math-pedagogy

[hasty widget]

😂

And the worst part was that the learning curve was steeeeeep

In one class we went from an intro to vectors through dot products and cross products to divergents and curls

It was 3 hours of progressive neurological disorder

[wicked minnow]

wym dats ez

[hasty widget]

for you

[river steppe]

Lol

[civic tree]

lol

[limpid mantle]

how do you teach to someone who doesn't want to learn

[pearl fossil]

u don't

Xd

[hasty widget]

Or you take the Asian approach

Take a stick to class

Jk

@wild dune sounds interesting, though are other teams going to be able to listen to the other's guesses?

[limpid mantle]

lol

ive been thinking about the stick 🤔

problem is, it's my sister

[hasty widget]

Or just give a depressing lecture on the importance of math > to get good grades > how institutions value math > to have opportunies

[limpid mantle]

lol

I only want her not to fail her high school math classes

[empty fable]

Anyone know a good place to learn/review calc 3?

I helped someone in here earlier with it and I was a lot more rusty than I should have been and want to brush up on skills

Please @ me with suggestions. bed time for me

[severe chasm]

@empty fable https://www.youtube.com/watch?v=tGVnBAHLApA&list=PLDesaqWTN6ESk16YRmzuJ8f6-rnuy0Ry7

[hexed perch]

this guy is awesome

[wise onyx]

Yeah he is

I watched only 1 of his videos for review for my calc 3 final

Was good

[brazen glade]

anyone here good at statistics

[turbid zenith]

@wild dune What sorts of functions?

[brazen pendant]

So we have this system where our students have to solve three “core exercises” throughout the semester to get a grade bonus. the first one was released and is like impossibly hard (relates to the extremely black magic-y Golub-Welsch-Algorithm for Gauss-Legendre-Quadrature, which is not understandable even with a solid linear algebra background… and the students haven’t even covered inner products yet…)
I’ve written a mail about this to the main assistant, hope it gets changed

cause like, no student will be able to solve this

I’m questioning if I could

[turbid zenith]

Ah very cool

Interesting idea 😃

Depending on the level of sudent maybe like $\sin(\pi x)$

[burnt vessel]

DMAshura:

[wispy slate]

1+1 = 3

u all didn't know it lol

[astral fox]

@brazen pendant it's bonus tho, right?

[brazen pendant]

yes, but these will be exercises that they should expect to be useful and worth doing

last years were mostly pretty cool actually

[astral fox]

were they difficult?

also how much bonus

[brazen pendant]

not nearly as much as this, they were a bit time-consuming but generally fair

+0.25, on a linear scale from 1 to 6 with ≥4 required to pass

(i.e. 5%)

[astral fox]

each?

[brazen pendant]

no, if you do three

[astral fox]

hmm

that's not a ton, but it's not a little

[brazen pendant]

that’s about the most of a bonus you’ll like, ever get

[astral fox]

yeah

[brazen pendant]

in any subject

[astral fox]

tbh answering (more than n) questions right on a final exam usually bonus

[brazen pendant]

also there’ll be more than three of these, but I can’t just tell my students ”just ignore this core problem, it’s actually just bad”

[astral fox]

maybe also suggest some more and let students choose 3?

[brazen pendant]

that’s already the plan but we don’t know how many will come

I think we had some six-ish

and had to do 3

[astral fox]

umm

you could do jordan decomp?

for C

[brazen pendant]

they’re only in the beginning of linalg 2

[astral fox]

hmm

dual space stuff?

[brazen pendant]

covered but not understood likely

:P

[astral fox]

all the more reason

[brazen pendant]

we’re talking second semester students

[astral fox]

im a second semester student

[brazen pendant]

second semester physics students

[astral fox]

ooof

umm

are physics related stuff okay?

are these motivated students

[brazen pendant]

probably,
probably not

this course has a reputation for being bad but doable to pass, essentially

so students are not exactly going to go the extra mile

[astral fox]

i mean they're in physics

[brazen pendant]

tbf so was I when I took this course

and I aced it :P

[astral fox]

well they'll probably need to know how to work with complex vector spaces so do some stuff on that?

[brazen pendant]

I’m not quite sure why you’re suggesting kinds of exercises to me

I’m in no power over the exercises beyond giving feedback to the main assistant

or the prof

(and it’s a numerical methods course, focussing on ODE)

(but they’re doing quadrature now as a warmup)

for reference also, the first core exercise we got (which I assume will be featured again next week or the week after) was implementing a bunch of ODE solvers and plotting the solar system with them

which is just really cool

(they gave initial values ofc)

[limpid mantle]

what's the purpose of this channel?

[meager pewter]

Anyone that has read/done the exercises in Concrete Mathematics by Knuth?

[lethal leaf]

what about it?

[turbid zenith]

Damn, well I missed it

Though I do have a question if anybody's up for answering it

What do y'all think of the way that complex numbers are currently introduced/taught in (your school system)?

[lethal leaf]

complex numbers are a dumb name but I think they're taught fine

I wasn't taught like "ooooooh these are scary" and never felt that way

it was just taught as "here's another way to write negative square roots"

[turbid zenith]

Anyone else?

Thank you @lethal leaf

[weary veldt]

I think it's taught quite nicely with an emphasis placed more onto the Argand Diagram and Geometry side of things rather than the algebra component. Some solutions to hard problems using algebra can be very elegantly solved by thinking geometrically.

[limpid mantle]

I don't even remember how they were taught to me

but it sticked

"this means the parabola doesn't touch the X axis"

I think i was actually introduced just as a number with the property that i^2 =-1

and they are kinda vectors

I used them a lot in school because I learned electricity there

and so we used them lotsa

[turbid zenith]

I feel like a lot of the time when they're introduced it's completely algebraically, and that kind of annoys me

"How do you take a square root of a negative number? You can't. But it's okay, we'll make up an imaginary answer."

And then if you're lucky, at the very end of the unit you might learn to graph them

[ocean bobcat]

the square root of a negative number only exists algebraically

as evidenced by the fact that we called the reals the reals

the complex numbers are mighty handy for mathematics but the things in real life that they measure are abstract while the real numbers have very concrete existence as measurements

the nonnegative reals, anyway

visualizations like the complex plane or thought experiments like "what are the roots of this obviously rootless quadratic " are useful to help you get your bearings but anyone with a solid grasp of basic algebra should just be able to live with the declaration that you can now write down things of the form "a+bi" where "i^2 = -1"

[turbid zenith]

See I have to disagree

If you think of them geometrically, it makes much more sense and is much more motivated

Just by introducing the idea of "Hey we have a number line, and we can move along it and stretch along it ... what if we could also rotate off of it?"

