math-pedagogy

[turbid zenith]

Why involve epsilons and deltas in the first place at the high school level?

[tame tulip]

the ap calc exam was annoying for me because my scrap paper was like weird

like usually for mcq i would just do the work on the sides

but with a digital exam your work is disorganized and you dont know where it points to when ur done

i dont think any mathphys mcq exams should be done digitally, show your work stuff is fine though

[sick bough]

why not? genuinely, high schoolers are smart enough to understand it after some practice, and it's good knowledge to have instead of a halfbaked understanding of some rules that you can't always apply

[cloud zealot]

thing is, you have to motivate it somehow and it's not gonna stick for most if they don't see why they need to learn it, and most aren't moved by appeals to a need for rigor when it appears than the handwavey definitions they were given suffice for the canned problems they've received so far. even if you do decide to teach the epsilon-delta definition, do you choose to incorporate the whole paradigm into all further discussions of limits like with derivatives or integrals? you could choose to bite the bullet and make calculus classes into spivak-level courses everywhere, but to be quite frank, the primary beneficiaries of a high-school calculus class aren't future math majors and they will move along in life fine without ever knowing about epsilons and deltas.

i actually would like to see more rigor in a calculus class, but if revolutionizing the entire education system to support rigor isn't on the table, then problem-solving should be prioritized over rigor

[sick bough]

applying half understood rules is weaker problem solving skills than being able to adopt and apply the ideas of a systematic framework -- it's not really about whether they use epsilon delta specifically, it's about developing the reasoning skills to be able to use epsilon delta, which is useful far beyond just those who would go into quantitative disciplines

[cosmic ibex]

It's not really clear to me which alternative to "epsilon-delta" we're comparing to. Intuitively the major stumbles of the usual epsilon-delta definition would seem to be (a) Greek letters, and (b) writing the thing down with symbolic quantifiers rather than words. But it ought to be possible to convey the content of the definition without using either of those -- and I'm unsure whether that is included when someone says epsilon-delta can/should/shouldn't be taught at the high-school level.

Even when using words, there's still a choice between just saying "no matter how close we want to get" and explicitly stating the degree of closeness as picking a maximal distance as a number. Is that the operative distinction between epsilon-delta or not?

I suppose it's also possible to explain it so handwavily ("we can f(x) to be as close to L as we want just by picking x close enough to c") that it becomes actually unclear whether, say, 0.5 is a limit of sin(1/x) as x->0 or not, unless one has already met a more careful definition.

[midnight scarab]

Yeah, it should be "f(x) is as close to a constant as we want, on an appropriately small interval around a" (here I'm using the French and general topo convention of not excluding the point a itself from the limit ; and yes this is equivalent to continuity at a)

[cosmic ibex]

Unfortunately I think the convention about excluding the point itself or not needs to be taught explicitly somehow -- despite being a pretty inconsequential choice from a more mature mathematical perspective -- because it will be relevant on the standardized test almost certainly.

(Unless we're talking about revolutionizing the entire education system, that is).

[supple flume]

does anyone have a way i can overcome my belief that i dont know enough maths to teach,
i know that i know enough otherwise i wouldnt be here, i just sometimes get stuck and then get into a sort of the person that im trying to teach thinks i dont know anything, lose money, idk 😭

i am really bad at communicating things sometimes too and idk how i can improve on this too

[marsh thistle]

In some instances (e.g. more specialized courses?) I think it's not uncommon to basically be learning the material alongside the students, you just have to do it at least a week ahead of them
So it might be worth shifting your perspective from "do I know enough" to "have I prepared enough", and the latter is something you have more control over

[supple flume]

ah so lijke

reviewing the syllabuses

im teaching curriculums unfamiliar to me so maybe i should reviewww ahhh

unfamiliar as in i didnt grow up with it< like i know the things, just everythings worded so weirdly idk really lol

[marsh thistle]

Yeah you certainly need to become familiar with it but I think because of your higher level of experience / maturity you can do it relatively quickly and confidently

[supple flume]

ah yea i have some gaps just cuz i wasnt taught some of this hs stuff or it's been so many years since i saw it

so is it a good standard to like ask the person ur teaching what ur gonna be doing the week aftert

[marsh thistle]

Are you tutoring a single student? Maybe if you tell us the type of teaching you have in mind someone can give you more specific advice

[supple flume]

it's one on one yes

at like a center

im more worried about like the higher level subjects like ofc i can teach primary school and stuff thats more of me dealing with kids being kids

[midnight scarab]

Yeah I agree. I didn't want to bother in my message because it's a pain (and imo a 🥖 win for not complicating things by excluding the point), but it's of course very important for standardised tests because changing just f(a) is a typical question

[cloud stream]

I didnt know the names of the greek letters or what they meant until like freshman year of college

as in, i felt stupid because i didnt understand "real math"

it would be helpful to put up a chart of the letters with their names and emphasize "this is just an alphabet"

[cloud stream]

can i dm you resources n stuff? Im also like, 20 and ive been autistic about pedagogy for the last week lmao

check out https://betterexplained.com/

some ideas: i think students learn best when the teacher is another student because theres an emphasis on exchanging perspectives and a teamwork that leads to more creative thought

a teacher should be open about what they know and genuinely ask students for their insights

this is why i dont like pre-made lecture notes and typeset stuff. its anti-annotation, it wards of an empathetic connection over stuff that people find interesting

If youre curious about ways to teach math and physics you can find short papers on sci-hub that give great insight

like "an alternative approach to lagrangians" and "on the invariance if spacetime" stuff like that

[valid snow]

well I mean how else would you introduce calculus

[valid snow]

omg thanks

I'll check it out

[cloud stream]

^^

[valid snow]

I sort of agree and I always try to be as interactive as possible when it comes to teaching

but sometimes I'm worried that especially as a student you can come off as incompetent

but maybe it just derives from my poor intuition when it comes to explaining these concepts

[cloud stream]

ive read that learned helplessness can be passed on to students when an authority figure gets frustrated and scared- i think that its important to humor yourself and admit when you dont get something and be excited to figure it out

ive never met a human thats 100% confident about everything always and its insane that we ever expect that of people

when im teaching an idea to someone and i think my intuition is lacking i ask them what they think

https://pz.harvard.edu/resources

i carry these thinking routines around with me so that when i get confused i have a good reference on how to figure it out on the fly

i like your website link btw its pretty

[valid snow]

damn this is all really helpful

[valid snow]

website link?

