraith]

maths is too big for that

also “advanced/olympiads” doesn’t make any sense

[latent edge]

Math Olympiad is the way to deteriorate your math knowledge

[rocky shuttle]

[fresh comet]

[pastel tusk]

yeah but the reason i was confused is that we often say that sqrt(4) = 2 is correct and sqrt(4) = -2 is incorrect, so does the same apply to complex numbers

if yes then it would follow that $\sqrt[3]{i}\ne-i$

[fathom swallow]

DiamondPanda16

[visual thorn]

I'll join the search with you.

[visual thorn]

Let's look at the cube roots of i. They are
sqrt(3)/2 + (1/2)i,
-sqrt(3)/2 + (1/2)i, and
0 - i.
According to the definition above, we pick the one with the biggest real part. That would be the root with sqrt(3)/2 as the real part.

If it was a tie we'd pick the one with the positive imaginary part. Real parts and imaginary parts are both real numbers, and the real numbers are totally ordered, so we can do this.

[pastel tusk]

yeah it just feels a bit unnatural that although one of the roots is just -i, we still choose a more complex number as the "principal" root, but i guess it makes sense mathematically so its fine

[visual thorn]

This is just a subjective feeling that you have. You want the cube root to be easier to write out. To see why the definition above is better, let's look at something like the cube root of 0.001 + i. What do you think the cube root of this number should be?

[topaz spoke]

is there a way to just see if a diophantine equation has solutions or not without iterating the variables?
like let x=97: x=k(4n+1)+3n?

[static loom]

wdym, what's the original problem you're trying to solve

[topaz spoke]

I've been working with 6n+-1 and identifying patterns in the properties of n and whether a given n produces a prime or composite. it would be very beneficial to not have to iterate k,n for larger x.

[static loom]

it sort of sounds like you could have some simplification if you use the chinese remainder theorem but I'm not sure I understand the connection between 6n+-1 and x=k(4n+1)+3n or what you're iterating k and n over exactly, I assume you're trying to find positive integer solutions in k, n for every x?

[topaz spoke]

oh, sorry, that was just an easy example.
For 6n+1
n = k(6i+1)+i where i and k are whole numbers
n = k(6i-1)+5i-1 where i and k are whole numbers
these two equations produce all of the composite numbers of the form 6n+1.
i also have a set of equations for 6n+5.

so having a way to test an x in place of n and determine if there are or are not integer solutions for the equation would quickly tell us if the x would produce a prime in 6n+1

using CRT can drastically reduce the search space i was just curious if anyone had a more direct method.

[static loom]

hmm I don't see how that works

can you show how you use those two equation to make a composite number of the form 6n+1 and show a proof of how it doesn't make primes

[topaz spoke]

well lets say k=1 and i=1
1(6(1)+1)+1 = 8
6(8)+1 = 49 which is composite.

these equations were derived from observations i made from looking at n from 6n+1 and noticed periodic patterns in when n produced composites. specifically if n%5==4, or n%11==9, or n%17==14

[static loom]

hmm k=4 and i=1 makes the prime 29 4*(6*1+1)+1 = 29

oh I'm mistaken that's just hte n

[topaz spoke]

right. so that plugged into 6n+1=175

[static loom]

I see how they work now

[topaz spoke]

while not a proof i have checked these equations out to 10,000,000

[static loom]

the first one is when you take (6i+1)(6k+1) and expand it out to make 1+6n with n=k(6i+1)+i so it's composite by construction

I imagine the other one is pretty much the same thing with like (6i-1)(6k+5) or something to that effect

[topaz spoke]

exactly

[static loom]

that proves they're composite by construction then

[static loom]

it proves the observation

[topaz spoke]

well specifically they came from the observations when n is congruent
4mod5
1mod7
9mod11
2mod13
14mod17

and so on

then n produces composite.