[wispy slate]

i hate maths

[turbid zenith]

The whole concept that numbers can also describe rotation makes it much more down to earth

I'm sorry to hear that @wispy slate

[tawdry venture]

@wispy slate great, then why are you here?

[wispy slate]

so i can improve

[tawdry venture]

okay, fair enough

[ocean bobcat]

i will agree that the complex plane is a helpful visualization, especially for interpreting complex multiplication; however, suggesting that there is a hitherto unknown "rotation" to the real numbers seems unnecessarily confusing, especially as an introduction to complex numbers, given the fact that in most applications the cartesian form of a complex number is a lot more arithmetically useful and students struggle with exponents and logarithms and the associated rules that are requires to use polar form correctly

[wispy slate]

sorry that’s to much to read

[ocean bobcat]

as someone who realized early on that algebra was just "push the symbols around and don't make mistakes" i found complex numbers a cakewalk and was really thirsty for what i know now to be ring theory

i think that visualizations and appeals to intuition make good supplementary learning material but that it's not useful to try to hijack intuition unless you can do so perfectly (by which i mean, in a way where wrong interpretations can be very quickly recognized and weeded out)

[wicked minnow]

Related:
https://matheducators.stackexchange.com/q/11436

[turbid zenith]

@ocean bobcat When I taught complex numbers to my geometry class as being fundamentally about rotation, they were a lot more comfortable with it than a lot of Algebra II students I'd taught

But I think I'm just going to disagree with you fundamentally here

Since the way you think about math is like ... the antithesis of how I think about math and how I try to get students to think about math

[wispy slate]

idk maths is big noob

[turbid zenith]

(i.e. nothing but symbol-pushing)

[wispy slate]

i think ima come on this everyday and complain that math is hard

[unreal ledge]

I think both is important. It helps to have the visualization, but take that away, it shouldn't tank a student

[turbid zenith]

Sure, that makes sense

My ideal introduction would be to introduce i as a number that upon multiplication rotates a number by 90 degrees -- from that you can easily extract powers of i, and then you can let the algebra take over from there

As in i acts algebraically just the way you'd expect. But it feels like it "comes from somewhere".

You don't have to do DeMoivre's Theorem in its full trigonometricity to start thinking of complex numbers in terms of rotation.

[ocean bobcat]

the trouble i have is that in my (admittedly limited) tutoring experience people will react positively to pictures just because they go "aha, yes, a picture, this is pleasing to the eye and i can parse it" but whether it sticks from the perspective of comprehension is a 50-50

[unreal ledge]

I wonder if a student would have trouble with that approach, without knowing vectors?

[turbid zenith]

I've found they don't --- though it depends what you mean by "knowing" vectors

Again you don't need to know the full generality and mechanics to start playing with the ideas

[wispy slate]

how do i improve in maths besides practice and effort

cause i’m a lazy individual

[turbid zenith]

@wispy slate Try to see a reason for everything you're doing. Like why it works.

If you understand why something works it's a hell of a lot easier to do it and not feel like you have to memorize a bunch of arbitrary rules.

You'll always have some memorization to deal with but it makes it much less painful.

[ocean bobcat]

"besides practice and effort"

no such thing

[turbid zenith]

Yeah, practice and effort can't be avoided. But you can refocus HOW you practice and WHERE your effort goes.

[ocean bobcat]

how can you expect to become good at a thing if you don't want to do it

[wispy slate]

idk sounds like to much work

[ocean bobcat]

rip

[limpid mantle]

if you don't put the work in, you'll never learn shid

that's it

[limpid mantle]

who self-study here

is it possible to go deep into math all alone?

[young stream]

I’ve gotten reasonably deep into number theory, topology, and kinda into complex analysis at a late undergrad or very early grad student as a high schooler over the last year or so

[turbid zenith]

I've done a lot of self-study

And yeah it's pretty possible

[old badge]

doing an algebra2+pre-calc+some calc over here

(primarily learning alg2, bur messing around with the other 2 and gonna acrually learn over the summer)

i believe it's very possible

quite fun too, and more controlles

no teacher controlling what you're doing

just syllabi and what you want to learn

[strange bronze]

One thing that I've been thinking about recently: to what extent is "humour" valuable in mathematics education? Is it just distracting?

Like using the above to illustrate the concept of a complement of a set

[civic tree]

hehe

[strange bronze]

It's funny, but does it actually make learners form useful connections, or does it just obscure the concepts?

I also recall old memes like:
"a wild e^x appeared!"
"Go, calculus student!"
"Calculus student used d/dx!"
"It wasn't very effective..."

Or whatever

[civic tree]

ok those memes are just bad

[strange bronze]

Are the "connections" formed by these jokes/analogies actually meaningful

[civic tree]

the bit above sounds okay but idk enuf about sets to say how much it's distracting

[strange bronze]

Or even just something like "we don't write the × symbol when multiplying anymore because mathematicians are lazy"

To beginning algebra students

I mean, on one hand, I'd imagine a lot of students would feel more excited/engaged in the material if it feels more.... Personable? I guess

Or like they're using a "trick"

But on the other... Yeah, there's a reason "trick" is a bit of a slur in mathematics

Like in the above example, it obscures the real reasons we avoid × (looks too much like x, makes polynomials and formulas look messy, dilutes the connection between multiplication and fractions, ultimately unnecessary)

And even if you explain it like that... Id imagine introducing it as a "hack" would still make students view it as such

[ocean bobcat]

math meme facebook groups are the only way to stay sane for some

though arguably those people are already way past insane

[lime echo]

Hmmm, currently picking modules (deadline is still a while away) for my MSc, and this is what I've got so far:

1. Differential Geometry & Lie Groups
2. Advanced Partial Differential Equations
3. Complex Function Theory
4. Modules & Representation
5. Harmonic Anlaysis
   I need a total of 6 (+ a 2 semester project) and curious if anyone had any suggestions o:

Currently eye-ing up Semi-group theory, Geometric group theory, or Hyperbolic geometry

Could pick a statistical module, or even an OR one

[lime echo]

Any thoughts? o:

[brazen pendant]

I don’t have any real thoughts except hyperbolic stuff is cool… but geometric group theory sounds fun too, even though I have no clue what it entails

[lime echo]

I just talked to my tutor, asked him the question I dumped here

he said it seems like I enjoy analysis, so if I wanna do a PhD I should focus on analysis themed modules

moreover, since I picked all the availible analysis modules offered, just pick what I find interesting

[boreal sentinel]

Sasha and Sascha

[lime echo]

I ish superior one!

[scarlet perch]

t!choose sasha | sascha

[hot storm]

🤔 | Colorodo Brown Stain, I pick sascha!