[valid snow]

true that, I'm still a student after all

I might give it another try once I figure out how to not fail this semester haha

tutoring I mean

[cloud stream]

anilist

[valid snow]

ohhh thanks

[supple flume]

yes

[toxic harbor]

need some guidence in the thread: #foundations message

[tame tulip]

what completeness axiom do you guys think is pedagogically best for a first real analysis course?

afaik most books use the supremum property, but of course you can always start from cauchy completion + archimedean property, nested interval property + archimedean, and mct

at some point in a course these should all be tied together to show their equivalence imo

[cosmic ibex]

Hmm, the supremum property sounds like the one that most obviously "ought to be true about the number line".

[midnight scarab]

Yeah, either supremum or interval/squeeze

Though due to prior exposure, the decimal expansion is likely to be the one that students would think of

[cosmic ibex]

But that's part of what we need an alternative to, so we can motivate e.g. 0.999...=1 on some axiomatic basis.

[halcyon glade]

Not an answer, but here's a really cool physical demonstration of this: you press any two numbers, and the line connecting the two levels corresponding to those numbers lights up and intersects the middle at where their product lies

e.g. 9 * 6 = 54 in this picture

[halcyon glade]

I like how you can motivate the nested interval property very practically: if you make more and more precise measurements of something, you should be able to find the "true" value of it after an infinite number of measurements

There's a constructive analysis book that does real analysis without proof by contradiction along these lines

You can just define a real number by this nested interval scheme, as long as you define what it means for two of these nested interval sequences to be equivalent (which is rather intuitive—if I measure something and you measure something, we should have a way of checking that we're measuring the same thing)

https://onlinelibrary.wiley.com/doi/book/10.1002/9781118033357

[cloud zealot]

this is also reprinted by AMS

https://bookstore.ams.org/amstext-38

[quiet roost]

Fun fact about that : Assuming "finitely additive probability measures" are a good framework for modelling random experiments, it can be shown that there is at least one "probability" P (Here P(A) would be the "probability" that the number to be found is located in A) for which the rule "The precise number can be found after infinite measurement" fails almost surely. Idea of proof : Ultrafilter extension of a filter of neighborhood of a point that excludes the point itself.
Of course, in the usual case like discussed, when the point is fixed and so with no uncertainty (so the "probability" is a dirac measure), it works as expected.

[torn apex]

I can't quite formulate this idea coherently but I realized last night that most of my math interests are literally nothing more than a proxy for liking shiny visual things. smh
I was in the middle of prototyping this knot visualizer game and in a span of 15 mins, I've reversed my decades long position on knot theory being utterly boring and useless.
If I induct that experience over to the liberal arts/"not math" crowd, then I would imagine the same process can happen for them 🤷‍♂️

Does anyone know any work or math education research on this topic?

[scarlet panther]

What do you use for math worksheets, either conceptual learning in the classroom or for quick practice problems? When I would want to just work out some random problems, I would look up worksheets on Google and just use some of the first results, like math-drills. Kuta also shows up which looks like a good software for making worksheets. Are there any particular favorites?

[echo bloom]

Hey Guys, idk where to post this question but here looks okey to post it; So guys i have to start studying with ai because i cant afford a tutor in my country its so expensive, my new challenge its physics in college.
I have to start studying with AI to start doing good in college, my new topic is kinematics in two motions and idk how to start. I wanna know if there is any prompt, app, etc to start studying in a proper way so yeah any tip, prompt, how to etc will be helpful. Good day, and thanks!

[austere delta]

Why do you "have to" start studying with AI?

Most people study without extensive tutors

[echo bloom]

hey bro! thanks for the answer, i’ve never study with a book, so idk where to start you know?

[austere delta]

But you're enrolled in college right?

So then you'll have a curriculum, and exercises, and office hours, and peers, right?

I'd start with one of those things

[echo bloom]

well theres the thing bro, im in Panama and in my college theres no thing as office hours and our professor DONT put us any practices, quizes etc, hes the baddest prof in physics… So my peers and i are very but very like lose you know

[tall bolt]

My UG also didnt have office hours, but im quite sure you will have a curiculum, some reccomended books to read, and those books will have practice problems etc in them. Also for anything at the early UG level there will be very good resources online, I dont know of any spanish sources, but I assure you they will be out there

I would very much caution against using AI for anything other than "Where can I find resources about topic X" because you just dont know enough yet to verify if the output is any good

[tawny slate]

i think this topic is a better fit in #study-discussion

in general, you will do better for your study habits if you avoid AI as much as possible and stick to traditional sources

try to find downloads for books, #book-recommendations might help you find some quality sources and other material, even youtube nowadays is often better than AI (as long as you avoid the AI generated videos, obviously)

the reasons for avoiding AI and choosing traditional sources:

• primary sourcing
• much less prone to errors of all kinds, both innocuous and serious, both in minor steps and overall design
• because of the chaotic nature of errors AI are prone to, it is only a good resource for specific tasks and for people who already have competency in said area
• getting in the habit of using AI is also generally bad for your cognitive development, you use less of your brain learning and hurts you in the long run (academic neuroscience studies support this)
• you don't lose much by not using AI, don't let anyone tell you otherwise. i have generally used almost zero AI in my math and programming work and I'm doing perfectly fine, both as a professional and in my hobby

the guideline i use is:

if you have a query/task that needs to be done:

• can it be done without AI?
• do you understand how an AI output can potentially pose problems? are the consequences of those problems manageable?
• can the AI output be verified for correctness and accuracy?
• will you verify the AI output for correctness and accuracy?
• do you understand your standard for quality outputs?
• will you hold AI output to that standard, or will you just accept whatever lower quality standards it generates?

if you can do it without AI, do it without AI. if you cant or wont hold it to correctness and quality standards, don't touch it

[echo bloom]

thanks a lot for the response, ill check it out

[echo bloom]

thanks a lot king!