[static loom]

well doesn't matter how you got it at this point, let me explain a bit more why

[topaz spoke]

so when n == 4%5 and is plugged in to 6n+1 it will produce a multiple of 5

[static loom]

Take n = k(6i+1)+i and plug it in to 6n+1 and you get:
6k(6i+1)+6i+1
Notice (6i+1) appears multiplyin 1 if you look at it,
6k(6i+1)+1*(6i+1)
Now factor out the 6i+1
(6k+1)(6i+1)
This is composite unless i=0 or k=0

[topaz spoke]

right.

another way to look at it is if
n%(6i+1) == i where i is a whole number
or
n%(6i-1) == 5i-1 where i is a whole number
then n produced a multiple of (6i+1) or (6i-1) respectively when plugged into 6n+1

[topaz spoke]

anyway, with the equations here producing all composites of the form 6n+1, we can reform these to test whether a value x would produce a composite or a prime. for large values of x this gets computationally cumbersome. using modular reduction and CRT we can greatly reduce the search space. but if there were a method to just determine if there are integer solutions this would be a very quick primality test.

[static loom]

unfortunately it's not, the approach is basically equivalent to brute forcing every possible factorization of the form 1*1 and 5*5 mod 6

sorry I'm probably sounding like a wet blanket here

[topaz spoke]

thats ok, I appreciate you taking the time to talk about it in general.

[static loom]

cool yeah have fun

[topaz spoke]

thanks

[arctic sand]

yo can someone help me im stuck in a roblox game rn and idk this math question

4a+6b=10
2a-4b=12

what does 12a equal?

[vivid halo]

use noggin

[arctic sand]

whats a noggin bruh

[topaz spoke]

4a-8b=24

[surreal sapphire]

please read #❓how-to-get-help

[cyan vigil]

Hi

I have a problem
Which is how to be a mathematical thinker
Or how to approach a question
Many times i althouh i have the information and memorize i cant solve a question or think logically
I have some openings in question like when i see a fraction i should multiply it to get a whole number
Or taking a common factor
Or even breaking down question
But in many times i can't do that and i can't think logically althouh i solve alot questions
I think the problem is the way i think or that i can't understand and the learning in my country isnt good
It depend on memorizing more than understanding and deduction
Ah so how to deduce thats another point 😂

[timber flame]

anyone have gce math past paper in 2023

[neat lintel]

Essentially, it all boils to practice and exposure
The more proofs you read, the more you are exposed to methods and common problem solving techniques, the better you get at coming up with stuff on your own
Although there are books on problem solving in math that you can refer, I personally never really picked one up, it were mostly my comp math skills that kinda helped me

[high nebula]

did any of you do the kangaroe competeinoal test

if you did, how was it

[verbal karma]

Another suggestion for this is to be as lazy as possible when solving math problems. The more lazy you are, the more likely you are to come up with an elegant solution that solves the problem without much effort. Math is not a field that you can be good at in a day. Learning things takes time and experience to ground your intuition and curate your maturity in mathematics.

To be frank, I study probability for over the span of 7 years and understand almost nothing about it. I still need to look up the pmf of the geometric distribution or need to look at the real analysis and measure theory book for the definition of integrals.

[cyan vigil]

I know this but the real problem is understanding basics in our school tell us cos 90 =0
But they dont tell us why i didn't understood alot of math basics
So now in my vaction I must search in books such as alg and trig 2e

[cyan vigil]

Wow

[cyan vigil]

And when i understand it well and where it come from its a very good felling

[verbal karma]

yeah. and this is also another problem: the more you learn, the more you realize that you know nothing.

[cyan vigil]

As an arabic person i must search for knowledge in another videos

[cyan vigil]

That right i felt that

[cyan vigil]

In our countries we memorize the qurstion and its answer and with a new idea my brain is turned off😂😂

[verbal karma]

It took me 3 years to finally understand how to factorize polynomial, of which at that time it is already 3 years too late for the algebra test lol. But at least I am glad I understand it now.

in my country, it usually is the memorization too. and I am really bad at that

[cyan vigil]

Same 😂

[cyan vigil]

Great bro ❤️

[verbal karma]

like, you have to know sin(A+B) formula by heart. I don't. Good thing is, I realize that I can use my complex number knowledge to prove that in the exam hall. That was the time I felt like a genius.