[scarlet perch]

oof

[old badge]

hey do hyperbolic geometry @lime echo

it's so very fun and stupid

i don't even understand it bc i havent taken a coirse on it

but i love it

i'm surprised that's even an option

also what's an MSC?

[wispy slate]

yo some basic question

2x+1 / x

is the same as

2x+ 1/x

?

whole thing over x vs only the 1 over x

is it the same

no

[indigo shale]

you can distribute it tho:

$$\frac{2x + 1}{x} = \frac{2x}{x} + \frac{1}{x} = 2 + \frac{1}{x}$$

[tawdry venture]

why is your latex render in times new roman

[wispy slate]

why not

[tawdry venture]

times new roman < computer modern

[brazen pendant]

computer modern < libertine tho

[boreal sentinel]

Wingdings > comic sans

[warm lintel]

braille > wingdings

[boreal sentinel]

Nordic runes > braille

[weary linden]

Hello, and good morning everyone! I've just started my first College Math class this week, and it's giving me a bit of trouble. I am trying to do it mostly on my own without getting a tutor involved. I am having problems finding the proper equations, to get to my answer. I even looked online and was not able to get a specific set of rules to use, for this problem I am on. I was wondering if someone had a moment to tell me if I have figured out the correct steps to take, in this problem I am working on. (apologies for the wall of text!)

[brazen pendant]

don’t ask to ask. just ask your actual question, but do it in the right channel; this is for discussing how to teach math n stuff, not for math help

[weary linden]

I tried, but I have no permission in the mathematics channel under general.

[brazen pendant]

(see #info)

[weary linden]

And I am not sure what this falls under.

[brazen pendant]

because that’s not where to ask questions

when in doubt do it in a question channel

which are… made for questions

[weary linden]

Under MATH HELP: OPEN?

[brazen pendant]

yes

(ofc go to one that’s not occupied)

[weary linden]

Again, I am not sure what this problem falls under, it doesn't seem to fit any of the specific criteria listed for any of those channels. And my problem is finding the equation. Could you recommend one of the channels for me?

[brazen pendant]

#help-1

[weary linden]

Thank you.

[fading robin]

Are you guys grad TAs?

[boreal sentinel]

Not a grad nor a TA

At your service

[brazen pendant]

not a grad but a TA

wait I thought you did your master’s, rj?

[boreal sentinel]

Oh wait I got confused with being a phd

Then in that case I'm Sascha's inverse

Grad but not a TA

[brazen pendant]

so I’m (I/J)/(I/R)

got it

[boreal sentinel]

LMAO

Time for a new nickname

[tepid sand]

can a teacher invalidate a student's answer and solution just because "it's too advanced"?

something along the lines of "i didn't teach that yet"

[blissful knoll]

the only problem i see with solving an easier problem with a more advanced technique is if the method follows from the simpler statements you have to solve

circular reasoning and all that

tho it really depends on the teacher

[tepid sand]

i mean

i just used l'hopital's rule on 3 problems

that's it

it's not even that "advanced"

in fact, it was much easier using l'hopital's rule

[blissful knoll]

as long as you properly apply it i dont see a problem

[tepid sand]

instead of cancelling out common factors and stuff

[blissful knoll]

tho its always a good idea to try without l'hopital

[tepid sand]

im too lazy for that reeeeee

i actually double checked without l'hopital's rule and my answer is still correct

reeeeeeee

[blissful knoll]

but your teacher might decide to count it as wrong anyway

because teachers

[tepid sand]

but can i complain

i'm actually on a scholarship and in order to maintain it, i need to keep my grades above a certain value

and the problems my teacher didn't count as correct took a decent chunk off

[blissful knoll]

that seems weird to me

but if you wanna be sure, you should ask the teacher if its okay to use lhopital

[tepid sand]

the quiz already took place and the score's already there

so idk if i can still ask that

[blissful knoll]

oh

you can always try to reason with them

tho im not sure how effective that will be

since technically it is a correct solution to the problem

[tepid sand]

here's what i got

[blissful knoll]

at least in 3, lhopital cant be used right

if that says s -> 9 then its not 0/0

or inf/inf

[tepid sand]

i did manual approximation and it approached the same value iirc

hold on let me get my calculator

and if you check what 16/7 is

oh, it's 4 btw

not 9

sorry my handwriting's shite

[blissful knoll]

hmm then i dont know

[wispy slate]

come to #help-8

[bleak ingot]

Oh srsly

Orry

Sorry

[brazen pendant]

this is not a questions channel

this is in fact worse than #math-discussion

[crisp vapor]

ah shet haha sorry

[tall bay]

i whined about math education so much it finally has its own channel

but now i have no whining left to do

thats tuff

[spark flare]

Just whine to your heart's content !

[turbid zenith]

Does anyone have any suggestions for student-centered activities about graph theory appropriate for motivated/gifted high school students?

[hasty widget]

"It is also based on the conclusions of Krutetskii’s research, stating the existence of three types of mathematical ability: analytical, geometric and harmonic (combining the other two). The test was validated by a panel constituted by two university teachers of mathematics, one teacher of mathematics of the 2nd cycle and one 1st cycle teacher specialized in mathematics. . . ." - Ferreira, D., & Palhares, P. (2008). Chess and problem solving involving patterns. The Mathematics Enthusiast, 5(2), 249-256.

[weak hawk]

I succ at geometric

What's harmonic tho owo

[brazen pendant]

literally explained in the next four words

[weak hawk]

oh yeaH

my bad

[wispy seal]

@wispy slate Okay propose to me a number set

In which 1.9(repeating) fits in

[wispy slate]

what?

what do u mean a "number set" and "fits in"?

[wispy seal]

Is an element of

That's not the main point tho

What we're examining is this

[wispy slate]

any arbitrary set can be adjusted to contain 1.9repearing

[wispy seal]

and we see the limit supremum is 2

[wispy slate]

im gonna right 1.9h for that btw

[wispy seal]

...

But what number set is it in

[wispy slate]

cause of the hat

idk what u mean by number set

[wispy seal]

I feel like you're missing the point

like Z=integers, C=complex stuff

[wispy slate]

i feel like u're working with poor definitions

[wispy seal]

R-=real

...

I'm working with the traditional ones

[wispy slate]

there are uncountably many sets of numbers

[wispy seal]

Do you know what a real number is

Omg

Not those sets

R=set of all real n umbers

etc.

[wispy slate]

sure

so what is the question?

[wispy seal]

Read this

This is the definition

Now do you understand

[wispy slate]

im aware of that.
though those are not definitions of the numbers just a nice a heuristic for organzing them.

but okei

[wispy seal]

they're the definitions of the terms real...