[white fulcrum]

a lot of math channels have poppped up lately that I think are AI, I'm going mad bc I'm not sure. anyone else in this boat?

[quasi maple]

Do you have examples?

[tawny slate]

yeah there are a lot, in fact there is even an entire website that dominates search results that is completely written by AI, and they dont even hide it

[quasi maple]

oh YT channels

I thought you meant Discord ones lol

[white fulcrum]

yes I meant yt channels

[torn apex]

ah you just helped me realize why every yt creator is plastering their face all over their thumbnails.

[keen osprey]

Wow just discovered this channel it's amazing

[white fulcrum]

my psychologist met Isaac Asimov, I'm so hype

[turbid zenith]

Welp I'm not getting any grading done today

[tame tulip]

hahaha my friend told me someoen at penn state hacked canvas during finals week

[rapid tusk]

now if someone could do the same to brightspace

[slim path]

There are indeed but I almost never check out new channels unless someone ik recommends them to me in good faith lol. I know this only because some people pointed out a few and I went and checked.

Also a well known YouTube math content creator actually did a video on the type of AI recommendations her creator dashboard gets from YouTube. They were borderline nonsensical and buzzwordy.

I'd wager some beginner content creators and a few experienced ones are making some money out of this by using these recommendations. Most of the deniers who have new theories everyday will keep flocking there.

[halcyon glade]

What's the optimal number of people per group for small discussion groups where everyone is naturally encouraged to participate actively? There must be a good deal of research on this

[sick bough]

in my experience it's less about number and more about ensuring that each group has some people who know each other, some people who don't, and at least one more outgoing person who can bring everyone into discussion

this can be difficult to set up organically tho

[rapid tusk]

if I had to name a number just from vibes/experience I think it’s like 3-4

[quasi maple]

At least 2 ig

[undone epoch]

How do I teach someone who doesn't know even simplest operations like substition or addition, like teaching your younger sister? Where do I start and how do I progress?

[halcyon glade]

I think there definitely is a number

[ocean frigate]

everything is counting in the end

[sick bough]

show examples until they get it, then increase the complexity gradually as they accumulate more and more concepts and skills

[hardy needle]

just wanted to vent here, not sure if it really counts but I'm a grader for Calc I/Calc II at my school, and it kinda hurts me on the inside when im grading and seeing students missing free points by just not even attempting some problems

I aspire to be a professor one day so it hurts me seeing people miss free points on homework

[twin lichen]

Could it be time constraints?

Even for homework maybe they planned to talk to someone else about how to do it, and then ran out of time or forgot about it

[hardy needle]

Now that I think about it for that class, the prof releases the hw in a weird way (like sometimes they only get 4 days to do it, and sometimes it's like 20 problems)

So I guess I could kinda see it

But also they have to upload it as a pdf and submit and I think a lot of them don't realize the platform (gradescope) only allows u to submit an assignment as a single pdf, not multiple

I try and leave as much feedback as I can but who knows if students actually look at it

[knotty arch]

true, sometimes the problem is "overwhelming" in a sense that it dissuades the student from even attempting

[hardy needle]

makes sense, its a Calc II class but more oriented for engineers/science-related majors so more applied stuff

so some of the word problems are really dense

[abstract magnet]

I wonder if there are Calc II courses that lean towards pure math and give u a taste of analysis

[hardy needle]

maybe in more prestigious/rigorous colleges/programs, the college im graduating from rn didnt really touch much of that analysis/pure math behind the calculus

[rose dove]

usually honors calc does

for example ours reads spivak

[cloud stream]

it can be embarrassing to write down something thats obviously wrong

[hardy needle]

I can understand that, a few students don't know what to do and will put "idk how to do this" or "???" so I always leave feedback detailing the steps on how to do it

But the professor also has me write the solutions out and just puts it in the "correct" box in the rubric for them to see

[slim path]

There are. Where I did my UG, we followed Apostol for Calc 1 (Single Variable) and Calc 2 (Multivar and Intro to Linear ODEs). This wasn't any honors calc course of any sort tho but it's par for the course in my country since we see a lot of Calculus in High School. More math programmes should be doing this here but I only know a handful lol.

[rapid tusk]

many unis no longer offer honors calculus

[abstract magnet]

That makes sense

[abstract magnet]

That’s interesting, I took mine at a community college and it’s where I was first introduced to 1st-order logical symbols once we got to sequences

[slim path]

Why tho? Any particular reason?

[slim path]

Yeah we had a simultaneous run for a course on Foundations which did this, alongside Linear Algebra 1 and Intro to Probability

[cloud zealot]

not enough students taking it ig

[slim path]

That's sad ngl.

[rose dove]

yeah ours is no longer offered :(

[white fulcrum]

What does abundance mean in the table of elements for look and say sequence https://en.wikipedia.org/wiki/Look-and-say_sequence

[austere flicker]

average # of occurrences of that atom, per million atoms: https://sites.math.rutgers.edu/~zeilberg/EM12/ConwayWW.pdf

[white fulcrum]

Tyty

Are they rational or is the table just cut off

Also feynman and dijkstra share a bday, different years tho

[austere flicker]

i actually have no idea sorry 😅 i just pulled this from the wikipedia references

[shy grotto]

What’s yr advice to start?

[worn oasis]

Yo, I'm currently tutoring some HS kids on maths and further maths. How do you guys like to set your tests for students in terms of difficulty/novelty? I personally would want to set my tests harder than the actual exam, to prep them in case the actual exam is unusually difficult, but I also don't want to demotivate my students😭 So I'm tryna find a balance between the two ig

and by "harder" i mean more novel/requires more insight, not in terms of tediousness

[rapid tusk]

make some of the hardest (harder than actual exam) ones extra credit maybe?

[worn oasis]

Hmm the timings tight enough as is im not sure students will have time for extra credit

a full paper is 3 hours and 100 marks, no mcqs

[quasi maple]

forget the marks, how many questions is that

Because in the UK an equivalent paper is just 90 minutes long for the same number of marks

(for around 14-15 questions)

[jaunty yew]

Be like Ireland in the Leaving Cert and make the lowest point value 5

[worn oasis]

around 10-12 on a full paper, short questions can be 4 marks while long, heavily context based question can be up to 15 (multiple parts)

for context this is a past year paper for pure

[zinc dove]

How many students per class are there?