It is like Eureka moment. That is what keeping me in the mathematics loop

[cyan vigil]

Yeah that things that make me want to understood every single point of some basics

[verbal karma]

What you can do now is probably stop before using the formula. Stop and think one step back: can I do better? Is there a way I don't need to memorize anything other than the common knowledge?

[cyan vigil]

The bad thing in our country that in last year of high school you must choose either to be a math student or a science student
So when you enter college you choose a math college or engineering

[cyan vigil]

Thank bro ❤️

[verbal karma]

but math is science, at least usually associate with science department

[cyan vigil]

I mean with science biology

[verbal karma]

yeah. math is one of the branch of science elsewhere

like, you can't do ecology (subfield of biology) without calculus...

[cyan vigil]

I know but you either choose math or biology it decide what college you enter

[verbal karma]

weird. maybe if the current system where you are does not fit your needs, you can consider studying elsewhere. I know it is hard to do but consider it as one of the possible choice.

[cyan vigil]

Yeah its hard but as you said make as a possible choice

Thank bro for your advice ❤️

[native breach]

What are some good resources to get prepared for calc 2. I just barely passed pre-calc W/ trig and calc 1. I kind of know how they work, but not on a level I am confident enough to explain or teach. I want to relearn trig and calc 1. My ultimate goal is to get my mechanical engineering degree. All your recommendations and help is much appreciated, I can't wait to get involved in this community more!

[wild ferry]

how does one overcome a lack of mathematical confidence

like, I passed with Bs from a relatively meh undergraduate institution. I got Bs in my first semester of graduate school, then dropped out.

as I recover from depression I'm wondering if the thought of me being genuinely just bad at math is true or not. I can't solve competition math, I looked up the solutions to homework, yet I passed exams. idk what exactly would give me the confidence/will to try and surmount my lack of math knowledge at this point, given that I don't rigorously know math

[river moon]

competition math is far removed from what is taught in university and what is done in math research

[glass slate]

Discussion >>> Discussion 2

[verbal karma]

I assume that Calc 2 is integral, right? If you have no prior calculus experience (like, never took it during high school) then you can start from the traditional calculus textbook that you should have from Calc 1. Khanacademy is also a good place to start or AP Calculus BC materials can help you with this as it designed to be used on high school students.

[verbal karma]

Honestly, I would not be surprised if someone at the graduate level could not solve the competitive math problem. Those questions are designed to be puzzles, unlike what graduate students usually encounter, which requires a different mindset to solve. You know that competitive math has solutions, but your work in grad school might not even have a solution or a satisfying solution.

And B is not a bad grade.

You did get into the graduate school and that is one of the proof that you are capable of learning

What you have is called "imposter syndrome".

[upper patrol]

also you just don't learn the techniques for competition maths. on the extreme end most maths graduates dont learn euclidean geometry at all, much less be aware of what "pascal's theorem" or the "brocard point" is

and dont forget people regularly get <10 on the putnam. even then putnam is easier than competition maths.

[narrow thicket]

How bonkers is it to try to switch to the math department? I'm a computer science phd, but I just feel the way math people are working on my problems is more interesting and efficient

[neat lintel]

Could I ask the question "How to learn math" in the math forum...

[neat lintel]

🙏

[copper ridge]

Hi I need some help with a flask web-app i am working on. it works, but i need it to print the image generated (successfully) by matplotlib on the webpage, and also there are a couple of minor issues, i need help with.

[analog bridge]

I'm a 23 y/o born without my left hand, and my right hand only has 3 fingers, so writing by hand is nearly impossible, so I have to do math on the computer. I used to have something called CX CAS when I was in school I think, but this thing seems to only be purchasable by schools, not private individuals, and I'm looking for a new software to do basically everything math-related, cause I can't write at all. I'm doing high school math, I guess you'd say, I'm Swedish and here I'm doing the equiv of high school math, is the best way to explain it, I think.