You can't just go say a real number is only a whole integer

which is what you've been suggesting

[wispy slate]

that is not a definition of the reals that sufficies to do arithmetic or anything of equal complexity eith the reals

and i didnt say that

i didnt say anything like thay

[wispy seal]

what are you talking about. Provide an example.

[wispy slate]

that*

[wispy seal]

you said .9h in your notation is not real

[wispy slate]

what are you talking about?

[wispy seal]

multiple times

[wispy slate]

i said 1.9h8 is not a real number

[wispy seal]

to quote it's not a real number

...

exactly

[wispy slate]

lmfao

1.9h is a real number

1.9h8 is not

[wispy seal]

...

I will admit that while I strongly think it's a rational number because of limit epsilon definition, since I'm not confident I'll leave that unsaid. Look at the irrationa ldefinition

that's still a real number

even the wacky infinite number

[wispy slate]

okay, what do you think an irrational number is?

[wispy seal]

Any non imaginary number

[wispy slate]

and what do you think a real number is?

[wispy seal]

a real number is any number expressed on the real number line

[wispy slate]

okay, thats a circular definition

i can just as readily ask, what is the real number line

[wispy seal]

Fine

a real number is a value of a continuous quantity that can represent a distance along a line

Dictionary definition

[wispy slate]

well, that's not a mathematical definition

and arguably not a platonic/physical based one

[wispy seal]

it is from wikipedia I can find the wolfram source

[wispy slate]

i am asking you what you think a real number is

[wispy seal]

Consider the set of rational numbers, ℚ.

For any two Cauchy sequences of rational numbers 𝑋=⟨𝑥𝑛⟩,𝑌=⟨𝑦𝑛⟩, define an equivalence relation between the two as:

𝑋≡𝑌⟺∀𝜖∈ℚ>0:∃𝑛∈ℕ:∀𝑖,𝑗>𝑛:∣∣𝑥𝑖−𝑦𝑗∣∣<𝜖

A real number is an equivalence class [[⟨𝑥𝑛⟩]] of Cauchy sequences of rational numbers. (See Equivalence Relation on Cauchy Sequences.)

The set of real numbers is denoted ℝ.

I'll admit I have no clue what that means as I didn't take a class in set theory

[wispy slate]

that's certainly one such definition

[wispy seal]

If you can understand that, than I'm sure you win

It's the formal definition

[wispy slate]

okay, so this is a definition of real numbers. there are multiple.

[wispy seal]

Informal one I go by: Any number on the number line is referred to as a real number.

This includes more numbers than the set of rational numbers as 2‾√ for example is not rational.

The set of real numbers is denoted ℝ.

[wispy slate]

however, it relies on a particular notion of sequences, differences between sequences, and convergence

for these reasons, i think 1.9h8 is not a real

[wispy seal]

I feel like you're messing with me: the definition of a real number is pretty solidly set

[wispy slate]

im not.

and it's not.

[wispy seal]

and it literally says up there that real numbers can be ifninite

With infinite terms

And 1.9999h8

[wispy slate]

there are many things that satisfy thar

that*

and the reals are not unique in that regard

[wispy seal]

has no difference fro msomething with infinite terms

[wispy slate]

there are, for example, surreal numbers

and hyperreals

and infintesimals

the real line can be thought of as having "gaps" that are too big for any real number to fill.

which is where infintessimals come in

[wispy seal]

HMm reading up on it

Okay, I'll admit I'm not at all experienced with the concept of surreal numbers, but it seems to me that .9h in this case does not equal 1

@wispy slate

[wispy slate]

yes. .9h in this case id say equals 1

[wispy seal]

@wispy slate But if we use the definition of surreal numbers I've found, it seems like that would not be the case

correct me if I'm wrong, but it seems like surreal numbers are based on the idea that infinitisemal [1-.9h] does not equal 0

Now, if we go ahead and assume the real numbers are complete... doesn't 1.9h8=2

[tawdry venture]

you need to first define what $1.\overline98$ means, and if you define it as $1 + 0.9 + 0.09 + \cdots$, explain why you're putting that eight there

[burnt vessel]

Ann:

[tawdry venture]

and what, for example, something like $1.\overline97$ would refer to

[burnt vessel]

Ann:

[wispy seal]

@tawdry venture Well I still rather firmly believe that if we assume the real number line is complete, that would all be 2

Because we can just subtract the .0h7

And then we get .9h

added with .0h7

[tawdry venture]

that just kicks the problem down to

what even is $0.\overline07$

[burnt vessel]

Ann:

[tawdry venture]

and how's it different from 0

what is $0.\overline01$?

[burnt vessel]

Ann:

[wispy seal]

@tawdry venture if we assume the real set is complete it is 0 isn't it

They all become an epsilon delta limit

Which goes to 0

[tawdry venture]

no i mean

you have yet to define $0.\overline01$ to me

[burnt vessel]

Ann:

[wispy seal]

Now that I've read up about surreal numbers, I can kind of see what you were trying to argue if you use a different definition for reals where infinitesimals have actual values....

[tawdry venture]

you can't make any statements about it before you define it

[wispy seal]

It's 0...

If I assume the real set is complete because I can definite it as 1/10^n

[tawdry venture]

so you define $0.\overline01 = 0$?

[burnt vessel]

Ann:

[wispy seal]

as n-> infinity

[tawdry venture]

the limit of $10^{-n}$ as $n \to \infty$ is indeed 0.

[burnt vessel]

Ann:

[wispy seal]

Then I’d definite .0h1 as zero if the real set is complete

[tawdry venture]

so this begs the question

why even bother with $0.\overline01$ in the first place if you're defining it as zero right off the bat?

[burnt vessel]

Ann:

[wispy seal]

Well why do you need to define it? In cases like 1.9h8 you can use the method of subtracting and taking the limit to get 2

So long as you can prove for n>N x-L<E

[tawdry venture]

$2 \cdot 0.\overline9 = 1.\overline9$

[burnt vessel]

Ann:

[wispy seal]

Hm okay yeah that’d probably be the logical conclusion of me using complete real sets. On the other hand if we kind of abuse notation

We can use infinitisemal values like .0h1

And subtract them out

And make everything in terms of .9h+some small value

[tawdry venture]

you're making no sense

you're literally not making any sense whatsoever

[wispy seal]

Okay why can’t we turn things like 1.9h7 is 1.9h+.0h7

Take the limit for 1.9h as 2. And turn .0h7 as zero

[brazen pendant]

one way to define $0.\overline{0}1$ would be as $0 + \varepsilon$, where $\varepsilon$ is a number defined to be smaller than $\frac{1}{n}$ for all natural $n$, but bigger than $0$

[burnt vessel]

Sascha Baer:

[brazen pendant]

(hyperreals)

of course, ε is not a real number

but you can certainly define it

and study its properties

[onyx knoll]

ooh cool math education

i need that

[brazen pendant]

then read the channel description cause this channel has a different purpose

[sterile rover]

ok here's a bit of an odd question

wth is calculus?

see where I am from, calculus is not separate from analysis

in calculus do we just postulate the computation rules for limits and derivatives and integrals

without any proofs?