[nocturne thorn]

AAAAAAAAAA

Question 2 should really drive at the point that a bare harvesting term like this is kind of broken for real life models. The system is set up such that you could get negative population from technically physical starting conditions.

(The rule of thumb is to never have a deletion term that doesn’t immediately zero out when the population is itself zero)

[atomic elk]

funily enough global south unis use SPivak if they wanna make you go that route, you can just check before

[abstract magnet]

Yall im using Claude premium to help me study Real Analysis (Tao), is it alright as long as I use other sources on top of that

[rapid tusk]

1. wrong channel
2. actually read the book instead of feeding it to an LLM

[abstract magnet]

1. Oops
2. I am

[hardy needle]

rudin ruined my life

[rapid tusk]

you and me both

at least it’s over

[hardy needle]

praying for no rudin in my masters program 🙏

[mortal crag]

no

[abstract magnet]

No bueno?

[mortal crag]

its not good

learn the old fashioned way

also #study-discussion

[abstract magnet]

Ur kind of right

But I’m not solely relying on it ofc

[mortal crag]

its better to not use it at all

[abstract magnet]

Makes sense

What I mainly do is read the text, write down definitions/important notes, do the exercises and check with various resources to see how my proof is

[nimble escarp]

Book recommendations for calculus (or series of books)?

• Large
• Modern
• Comprehensive
• Starts undergrad, builds into advanced concepts

[rapid tusk]

starts undergrad, builds into advanced concepts

idk what you mean by “advanced concepts”

just pick up an analysis text at that point 😭

also #book-recommendations

[nimble escarp]

Needs to cover topics like calc of variations, differential geo, etc too

[rapid tusk]

no one book or series covers that all in one afaik

[nimble escarp]

That can be split into multiple books. The book needs to be comprehensive and modern that’s all

Not 1900s style

[turbid zenith]

Look into Adams/Essex

It has a surprising number of advanced topics

I got the newest edition (10th) on Amazon

[hardy needle]

James Stewart, Essential Calculus 2nd edition 🔥

[vestal tangle]

a course in mathematics for students of physics

by sternberg

it doesn't start at the very beginning. if i remember right it assumes you know what a limit is and you sort of already know about the derivative

but it covers linear algebra from scratch and develops multivariable/vector calculus, covers some differential equation stuff and moves into differential forms and some baby differential geometry

it's a very unique book

[upper crag]

well i have some question books 4 u

higher alegbra: hall and knight

differential equations:bernand and child

complex analysis: serge lang

real analysis: lewin

ez

[white fulcrum]

A student the other day insisted a day was 12hrs and that 24hrs was actually one day and one night

[austere delta]

In my language we have a word for a 24 hour period, so this checks with me

Though I wouldn't say a day is 12h, but rather the time from sunrise to sunset

[white fulcrum]

what language?

[austere delta]

Norwegian, the word being døgn

Apparently the word exists in English as well
https://en.wikipedia.org/wiki/Nychthemeron

[nimble escarp]

I’m planning on getting this one along with a few others. How’s it compare to “Vector Calculus (Jerrold Marsden)”?

[nimble escarp]

sweet, sounds like what I need

[tawny slate]

had a casual conversation with an adult the other day about math

he said math was just a bunch of made up beliefs that dont work. i asked why he thinks that

he gives an example: does 2+2 always equal 4? no, because consider adding 2 chickens to 2 rocks

i had to defenestrate myself from the conversation before my autism overloaded somewhere

how would you guys have responded

[sick bough]

I would say that if he can't see why 2 chickens and 2 rocks is four things, then the problem is his lack of imagination, not with mathematics

[tawny slate]

i actually tried a similar approach: "its not the math that is wrong, you select the math that fits your use case"

this particular approach is to select the use case that fits the math, which is I think the same main idea but just weirder and less pragmatic, but either way this person was absolutely not convinced because he seems hung up on the fact that you could still pick bad math

then i simply said "but you can always pick bad math, why would you choose a bad interpretation?" but that just invoked a response of "but people treat math as if its factual and is always right" and you can imagine how it went from there

[hardy needle]

I'm not sure, at my school we used it for calc 1-3 since it covers all of it

Stewart that is

[nimble escarp]

You should’ve answered yes. Its just a new set.
Or you could invent any nonsense and he wouldn’t know anyway.

[tawny slate]

what would be the point in that?

[midnight scarab]

Yeah I'd just say that "2 things + 2 things" is 4 things sure, but if you want to know what kind of things, then "2 chickens + 2 rocks" is 2 chickens + 2 rocks...

And then he'd obviously insist one way or another and I'd just regret being here

[little drum]

i wouldnt really take part in such a conversation

there's a big difference between someone who says "i dont understand how math works" and someone who says "math is made up nonsense that doesnt work"

i think the latter kind of person isnt going to be able to be convinced of much

[rapid tusk]

the “mATh iS ObJeCTivE” nonsense drives me up the wall

back in hs I remember someone unironically writing their undergrad admissions essay around it

[white fulcrum]

math is objective except sometimes #foundations makes me question that.

[quasi maple]

"But what is math?"

https://klipy.com/gifs/michael-vsauce--k01KS3V8D913ATW1ACSADSRV6M4

Honestly if someone wanted a genuine conversation on the "2 chickens + 2 rocks" issue, you'd have to acknowledge that the baseline understandings of what "maths" is between the two ppl in the conversation may not be coherent

(ffs what is it with me and unnecessarily long sentences)

[quasi maple]

* -issue, you need to check whether you agree on what "maths" is

[tame ridge]

would've said "ur right", then ask him if he can give me change for 100, then hand him 100 stones

[vestal tangle]

what drives you up the wall about that?

[tawny slate]

probably the closest thing to a good answer so far, but obv id tweak this to be more socially appropriate

[halcyon glade]

I think it's an interesting question

It's not clear to me why math seems so necessary to our theories about how the world works yet somehow it's broadly applicable across the sciences

I would probably respond by asking them for more details about their belief system?