Any ideas would be greatly appreciated, I want to get started but it's very hard to find good info on programs, cause when you search for programs, usually you don't get programs to replace writing by hand, it's just ones for visual representation, etc.

[jagged forge]

if by "cx cas" you mean the ti nspire cx cas calculator, you can definitely purchase them as an individual, and i happen to own one myself

[analog bridge]

so, i'm not looking to buy a physical calc, it's the software version

[analog bridge]

it has the calculator in digital form, but also a ton of functionality in the software that allows just doing math in general

"TI-Nspire™ CX CAS Student Software"

[jagged forge]

ah, ok, i don't know much about that

[analog bridge]

my point though was that hey, maybe there's even a better software out there? Cause it wasn't the most convenient thing ever, but it worked

yeah its really hard to find out cause 99.9% of people can write by hand

[jagged forge]

there's mathematica, but i've never actually used it more than a couple of times, and it's also kind of a programming language, so idk if it will be that easy to use

if you just need to do charting and graphing, there's plenty of free tools like desmos that can do that very well

[wild lantern]

You can set up flask to serve certain directories for things like images. You would store the image in those directories and then generate html containing the path to the image in flask to serve it.

[analog bridge]

for me it isn't even complicated stuff, it's just things like linear equations, algebra, trig, etc

at an earlier high school level, again, so not anything crazy

[jagged forge]

maybe you could learn LaTeX for equations and then desmos for anything visual

[visual breach]

What kind of math?

[jagged forge]

lots of people here take notes using LaTeX instead of handwritten notes

[analog bridge]

it was 5 years ago i did the last bit before this in school, and I'm only now looking through the course in swedish, so I can translate a little, but it seems like things like log, polynom, 2nd grade equations (correct translation?), trig, statistics (dunno to what extent)

[analog bridge]

I'll look it up thx

[jagged forge]

you can get started practicing it in #latex-testing and #latex-help

we have a bot here that renders latex: $ax^2+bx+c=0$

[fathom swallow]

suremark MSC2020 60G40

[analog bridge]

thx i'll see, though as per usual the path of least resistence may be easiest, just think i found a way to circumvent the free trial thing so i may be able to just use the software im used to, dumb thing is im willing to buy it, it just isn't available

[pulsar pagoda]

This problem is so annoying, i had the same issue with Cisco equipment -.-

[lofty mango]

Can someone explain me
What's relevance of 1st law of Newton since it can be derived from 2nd law easily
I have my interview on 13th😭

[raven plaza]

One could interpret the first law as actually being a definition for inertial frames

[lofty mango]

Ooooo like there is no reference of acceleration there that's why

[pure hollow]

How please enlighten me

[north topaz]

F = ma, if a = 0 then F = 0

[lofty mango]

Like 2nd law says rate of change of momentum is directly proportional to force applied and 1st law says that body won't change its state of motion or rest unless external force is applied
So basically a body's momentum will change only if force is applied on it

[pure hollow]

Oh like that I see

[lofty mango]

Yeah sir

[pure hollow]

Clever

[lofty mango]

I hope just they don't ask me these kind of questions

[pure hollow]

They can ask worse

[lofty mango]

😭

[pure hollow]

Nah chill man gotta keep ur head cool at an interview

Be witty but idk if that works

[lofty mango]

Yeahhh I gonna try to do that lol

[lofty mango]

Yuppp

[pure hollow]

Honestly they'll be asking trick question to see how u would react to it

[lofty mango]

Yeahhhh most of times they do that only

[outer heart]

guys in desmos
sin(x)
and sin(sin(x)) graphs are literally the same
is it supposed to be that way
cuz i cant comprehend it 😭

[solid snow]

but they aren't ?

[outer heart]

im writing it wrong prolly

[old oak]

<@&268886789983436800> do we allow this kind of thing?