[normal aurora]

where I'm from calculus is just anything involving differentiation and integration

so limits aren't included

[sterile rover]

ok

question stands though

[vestal quiver]

There's no "calculus" either where I'm from

[sterile rover]

there's no proofs in calc is there

[vestal quiver]

In France, mathematics teaching is divided in 3: analysis, algebra and probabilities

[normal aurora]

no mechanics

[vestal quiver]

that would be physics

[sterile rover]

CM is 99% mathematics tho

the other 1% is newton's third law

anyway back to calculus

[vestal quiver]

mhmm

[sterile rover]

I might be able to find what a calc curicculum looks like

[vestal quiver]

do you mean it's mostly calculations?

[sterile rover]

but how is it taught?

[normal aurora]

in america they use a bunch of weird labels

[sterile rover]

I mean,

when you introduce derivatives

what do you even say?

if not lim df/dx

[normal aurora]

probably some weird handwavy shit

[sterile rover]

hmm, I probably need a USian

[normal aurora]

hmmm

https://www.khanacademy.org/math/calculus-1

seems quite good actually

[sterile rover]

dang that looks like cancer

[brazen pendant]

for me “calculus” is essentially analysis sans the rigor

basically, we have calculus in high school (learn the rules of integration and differentiation “intuitively” or computationally) and then analysis if you’re a math or math-adjacent major first year uni

no epsilons in calculus

but of course we don’t call the course “calculus”, we call it “mathematics”

because our high schools don’t have modular courses

you just have math

and the teacher has to teach certain topics till the end

[normal aurora]

in the UK we have

'Maths' and 'Additional Maths'

then 'Maths' and 'Further Maths'

[brazen pendant]

the word “calculus” really doens’t even exist in German tbh. the fundamental theorem is called “Fundamentalsatz der Integral- und Differentialrechnung”

[sterile rover]

Infinitesimalrechnung ?

[brazen pendant]

that would be infinitesimals, ie hyperreal stuff

so no

[sterile rover]

uhh no?

Die Infinitesimalrechnung ist eine von Gottfried Wilhelm Leibniz und Isaac Newton unabhängig voneinander entwickelte Technik, um Differential- und Integralrechnung zu betreiben.

[brazen pendant]

never heard it called that

[sterile rover]

hmm

[wispy seal]

Hmm calc as I was taught always included the formal limit definition to prove stuff

[wispy slate]

they just say "here's the actual definition of limit" and then for the rest of the course there are no rigorous proofs

[wispy seal]

@wispy slate not always

My calc class tried to prove it at least explain why everything was

Chain rule, product rule,

Actually I forgot why product rule is a thing

[wispy slate]

lol

[wispy seal]

I could probs prove it through chain rule abusive notation 🤔

I think it’s proven actually through limits tho

:bleh

[wispy slate]

prove it through multivariate chain rule

[wispy seal]

I was thinking something like that

Wait hmm that might not work

[wispy slate]

why?

[wispy seal]

I only got six hours of sleep so I might be doing math wrong

¯_(ツ)_/¯

Hmm assume f=function u * fiction g both in terms of x

Yeah okay I don’t see it

I’d have to try the limit way

Yeah I looked it up and there’s a really elegant chain rule proof

https://math.stackexchange.com/questions/2870420/a-proof-of-the-product-rule-using-the-single-variable-chain-rule

[civic tree]

yus

[soft valley]

is not this for math teachers?

[civic tree]

it's for any discussion of math edcations lol

[soft valley]

oof

[civic tree]

the description is kinda

strict but no on ecares

as long as it's on topic

sure

[soft valley]

In the "high school" (meant for 16-19 year olds here) you can choose differential equations, matrix calculus etc

What should I choose lol

[civic tree]

wtf

that's kind of better than most american hs

lol

[soft valley]

lol

[civic tree]

the most we get to is like

calculus in senior year

[soft valley]

it is a special math high school though

[civic tree]

lucky

i wanna be in a special math hs

[soft valley]

there is also like science n stuff

[civic tree]

my highschool is just known for having kids that are above average and nothing else

no real focus in any subject

exemplar test scores and nothing more

it's sad

[soft valley]

also the most motivated can do university courses

🤔

idk

[civic tree]

we just have a bunch of aps

and ib courses

and like

it's so dry tho

[soft valley]

oof

[civic tree]

we just

do them

:(

[soft valley]

we do not have that

we have ib high schools tho

so yeah there is 15 optional courses for u to take in math

[civic tree]

jesus fuck

i want

take me with u

✋

[soft valley]

sure

[civic tree]

yus ty

[soft valley]

there is game theory and basics of analysis

and statistics

and some math competition courses

[civic tree]

😭

[soft valley]

😭

[civic tree]

envy maximizes

im gonna go to my bed and cry now

[soft valley]

dont cry fly to Finland

Helsinki is the city

😄

[civic tree]

okay !!

[soft valley]

there is an entry exam tho

nothing that hard

just the stuff that has been taught in our schools

[soft valley]

"However, our mathematics high school is not just a high school. It is a community where mathematically oriented, special talented young people can develop their mathematical thinking skills beyond the usual high school level while being part of a group of highly respected individuals, but also working closely, eager to learn and develop."

sksk I am wheezing

[fervent topaz]

I'm not sure if this is the right place to ask, but I need help studying math.
My study style just does not work.
Any suggestions for approaching a math text book and studying/taking notes?

[wispy seal]

@soft valley I'd suggest De

[soft valley]

De?

[wispy seal]

@fervent topaz sure which thingo

Differential Equations

[soft valley]

oh

[wispy seal]

If your school offers it Linear algebra/multivariable calc ofc

[soft valley]

Yeah I thought about that

I do not think so

might be wrong tho

[wispy seal]

Lin alg is a pretty interesting class ¯_(ツ)_/¯

It's what a lot of modern computing is based on

Ofc all these classes depend on the teacher, but DE is very interesting

[soft valley]

I plan to study computer science

🙄

[wispy seal]

Then again, it can also be a waste of time

Multivariable calc in my exp. has stuff you actually learn

Diffeq felt a lot like Multi+extended Calc+some cool stuff

[soft valley]

is it hard lo

[wispy seal]

Depends. It's a HS class, so probs not as hard as it could be? Probs more introductory level

[soft valley]

idk about here

[wispy seal]

If you're into proof stuff, you can try complex analysis. But that probs requires DE first

Are you US?