Like what does it mean for a belief to work or not work in his framework

And are there things that he's confident aren't made up

It does seem like there is a fundamental tension between how mathematicians think about what math is and how it ends up getting used

[tawny slate]

oh, this might be promising

[tawny slate]

i do find it exceptionally interesting that half of the responses tried to find an interpretation that fits the math rather than find math that fits the use case

that leads to another interesting question (sorry for pulling the conversation in yet another direction), which is whether there is any actual reason you would do this in practice. i cant seem to think of any

[tawny slate]

actually i just realized i missed the "what is math" response whoops, also a promising way to go, and actually that's literally the conversation before that comment about 2+2=4 hahaha

[tame ridge]

I think their argument for math being subjective is somewhat weak: I could agree to some extent that there are things where it would not be apt to apply math. But that doesn't say math is subjective. That 2+2=4 is a consequence of the definition of naturals. And the notion of naturals can be applied to many things irl. But this is not saying that any two things can be added to make intuitive sense: add two drop of water into a bowl, then another two. Do you necessarily get 4 drops of water when you pour it out? Maybe not. But we can apply such additive/multiplicative rules to a system, like a monetary system where amount of money is defined by a number

I agree that it might be subjective where math can be applied: the example he gave may illustrate this. However, math does not claim that everything can be added, but rather claims there is a system where 2 and 2 are added to something we defined to be 4.

[vagrant meadow]

concerning. but i'm wondering how this (category of) technology could potentially be used for good (ex. in the classroom). i never learned manim, but i always wanted to. it seems we're at the point where there are low effort ways to generate 3b1b-esque "quality" content personalized for our students/lecture material/etc.
https://www.youtube.com/watch?v=mRO_QonhC2c

[surreal tinsel]

Hey i just watched that this morning

[vagrant meadow]

haha me too but i've been thinking about it all day

supposedly this tool can take in a prompt like "explain why derivatives are slopes" and generate a manim video explainer for it. interesting. dunno how much i would use it personally, but maybe in the hands of a more creative instructor this could have a serious productivity boost
https://github.com/HarleyCoops/Math-To-Manim

i guess maybe open question: has anyone here actually used manim for their lectures/teaching? if not, would you consider using an ai-powered tool to integrate manim into your pedagogical repertoire

i honestly dunno how i'd feel if i could just feed a blog post or set of lecture slides/a handout into some tool and get some sterile polished ai slop generated from it. maybe if it was actually good, but it might feel a bit soulless compared to something i wrote or made completely myself.

it's one thing to put a handout into an AI to double check for typos, that the math works out nicely, or for weird wording, but i would never just ask AI to generate a worksheet for me based on like a topic. i have to write the questions myself or else it just feels wrong. but a customized animation from something i did write myself? that's weird to think about. probably would lean against using it.

[rapid tusk]

manim etc feels a bit oversaturated now

maybe I’ve just been on yt too much

[nocturne thorn]

No on the AI powered tool.

Because students can pick up the vibe of when the teacher does or does not care. And slop lessons are a clear demonstration of uncaring. And if the teacher doesn't care to teach the material, why should the student care to learn it.

"But it could take out the grunge work in teaching!" The grunge work is where the teacher can insert their caring. Caring isn't about the surface level energy. Pedagogically, students benefit when a teacher is plugged into both making sure the lessons land precisely and keeping their fingers on the students' pulses.

[little drum]

having taken a maths course that was written by AI, i can confidently say it should be avoided (for pedagogical purposes) at all costs

[rapid tusk]

my condolences

[hardy needle]

How the hell does that even work

Course written by AI?

[little drum]

the notes that the lectures are taught from, and all of the problem sets, were written by chatGPT

[hardy needle]

😭😭😭

That's fuckin terrible

[little drum]

it really was

[sick bough]

it can be done well but the thing is that if you care enough to do it well you'd just do it properly

[hardy needle]

I think it's cool to use AI as a reinforcer (i.e makes more problem sets, mock tests, ask for some concrete examples/counterexamples)

But to use it to essentially teach a whole course is crazy

[tame ridge]

I feel like in some cases, if you have the vision for some visualization, and you let ai to write the code for which u check/edit it's fine. Maybe you want some graph which will take too long to plot without some head start so you let ai give you a sample for which you edit on. It gives teacher time to focus on stuff they feel maybe more important.

So I can get behind using AI for lectures/Manim (and of course, not to the extent where you make let ai make lecture and call it a day). Especially if your purpose is to use it to give extra stuff to enhance a lecture that you wouldn't otherwise have the time to make yourself.

[little drum]

i dont agree on any of these

my experience was that the problem sets it generated were much too easy

[sick bough]

yeah it tends to prefer relatively "book work" problems, which are good for tests but not so great for psets

(and only if the tests are closed book obviously)

[little drum]

i have tried asking it to generate mock exams in courses ive taken and to be blunt they were riddled with erros

[tame ridge]

i think you can specify difficulty. I have tried letting it make hard GRE practice and my god, it's hard

[little drum]

and it isnt good at coming up with non-trivial examples either

[sick bough]

i've never had this problem (at least with gemini's pro model)

the questions are all correct they just generally aren't too challenging

[little drum]

it's possible it's been improved since i last tried at least that, that was a year ago now

[hardy needle]

Yeah I would say it has improved, especially if you give it a layout/framework of a reference exam

[sick bough]

yeah i gave it the lecture notes and some past exams

[hardy needle]

But sometimes it does just end up making a few problems that are just regurgitating a statement or something you wanted more "in-depth" application

[sick bough]

yeah and it doesn't really ever come up with more "creative" problems where the content is applied in a more oblique way

[rapid tusk]

i wrote for a math contest during my undergrad

just for kicks I’d see what gpt would generate and it was

so

so

soulless

[little drum]

i feel like we're hedging too much here... this is what it just does

[nocturne thorn]

AI makes it really easy to turn your brain off and accept its output. In fact, that's the default behavior of using it (as in, the behavior you get by doing nothing else after putting in the prompt)

[little drum]

out of 168 problems in the course i took that was written by chatgpt, maybe 1 or 2 were actually challenging

[nocturne thorn]

It also removes the opportunity to think carefully about problems and tangible-ize them