Seems not

[plain island]

no

[odd narwhal]

Not without approval

[untold sapphire]

@pulsar pagoda

[pulsar pagoda]

Ok

[untold sapphire]

yeah so what's your interest in digital signal processing? I've moved away from electrical engineering over the past few years so my practical advice is very rusty

[pulsar pagoda]

Operational amplifiers

[untold sapphire]

yes, they're wonderful!

truly beautiful devices

[pulsar pagoda]

Yeah thing is I don't get any physics nor cálc in My major

[untold sapphire]

what's your major

[pulsar pagoda]

So i want to compensate for that cause im getting an offer for a Masters in ER

[untold sapphire]

Ah, ok.

[pulsar pagoda]

EE

[untold sapphire]

Oh!

[pulsar pagoda]

Software engineering

Like ive been pivoting to apostol calculus thats sort of introductory analysis (easier than rudin)

And i know basic LA

[untold sapphire]

Sure, I see.

[pulsar pagoda]

I Guess some electronics courses would be required like for analog electronic signals

But I have no idea where to start

[untold sapphire]

Wait is your major not going to teach you electronics

i'm confused i thought you are an EE

[pulsar pagoda]

No

Im in SE

Software engineering

The Master im getting an offer from is EE

[untold sapphire]

Ah, I misunderstood

Well, do you want me to like, talk about the textbooks I read in school?
I am sure you could like, look up MIT open course ware and see what the textbooks they use in their classes are

[pulsar pagoda]

Sure

[untold sapphire]

I used "Electric Circuits" by Nilsson

and "Basic Engineering Circuit Analysis" by David Irwin and Mike Nelms

[pulsar pagoda]

So i see both involve Fourier analysis, how is this different from lets say harmonic analysis? Is that just a math thing?

Also there is no differential equations course in my major but the 2 volumes from apostol give an introduction to it. Maybe ill pick something else if I feel the need

[latent edge]

I did harmonic analysis through number theory. I think it just depends on what you want

More applied/pure

[pulsar pagoda]

I Guess since it's EE applied would be My bet

[latent edge]

the good old DFT

[pulsar pagoda]

https://tenor.com/bm8d9.gif

[dense hornet]

Roots of unity

For the FFT that is

[fading zealot]

TIL that The difference between the nth triangular number and the nth square number is the (n-1)th triangular number

[bronze pelican]

Kinda obvious if you think about it geometrically

[solid yarrow]

hi yamin

hru?

[lofty mango]

Heyy f0xy sup

[fresh chasm]

hoy could I ask a doubt

how

[jaunty yacht]

just try to ask i guess

[fresh chasm]

can I ask it here/

?

[tranquil wasp]

ask in help chat room
thats what did

[jaunty yacht]

or you can try directly #math-discussion

[icy locust]

Is $δ_{ijk}=δ_{(ij)k}$ or $δ_{ijk}=δ_{i(jk)}$?

[fathom swallow]

luke1337

[vivid halo]

context?

[icy locust]

Oh

Maybe $δ_{ijk}= δ_{ij}δ_{jk}$

[fathom swallow]

luke1337

[latent edge]

levi civita or something?

[neat lintel]

is basic mathematics by serge lang too time consuming for a foundations towards calculus physics? 94% of 1 section consumes me atleast 3 hours

[narrow talon]

W'Hospital

[proven wadi]

bro suvat on falling stuff doesnt make sense

[odd narwhal]

This is kronecker dta

Delta

[latent edge]

usually you have 2 inputs

the generalized one is written differently

that's why

[odd narwhal]

Yea ik

But levi civita is epsilon

[latent edge]

yea

[cedar pilot]

Guys why was 6 afraid of 7?

sin(21)

[fresh comet]

because Seven murdered Six's family and friends which, quite frankly, was deserved.

[ocean harbor]

https://cdn.discordapp.com/attachments/937568987565404170/1241587158226305165/caption.gif

[ocean harbor]

hi higher!