[soft valley]

Nope

[wispy seal]

I went to a sort of mathy school in the US

[soft valley]

It is a math high school in Finland

[wispy seal]

And I'd say in my experience: DE was kinda useless but interesting how we learned logic stuff. PDE was like multi but worse (it had to do with the teacher liking Mathematica tons so it's meh)

Multi was good

[soft valley]

the only one if we do not count 1 weird place

[wispy seal]

very mathy and cool stuff

Lin alg: was cool. Really useful

Complex Analysis: was why I kinda gave up on math :L

Was too proofy

[soft valley]

which includes doing the whole high school curriculum in 2 years

🙄

[wispy seal]

OOF

I lost my helper status

[soft valley]

oof

I enjoy math anyway so I will take a few courses more cuz 30 in year is needed at least

(total in everything else ofc)

like English etc

[wispy seal]

oh this is a different system

[soft valley]

yeah it is

it usually lasts 3-4 years

[wispy seal]

Now that I noticed, I will say I'm a bit offended I was never told I was being taken off. On the other hand I was a bad helper

[soft valley]

4 years if u do it lil slower

well u can earn it again

[wispy seal]

Nah not worth lmao

I was being a bit dumb at 3 AM

[soft valley]

idk lol

oof

[wispy seal]

Anyway so I'd strongly suggest Lin alg

is very cools

[soft valley]

wish we had it

[wispy seal]

oh what are the choices then

@soft valley

[soft valley]

there are required courses but I am talking about the optional ones

classic geometry, game theory, diff eqs, matrix calc, statistics, basics of analysis, complex numbers and functions

what do u think? also some preparation for exams and math olympiad courses etc

[fervent topaz]

@wispy seal what do you mean which thingo?

[indigo hollow]

Can someone help me

about course or lesson

about characteristics method

[wispy seal]

@soft valley oh sorry take stat for real

Diffeqs is suggested

Matrix calc hmm I'm assuming that's multi calc

Yeah I'd take that

Complex depends how it's taught and what you're after.

Could be interesting

Also lmao MOs

I was shit at those was never careful enuf :/

@fervent topaz sorry when did I say thingo

Oh to the question you asked

what class is what I meant

[fervent topaz]

@wispy seal Calculus but honestly in general

[soft valley]

Oof

[wispy seal]

@fervent topaz for learnign calc

For me, it was not too bad as you can think of it in limits and real life

one thing that helpsi s proving stuff

doing problems ofc

[soft valley]

Cool

Thanks for your suggestions

[fervent topaz]

i just am bad at writing notes i think

[civic tree]

oh matrix calc is multivariable? so like not like insane matrices but just vectors? lolwut

[wispy slate]

lol ninja

[civic tree]

ya fam

wos worried they made yet another calculus field

again

there’s already like

200 calculus

s

[wispy slate]

calculi

[civic tree]

ye lol

[soft valley]

Oh yeah it is multivariable calc

So that and diff eqs?

And something else

[wispy slate]

what do you mean

[soft valley]

like what optional math courses should I choose

[wispy slate]

is linear algebra available

[soft valley]

don’t think so

you can take an university course but otherwise not

🤔

[wispy slate]

take the uni course then lel

[soft valley]

and ofc there is the stuff taught for all of us which is basically ”khan academy: algebra, precalc and calc, trig, vectors”

🙄

yeah I will if I have enuf time

Some do their math homework for 2 hours

[wispy slate]

and you do it in 5 minutes

[soft valley]

nah

[wispy slate]

lol

[soft valley]

I am not yet there

It is for 16-19yos

Smol ik

[wispy slate]

im also smol

[soft valley]

yesyes

ok I do my ”math homework” in few minutes but it is basic arithemics

so not real math

ik I spelled that wrong

[wispy slate]

ah ok

[soft valley]

yes

trig starts next year

👌🏼

or this year

[proper sky]

What is a gud math class to end with in senior year of high school

[topaz summit]

How do I develop an intuition for math? Big question, I know, but I've made it all the way up to calc 2, taken stats, do computer science undergrad research using concepts from probability and Bayesian inference, etc but I still feel like I'm struggling to wrap my head around the basics when it comes to reading the actual math. It's like approaching a new language every time and not remembering it the next time lol

Or like I'm not able to keep all the meanings for each symbol in an equation in my head and interpret the overall meaning

[astral fox]

do easy problems & verifications as you're reading

[topaz summit]

I've done that, lol. Like I said, it feels like everytime I'm approaching it for the first time. Even seeing the equation for a line in a slightly different form completely throws me off

It eventually comes to me because I work hard at it, but even after putting hours of practice into it, it still takes me twice or three times as long to do what plenty of others just kind of do. it's like I have some form of dyslexia but with mathematics

[astral fox]

if it works it works 🤷

math is hard

[topaz summit]

true. and it works when it works, until I'm constrained by time lol

oh well, c'est la vie

[deft bridge]

@topaz summit try taking to people about the math. Try to put yourself in situations where you'll have to explain it to others. Try to put yourself in environments that force you to think about it a more diverse set of ways. Not to sure what other environments though

[weak hawk]

@topaz summit Imo hang around people who are good at math and actually talk to them

Their passion is quite infectious

[soft valley]

I wish I could talk to people who are really good

my friend is good but the math we have now is pretty easy for everyone and should not be called math

[wispy slate]

there are people here who are really good though

[sweet swan]

What can people do with high level mwth degrees besides being a teacher

[wispy slate]

research

[hexed harbor]

Math improves thinking, and you can never have too much of that. Also, programming is kinda a form of mathematics.

[normal aurora]

silently hoping I don't become a programmer

[stuck lark]

My class is planning a revolution to avoid a math test tomorrow... French problems...

[unreal ledge]

One might say it's a French revolution

[limpid mantle]

une révolution s'il vous plaît

[wind river]

Mdrrrrr

[wispy slate]

mdr

[boreal sentinel]

vdr

[brazen pendant]

Today I wanted to hold my class, had planned to do everything on the projector

my laptop's VGA port broke, it seems

That was a fun improv and I need a new laptop set up till next week

[soft valley]

I want to become a programmer tbh

what math I should learn in order to become one?