[sick bough]

for reference i don't think extremely challenging problems are any more important than easy ones

[sick bough]

so i don't mind that it generates a lot of book work

it's not good if that's all ur doing tho

[little drum]

it's important to have a range

[nocturne thorn]

I don't think more challenging problems are what's needed. What is needed are problems that clarify what the math is doing

Like, if I were designing an analytical geometry course, I would make students do a problem where they calculated an as the crow flies direction of flight along a great circle

[little drum]

if im presented with 10 questions that are all 1 step deductions from the definition, i will get bored and do very few

speaking for myself, i do need some level of challenge to stay engaged

and the exam inevitably will have questions that are more than just bookwork on them

so you need to hone your skills on the non-trivial techniques

[hardy needle]

when i graded HWs for calc 1 i could just straight up tell when someone used AI it was kinda funny

and it was wrong too

[white fulcrum]

https://www.youtube.com/watch?v=mRO_QonhC2c

I've seen so much of this

[vagrant meadow]

I never said "slop lesson" though I see how that could be interpreted. I meant more like having AI generate a manim animation to augment a human written and designed lesson. ex. human lesson + AI manim animation

i mean I write blog posts. so I feel like I can pretty adequately write detailed lecture notes or bullet points for a lesson. ie the narrative structure of what to introduce and when.

but being able to easily generate a nice manim visualization of a concept, as opposed to adding something like "draw a visualization on the board" to my notes? honestly doesn't sound that bad.

[tame ridge]

I don't think "accept its output" is the default behaviour at least for me, especially given how much it bs on their proposed 'solutions'

to the extent I start ranting at the bot

[vagrant meadow]

yeah this is pretty much what I was thinking

I understand AI skepticism, but I think its best use case is the grunt work. when I was a TA the Prof wanted us to give the students textbooks problems as a worksheet. i could have screenshotted the textbook and put it on a word document to make something jank and ugly. I could have spent half an hour transcribing the problems in latex. but instead I screenshotted the problems and asked a LLM to generate the latex for them. that took about 5 minutes and I could easily check the problems matched the exact wording of the questions.

similarly I could spend a few weeks learning manim just to make a single animation for a single lecture I wrote. but the cost to output ratio is all wack. if I can just prompt exactly what I want and get a full manim animation in a few minutes, that's a pretty sweet deal.

[tame ridge]

damn ive never seen a worksheet in my undergrad career, it's still a thing in uni?

[vagrant meadow]

however, "generate a 15 minute video about linear dependence with a script written by AI and narrated by AI" is a "hell no" from me

[vagrant meadow]

for TA discussions yeah. these were worksheets full of questions fully written by me for linear algebra. I gave them as homework they had all week to do. i knew most would probably ask chatgpt to do for them, but I hoped that at least one student would find them interesting and helpful in learning the concepts and seeing how the concepts they were learning absolutely had applications.
https://eigentaylor.github.io/assets/pdf/linalgsolutions.pdf

other profs did stuff like a worksheet+quiz for discussions which was like reasonable I guess.

[tame ridge]

200 pages? damn do you get paid enough for that

[vagrant meadow]

https://giphy.com/gifs/hulu-only-murders-in-the-building-omitb-OcNMFiElHUqlXjgQJA

[nocturne thorn]

I don't mean it's a specific person's default. I mean that it's the default. In the sense that the easiest action to do is no action at all, and that you have to act to do anything else

[tame ridge]

but isn't that sorta saying "not doing something" is the default for anything someone does? I sorta just wanna see some supporting evidence because this claim really feels very diff from my exp with ppl around me.

Idk what percentage of ppl who use these treat them like they are the absolute truth, but in my exp, me and the ppl I hang with don't trust output at all.

but this probably is very biased cuz ppl around me do math

but ill prob gather more insight next year when im TAing a math course

[nocturne thorn]

Yes. Doing nothing is the default for anything anybody does.

That is the fundamental problem: GenAI makes it really easy to do nothing when you should really be doing something.

I have a (research) collaborator who literally went "yeah, I can't code, so I had ChatGPT generate all of my post processing code and just visually inspected to make it look right."

[vagrant meadow]

tbh if the discussion is specifically about "how could this tool be used properly" i don't see a knee-jerk reaction of "but it could be used wrong" as particularly relevant.

like, yes. but that's not what the discussion is about.

[tame ridge]

crazy lol like at least let the ai write comment and check it yourself

[vagrant meadow]

going back to this, i'd like to know what your definition of grunt work is. i wouldn't consider

• writing lecture notes
• designing worksheets/hand outs
• thinking of and designing test questions
• grading assignments
  as grunt work in the slightest. those are part of the basic human duties of a professor, that AI cannot and should not do.
  as i mentioned before, transcribing something from a textbook to a latex worksheet is basically what i would consider grunt work. generating a specific tikz diagram (because i never learned tikz 😭) to put on my lecture notes, or (as per the intial question) generating a specific custom manim animation to augment a lecture. those aren't things i would consider necessary tribulations for a professor/instructor, because those things aren't necessary. instead, those are things that could augment human-designed content.

[torn apex]

I've been using ChatGPT/Claude to turn my mental imagery into something tangible for long-term memory recall. Also to visualize a lot of math to make it tangible. attached examples

You can make these types of visualizations relatively easy. Here's a A Knot Theory game I helped make for a friend

[tame ridge]

that memory palace is crazy Lol

i thought it's some game

[torn apex]

haha; my hardcore RPG fantasy nerdom leaks through

fwiw, I found AI most like a force-multiplier when combined with my domain expertise applied to a different field.
My bg is in gamedev so I've been using AI to make RPG math & magic games for my 10 year old nephews (inspired from @turbid zenith references on using games/narrative storytelling to teach math)
caveat: not meant as AI hype. models can't do this unless you know how to make game art+program

[nocturne thorn]

I'm using the phrase "grunt work" slightly differently from you: I'm not using it as "things AI can help with", I'm using it as "things people would be tempted to use AI for in a curriculum because they're boring"

As you're using the phrase, sure, the things you define as grunt work are in fact things GenAI can help with, mostly. The custom manim animation specifically is something that I will push back on, though: if you don't know how to use manim and ask AI to make it for you, a visual demonstration of a mathematical concept is exactly the sort of thing that can go subtly wrong and be difficult to correct if you don't know manim.