[fresh comet]

hi Akira!

[trail tapir]

My final exam in like 4 days how can I memorize like 50 different formulas Im highsjcjool

[pastel tusk]

you most likely don't have to

memorise too much

what topics are you doing

[ocean harbor]

how's you

[fresh comet]

okie dokie so far today

[ocean harbor]

[trail tapir]

Geometry, Trig, Algebra

Hello?

[limpid abyss]

sup chat

[jaunty yacht]

wazup

[shy lynx]

Hi

[onyx scarab]

gay

[vast wraith]

i made a flag representing my mean lesbian frens

[neat lintel]

the flag is disappointed in me 😭

[vast wraith]

it's because you delete too quickly

[neat lintel]

[limpid abyss]

is this a slay moment? i cant tell

[grand pecan]

can a romantic relationship exist without sexual attraction

[fresh comet]

sure, I don't see why not

[wet mortar]

yea

[neat lintel]

yes

[grand pecan]

im looking at dating guru advice and i dont want a relationship where i need to make the person think im more valuable than them

[deep mango]

people will tell you it can, and it can, but its important to keep in mind that a relationship is healthy when it satisfies needs and desires of both people involved and oftentimes sexual attraction is a need someone is looking to satisfy from a relationship

so if that's not something that's present on your end, you had better communicate about whether or not its an expectation of the potential partner

and if it is, thats not a failing on their part

[deep mango]

that doesnt sound like something you should have to do in any healthy relationship

in fact i would say making your partner feel like they arent as valuable as you is probably a recipe for disaster

[blazing pawn]

I think your dating guru might be trying to tell you how to manipulate women

And not form a healthy relationship

[grand pecan]

my crush doesnt find me sexually attractive so i wanted to see if it was possible for us to date

[deep mango]

well, romantic attraction has a pretty strong effect of making someone more sexually attractive

so i wouldnt really worry too much about that if they're interested in dating anyway

but if the problem is like "their sexuality doesnt match my gender" then i think that can be kind of a tougher hurdle

[deep mango]

my point here being, that part of it might come with time

if you become good friends and a romantic attraction develops first

[grand pecan]

situation: I am high school male, she is high school female, I feel lonely after changing schools, she cares about me, I am considering trying to date, no conversation has happened

sorry if it seemed like i was in a relationship

[deep mango]

yeah sure

i just mean like

as you become friends and that becomes more of a possibility

the sexual attraction could follow and its not really something you would force

[verbal karma]

Why I found this situation like an optimal stopping theorem problem? I think that theorem can be applied here

Joke aside, relationship... regardless of it being a mapping or real life, you need time.

time to understand it

[solid snow]

move on

[deep mango]

kind of silly

[deep mango]

and dont always have it

[verbal karma]

true... that's why some people said winning love is like winning lottery

[timid bronze]

someone who truly loves you will love you the way you are

i dont believe they are the one for you

as hard as it may be

but the one takes time to find

unless theyre someone that just lacks sexual attraction in general

theres plenty of non sexual relationships thats okay

[steel vessel]

perhaps they r asexual? either way, if this is something that bothers you there is very little chance you can 'work around it' or 'change them' without becoming resentful or drained, it's good to know what you want

[steel vessel]

yessssw

[neat lintel]

hmm

yoo

anyone alive

is this a motivation channel??

it seems so by looking previous chats

[tranquil wasp]

nope.. only ded people alowed

[neat lintel]

oohh

jey god

hey*

[tranquil wasp]

sup

[neat lintel]

i think u r dumb

[tranquil wasp]

nah .. i a genius

[neat lintel]

u don't know how to manage worlds

[tranquil wasp]

i use ai..

very simple

[neat lintel]

ohh

chat gpt?

hehe

[tranquil wasp]

yep.. others are good too

u play chess ?

[neat lintel]

yhh

[tranquil wasp]

cool

[neat lintel]

so wanna play

i ain't good

maybe 900 elo

[tranquil wasp]

k .. but i have no pratice