[hexed harbor]

linear algebra, discrete math

matrices, which are part of linear algebra

[soft valley]

alright

[hexed harbor]

Oh and logic definitely

set theory, some at least

[olive mulch]

yeah, also calculus, number theory, combinatorics etc

[soft valley]

thanks

there is optional courses of multivariable calc later

[olive mulch]

basically it all depends what your goals are as a programmer, but in general you'll do fine with algebra, linear algebra, some discrete maths, some calculus and some number theory

[soft valley]

ofc they teach u basic single variable calc

sadly there is no linear algebra

unless you want to take a university level course

but in university there is

[olive mulch]

yeah, multivariate calc can be useful, simulation, graphics, AI, etc benefits from knowing some

ah, well if you're really motivated then you can get a primer on linear algebra for computer scientists / engineers etc

it's all very useful material

[soft valley]

well it has the most courses u can take in math in this country

so cannot really do better

[vivid junco]

lmao that pic

[wispy seal]

@proper sky if you want to go into math

some proof based course

@soft valley computer programming needs set theory right...

[soft valley]

Ye

I will take it later

I never said it isn’t needed

[indigo hollow]

hello

[wispy slate]

[indigo hollow]

I want to know how

Can I solve a PDE using Probability

some recommendation

for books

if possible plz

[wispy slate]

🤔

There is probably some niche context where it is.

But it'd be the other way around 99% of the time.

And even then there's surely a better way.

[indigo hollow]

I want to solve

fick law

in one dimensional case

[wispy slate]

Which one?

[indigo hollow]

pdv{C}{t} = pdv{C}{x}{x}

$$ pdv{C}{t} = pdv{C}{x}{x} $$

$$ \pdv{C}{t} = \pdv{C}{x}{x} $$

$$ \pdv{C}{t} = D.\pdv{C}{x}{x} $$

[burnt vessel]

Musbou:

[indigo hollow]

with D is positive constant

[wispy slate]

And what's your approach

[indigo hollow]

I am at the begining point

i tried to understand Characteristics method

but I didin't find anything suitable to my level

And I am trying to find some advices on a way to solve it

[brazen pendant]

please use the right channel

also please don’t answer questions in the wrong channel, just redirect

we might as well not have channels otherwise

[lost raptor]

What's a nice intuitive way to explain asymptote behavior to people with virtually only high school algebra knowledge?

[normal aurora]

it describes the general direction of the curve as you progress along it

[halcyon swift]

im not experienced with making diagrams and stuff but I'd like to ask if there are any places to look for a formal understanding of this addition algorithm. its super helpful for adding large numbers together.

[tawdry venture]

your diagram all but fails to explain the algorithm

[brazen pendant]

@normal aurora perhaps show how as you “zoom out”, the curve starts to look more and more like its asymptote

eg √(x)/√(1+x) looks like this from 0 to 5,

(and now we fiddle with wolfram alpha no not cut the y axis)

annoyingly, wolfram alpha seems to not understand mathematica syntax well enough

Plot[Sqrt[x]/Sqrt[1+x], {x, 0, 500}, PlotRange->All] just gives an “I don’t get it” error

but the point is that would look almost like a line

[halcyon swift]

@tawdry venture thats ok im just really bad at diagrams ill come back at a later time to try to make one that's better

[old badge]

wanna hear something? my girlfriend, who is in my advanced maths class didn't know the difference between circumference and area, and couldn't give me the formula

apparently her teachers just never prioritized it for more than a few short days, as it wasn't tested on

imagine being in high school maths and not knowing the circumference formula

American education in a nutshell

[spark flare]

I didn't know this formula when I entered high school either

[civic tree]

just derive it using magic

[brazen pendant]

or calculus

[old badge]

idk it just seems so fundamental to me

i mean, not fundamental, but

they just spebt so much time on it in my classes

actually, it seems the kids who did advanced math earlier got really screwed

they tookk 2 yrs of pre-algebra and stuffed it all into one, to muddle school kids with a subpar teacher

so they all did mediocre in algebra

now theyre in honors geometry and cant solve quadratics

math educatuon

[tawdry venture]

big yikes

[viral crag]

considering that I'm 35% through what I need to know for series/sequences/divergence tests

and have some knowledge of taylor, maclaurin, taylor identities etc etc

should I start using my prep review books now? Or should I wait until I've finished

ap exams are next month and I was wondering if the prep books could help accelerate my progress a bit

[astral fox]

should already be comfortable with practice tests tbh

[wispy slate]

Anyone know anywhere I can learn the stuff in the advanced math section online

[brazen pendant]

not really the channel to ask
textbooks are the way to go

figure out what you wanna learn in particular and well tell you how to get there

im just always here potato

[plain valve]

yeah but this channel as well - that's a coincidence lol

only channel i've checked today

[tawdry venture]

apparently not.

[unreal ledge]

I'm on mobile, the sidebar is hidden unless I look for it - which I never do. I assume a lot of people are in my boat

[wispy slate]

i should buy a boat

[civic tree]

5 wood in a u shape tho

[lapis furnace]

^^^^^^^^^^^

[civic tree]

yUh

[fading zinc]

I am currently self-studying a Measure Theory book. Would it be possible for anyone here to kindly review my progress periodically at your convenience and also quiz me as per your schedule?

Kind of losing discipline working on my own.

[prisma hawk]

Sidebar.

[spark flare]

I'll officially become a tutor tomorrow btw

[proper sky]

Nice

[brazen pendant]

private or at your school? what'll you be teaching?

[spark flare]

Private, l'll teach maths to highchoolers

I'll try negociating to see if I can tutor freshmen too but they want someone who is at gradschool for that

[vestal quiver]

French highschoolers?

[spark flare]

Yes

[vestal quiver]

are you not afraid that may be boring?

[spark flare]

Yes but I gotta make money 🤷

[vestal quiver]

Oh yeah indeed

[spark flare]

If it's too boring I'll stop,m and I'll try finding uni students online 🤷

But I'm registered in a tutoring website and I havennt found anyone

[brazen pendant]

the fact that you can TA starting from your third semester is one of the best things about my school, tbh

[spark flare]

But can you tutor uni students?

Or wait, TA means teacher assistant right

So you follow a teacher around basically?

[brazen pendant]

I am currently in my fourth semester and im a teaching assistant, holding 2h of classes (tutorials) per week and correct homework

I get paid for 15h

[spark flare]

Oh you do tutorials

How much do you get paid for that?