[tame ridge]

would u cite ai as a source if u plan on publishing any of those games? I honestly dunno to what extent should I cite AI if some day I start using AI to look at some examples/give ideas for a lemma I want to prove

[nocturne thorn]

It was absolutely insane. I'm literally spending the next working day or two just making an appropriate testing suite and tightening it up because holy crap I don't want to rely on "but it looks right" for literal actual cancer research

(I might also choose to rewrite it in Rust, because right now it's in R and apparently the analysis takes hours)

(But as I look at it, my estimated probability of that is going down because it's a lot of visualization, which is one of the areas Rust is weakest in and R is strongest in)

[tame ridge]

my dumbahhh thought R is short for Rust

[nocturne thorn]

Easy mistake! R is actually short for “Rot in the trash”!!

[torn apex]

oh this is just for fun; i wouldn't publish it outside of as a way to teach computer programming in a fun way with math.
I think selling it makes the ethics get murkey really quick and i honestly don't know how i feel about it

[vagrant meadow]

right and that goes back to my point that the question is "how can it be used correctly" and not "how might it be used in practice". i'm asking people in #math-pedagogy because the people who frequent this channel care about education, and i'm asking how a tool could be used properly. i think we're not talking about the same thing.
for the purposes of this discussion, i think it's fair to focus on the more constructive proper use, versus conjectured improper use. the latter also can't really be stopped because these tools already exist. and since it's not a discussion of creating new AI tools, i think we should focus on how we could productively use the tools that exist.

i would also push back on the manim example. because there's a difference between

• the AI made the visualization you intended incorrectly, which you can either correct yourself or ask the AI to correct (it's generally pretty good at taking direction/corrections)
• the visual demonstration is wrong and you don't even realize it
  the latter case, i think, indicates that the tool is not being used properly. so, i suppose you have a point that if i'm trying to cover up my lack of understanding of the topic by adding a flashy animation to compensate, then yeah that's a pretty bad idea. but also i would argue not particularly relevant to the question i'm trying to pose.

i will say that in a general conversation of AI, the kinds of things you're saying are generally very important. because being clear about what AI should not be used for is very important for a discussion of AI that could be viewed by a general audience. but i think it could save us a lot of effort to assume that those in #math-pedagogy can generally tell right from wrong in AI use case. (but maybe i'm wrong, and overestimating the "AI literacy" of those in here)

[vagrant meadow]

but i am glad you brought it up. because i think it would be super easy for a student to see a manim animation in lecture and have that increase their trust of their instructors knowledge. and if that animation is low effort and wrong because the instructor really doesn't have the knowledge, that's super dangerous. i hadn't considered that.

[turbid zenith]

To be clear, when I was advocating making a narrative part of teaching mathematics, I was referring to the narrative of “why would anyone want to study this thing? How did this concept evolve throughout history? How can we motivate the idea?” That is, using a storyline internal to the mathematics, not an external story like an RPG.

Not that there’s anything inherently wrong with an external story. But I want to be clear what I was referring to because you cited me.

Likewise when I’m talking about using games I am almost always referring to intrinsic games (Offenholley, 2011), where the concept being taught is integral to the mechanics of the game. That’s in contrast to extrinsic games like Kahoot where it could work just as well for, say, history or language.

[rapid tusk]

was looking through papers from a local math league i used to compete in in HS and saw this

why are teachers chatgpting trivial problems like this

[hoary gorge]

What are even those

[hardy needle]

😭 thats so chopped

It just looks ugly

[rapid tusk]

why all that unnecessary casework when you can basically instakill it

[plain pebble]

This is essentially how someone familiar with the above argument would write it

(Ie, they’re the same argument in different levels of detail)

I do agree that the first solution looks very AI

[rapid tusk]

Step 1:

Step 2:

[pure light]

yeah ai loves the numbered lists and headings and whatnot for responses far too short to justify them

[rapid tusk]

its just disappointing to see

bc its supposed to be the schoolteachers writing this contest

and gpting the solutions is just disrespectful to the students competing

[tawny slate]

like it has the base idea for an elementary solution, but messes up subtly in ways that feel so sloppy

like, when i write competition problems i keep the solutions clean and short, because thats the style of that sort of thing

but even if i were to write an elementary solution that quality is just awful haha

[tame ridge]

i saw 3k+1 and I immediately thought the Q was asking about collatz conjecture below 155

[rapid tusk]

"dEsCRiBe thE 3k+1 nUMbErS" i have never heard anyone use that terminology lmao

[quasi maple]

It's a little annoying to see that "someone" went through all that work for the smallest answer just to be 10

Then again, there was a help channel I was in whereby "0 mod 2" and "4 mod 5" was apparently far too difficult to combine

[torn apex]

I think we're in agreement, no? My point of departure from Offenholley is that the "external story" (e.g. the make it look pretty and visually appealing) is more important. You have to get people internally excited and then answering this.

“why would anyone want to study this thing? How did this concept evolve throughout history? How can we motivate the idea?”
The intrinsic game is relatively easy (e.g. the lessons follow a historical figure like Noether and trace her work in in figuring out symmetry and ring theory); the idea is to teach have the user develop/exercise the mental muscles by playing through a historical archaeological reconstruction of their key contributions.

The part that is hard actually making it fun enough that someone would play it on its own outside of a forced educational context

It's a tall order so i'm probably tilting at windmills but that's why it's just a side fun hobby. 🤷

[steel vortex]

<@&268886789983436800>

[fierce hare]

I have abstained myself from learning logic and proof for maths. The most proof based questions I solve these days are from linear algebra and I'm not good at it.

@cursive quartz

[slim path]

FYI, idk if this discussion is appropriate here given the channel description. This is more ideal in #study-discussion. I was referring earlier to the more technical comment about teaching students to (paraphrasing) compute before they understand when I suggested to move it here instead.

[fierce hare]

Ahh apologies. I am new here so I'll adjust accordingly.

[cosmic ibex]

<@&268886789983436800> casino scam.