[spark flare]

I think I lacked enthusiasm during my interview 😰

[brazen pendant]

@spark flare 28 Francs/hour at 15h/week for 14 weeks; 1 franc is essentially equal to one USD though you have to factor in the much higher cost of living

I only actively teach 2h/week, the rest is correcting homework and preparing, and occasionally helping out in the StudyCenter (which is basically an unstructured tutorial where people can go to solve problems and ask the TAs)

[spark flare]

@brazen pendant francs? Where do you live, the 20th century's France

[brazen pendant]

swiss francs

[tawdry venture]

CHF

[winged horizon]

what am I

[civic tree]

less than one

also real talk

do you think it's a good idea for me to start like a seminar kind of thing at my school

sort of seminar

it wont be super duper long talks

but like

smol presentations

monthly or biweekly

where ppl who like math can sign up and present at a competent level some math

[brazen pendant]

I mean do you have things to talk about?

slash know people who do

and do you have people who would listen to them

[civic tree]

i could come up with a few multivariable calc presentations

[brazen pendant]

if the answer is yes to both, then why the heck not

[civic tree]

but

yea the issue is

people

my school is supposed to be academic

but it's fake

its sad and there are like

many people i can imagine who'd want to hear and do presentations

but cant because of how much stress is already on them from all these other fake things the school makes them do

there are other people also who know more math

and they could also present too

but are they gonna is the tough part

idk how im gonna motivate this schoolwide

[brazen pendant]

I feel like the way to go would be get 2-3 more people on board to rotate with you on presenting and make it very clear than anyone is invited to join in

and in particular, absolutely anyone is invited to actually listen, because no audience makes it a bit noninteresting :P

[civic tree]

i see

yeah

ty tho

gud advice

[wispy slate]

Do ppl teach in this channel

[vestal quiver]

no, they rather talk about teaching

[civic tree]

i talked to one of the math teachers (who is also my supervisor for my IB paper ) about starting the seminars and he said that we could definitely do it, and told me that we'd work on creating a set of topics in advance !!!

im excited

he's very wholesome too we had a discussion about the nature of math versus art and why beautiful results arent seen in highschool because we're still working on the basics, while for something like art, people can understand already with a little bit of competence why some work of art is significant

he said that if we were to take what we were doing in highschool in a math class and apply it to art education, it would be like painting a canvas single colors over and over again

rip highschool maths then

im not fully on the idea of the comparison but eh

you get what i mean

anyway im just happy that something is gonna happen i think

[grim laurel]

That's awesome! I hope it goes well!

[civic tree]

wahoo

!!!

[brazen pendant]

I feel like it's less painting with one color and more painting by numbers

the results in high school can be alright, but there was no creativity involved, it's just following steps

[solemn glacier]

When it comes to actually having a solid understanding of maths

What cna I do that’s not studying my text book?

Don’t get me wrong, I don’t mind it, I spend 2 hours with it every day

But I’ve noticed a pattern with it

Th ebook does a good job at teaching me the subjects in theory

But then when I get to an mock exam paper, it falls a part because I’m not used to applying it practically

[brazen pendant]

I reckon a solid 50% of your study time should be solving problems

if your textbook has problems, do those; else find ones on google, there's problem sheets for everything floating around

knowing the theory and applying it are very different, but the latter can help you a lot in understanding the former

[tawdry venture]

theoretical knowledge without practical applications is exactly and precisely WORTHLESS.

[brazen pendant]

eeh
that's taking it too far

I think there's merit in knowing theory from fields you're not working in, because it means when you do need it you've heard of it and know what to look for

i'm not surprised you're constantly miserable with a mindset like that

[tawdry venture]

i should just shut up before i start spewing any more bullshit in the agitated state i'm in

[brazen pendant]

that's an extremely pessimistic outlook

(note for the confused reader: there was a deleted message)

[tawdry venture]

thanks for confirming it's all my fault, though

[brazen pendant]

look, I will not tell you it's not if you so much desire it to be

anyway, imo, knowing more is always good, but it is extremely important that pure knowledge is not enough to get you anywhere

in the end, results matter

if you know all the grammar rules but don't practice speaking you wont be holding conversations, nevertheless knowing those rules can be useful, and interesting in their own right

if your goal is not speaking the language but learning about it, why bother practicing to speak (answer: because it will still help you keep those rules memorized)

[dusky scarab]

Should be more like 5% learning theory, 95% struggling with problems imo

[brazen pendant]

unless you have a ridiculous amount of time, you'll never get anywhere at those speeds

you can't keep working on the same stuff for ages

[dusky scarab]

and that is indeed why I never get anywhere XD

[brazen pendant]

like let's say you study a few pages of theory for an hour. You now propose to solve exercises on that theoey for 20 hours

[dusky scarab]

At one point in last semester I tried proving lagrange theorem from (practically) scratch

Spent 14 hours on it

[brazen pendant]

something like 3 hours of classes (theory) and 4-6h of homework has worked well for me

which lagrange theorem

order of subgroup divides order of group?

[dusky scarab]

Yes

[brazen pendant]

how

that's like three lines

[dusky scarab]

Yeah if you know what cosets are XD

[brazen pendant]

a few more if you have to justify group multiplication to be bijective (when fixing one argument)

[dusky scarab]

yes I did not realise that for like 13 hours ok XD

To be fair a lot of that time was spent trying to prove some other difficult results

Like cauchy's theorem

In any case I doubt many people know how hard it actually is to come up with a proof of lagrange theorem

Because lecturers just blurt out the proof in class

that's actually one of the reasons I don't go to lectures

But imo, group axioms, relevant definitions, and the statement of lagrange's theorem is comparable in difficulty to an IMO3/6 problem

Anyway, getting back to what I was saying before - learning material usually takes almost no time at all anyway: really all you need are definitions, and then the "understanding" bit can be built when doing the problems

[brazen pendant]

yea it's definitely a proof with a lot of insight behind it

[dusky scarab]

Yeah it is XD

One of the main difficulties was actually realising that you had to start from the subgroup

And prove that all groups containing the subgroup have order a multiple of the subgroup's order

[wispy slate]

lmao tony

you were so surprised when i said 'bezout'

[dusky scarab]

yeah I still don't see how bezout is helpful XD

[wispy slate]

poor wony

spend another 14 hours and you'll see

[spark flare]

I'll have my first students in two weeks

Any advice on how to prepare

[brazen pendant]

if you can, look at their curriculum/materials. there'll be things they do differently than what you're used to and it's good to be prepared for that and not confuse them with your own favourite notations/tricks

[turbid zenith]

What course are you teaching?

(@spark flare )

[autumn trellis]

I think you must take take inspiration from Richard. Visit Aops ,click on resource then go to the video library observe his way of teaching. @spark flare

[wispy slate]

patrick who

[spark flare]

@autumn trellis thankq I'll check it out !

@turbid zenith maths, I don't know exactly but I think they're doing probabilities right now so probably (lol) this

[autumn trellis]

https://artofproblemsolving.com/videos @spark flare

@wispy slate I mean Richard Rusczyk.

[wispy slate]

oh

[autumn trellis]

I love his way of teaching.