[quasi maple]

skibi-dont

[nimble escarp]

Which one do you prefer and why?

[cosmic ibex]

For this particular case I think I prefer the left one. The right one seems to place more cognitive demands when reading, since it introduces the various moving parts before it reveals what it has to say about them -- in contrast to the left one which does it just-in-time.
However, as a general style, when the statements get more complex with more moving parts that you need to refer back to several times while digesting the statement, the style on the left will become confusing quicker.

[nimble escarp]

Thank you, I felt the same way. So I'm thinking of using the left, shorter version for smaller statements, and using the structured version on the right for more complex theorems

This for example

[cosmic ibex]

👍
The challenge is in figuring out when to switch over, of course.

[cosmic ibex]

I suppose it's just for the sake of example that the lambda_i are never mentioned after being introduced, right?

[nimble escarp]

haha yes, good catch. still a wip

[zinc dove]

What are using to write this?

[nimble escarp]

Obsidian

[fiery quiver]

How do yall feel ab introducing proofs to students in calc 1(i.e. ftc) but never assigning them any practice proofs? Is there any point to it? Roommate was showing me that his professor wrote down such a proof in his calc 1 class. I thought it was kinda dumb since you never practice with the language outside of seeing it, so its sorta like teaching philosophy 101, quoting something in Greek to justify what youre doing, then just reducing it all down to like rote process. It made him think he couldnt do proofs, but i could maybe see some benefits for certain students.

[vestal tangle]

i think a good math teacher should attempt to prove every result

doesn't necessarily need to be a super rigourous proof, but you should try to explain why w/e you're presenting is true

[cosmic ibex]

That would probably mean that students can't be told that, say, Fermat's last theorem is true.

[surreal tinsel]

Or a circle seperates space into a bounded and unbounded region

(JCT is nontrivial to prove)

[tame ridge]

I would much prefer things proved, otherwise don't use it/let us use it. So I never liked AB or BC calc because of this. But I would assign practice proofs. I think stuff like "find the derivative of x^2 and justify" (before you were taught power rule) could be the typa questions that practice proofs.

I can speak from my personal exp: I did not learn calc rigorously until a prof sent me some video lecture he prepared for me to watch that does calc in a more rigorous manner. It helped me a lot in understanding the material and help me answer many questions I had. I never did any practice when I was watching the videos. So at least for me, it was helpful even without practice.

Either way, is there reason to not assign proof type questions?

ig it could very well be a "for people who are interested" thing the prof is doing that is otherwise not required for the course they are teaching, in which case it's pretty good

[plain pebble]

There are usually gonna be things you want to use, but wouldn’t be worth the time to prove/look at a proof of
I think, unfortunately, that pretty much the only exceptions to this tend to be the first couple years of proof based courses at uni

[tame ridge]

i think thats more or less grad courses no? where prof start to skim proof etc.

But this could very well be a case for complex analysis, however my offering did some stuff on rectifiable curve and still didn't assume anything like jordan curve theorem

[plain pebble]

I’m not talking about skimming the proof
I’m talking about “I could explain the proof, but you’d learn nothing of value”
Like I frequently use a lot of theorems along the lines of “you can make surfaces sufficiently nice via isotopy”, without knowing the proofs
Even though they could probably be proven in a grad course

[tame ridge]

yeah but those are still like grad course/cross listed grad course type stuff right? Ive never seen these type of handwaving in my undergrad although i didn't take manifold theory course

[dim blade]

I think it makes a lot of sense to provide definitions and ask students to prove simple results. For instance, our calc 1 professor asked us to prove the derivatives table as one of the big assignments

[fiery quiver]

maybe im too cynical but the vibes i get from that professor made it seem more like a flex than anything lmao

[plain pebble]

Cross listed grad stuff doesn’t exist here
But depending on the year any or all of the following third year (final bachelor’s year) courses here can have unproven stuff:
Riemann surfaces
Algtop (fundamental groups and homology)
Alggeo (varieties)
Measure theory
Probably more that I’m forgetting
And these are just ones I took

[tame ridge]

aha i see. my exp on alggeo mea theory had been fine. I need to keep this in mind for grad school lol. Do they tell you where to look for proof even?

[fiery quiver]

roommate was mentioning how much shock and awe he felt from said professor flexing that he learned alg topology in under grad. maybe id have more of a reaction if i wasnt in this discord server but indeed im in this discord server filled with many dedicated people

[plain pebble]

For Algtop yes (the stuff was proven in my year but isn’t in others)
For AG/RS/Measure Theory no (it would be a couple more courses until you’d be able to)

[fiery quiver]

proving the derivatives table sounds like fun but idk it just sounds like a lot of algebra no?

at least if your definition is the usual one u see in like high school or first year in the US

[plain pebble]

It’s fairly standard in Europe to have AT in undergrad

[fiery quiver]

yep lmao

[plain pebble]

Yeah it’s doable at a HS level
It’s just a pain

[fiery quiver]

idk how much itd really help with understanding the prose of a proof early on ig

[tame ridge]

proving power rule for irrational power might be too much pain ngl

[plain pebble]

You prove it via proving the results for exponentials and logs
But yeah

[fiery quiver]

neat didnt know that lol

[tame ridge]

Oh i thought u define it as a limit of rational powers?

[plain pebble]

You can do both and it’s easy to prove they’re equivalent

[tame ridge]

u need some interchange limit typa stuff tho right?

idr exactly

[plain pebble]

You shouldn’t if you take on faith that exponentials are continuous

(Which is very easy for a hs student to accept without proof)

[tame ridge]

oh lol i thought by proving they meant fully and thoroughly

[dim blade]

I recall that it was a pain to prove em for hyperbolic trig functions

I don't think we were ready

[vestal tangle]

sure, but so what. i don't recall ever taking a class that talked about that

[dim blade]

You never had number theory?

Like modular arithmetic

[vestal tangle]

if it's something that's really intuitively obvious then i wouldn't care

[dim blade]

I think a better approach would be to tell students to trust that some things are true, learn how to apply these truths and gain an understanding later

[vestal tangle]

i have not, is that a core part of a number theory class?

[dim blade]

No

[tame ridge]

i do feel like one should be fairly rigorous at least on the core content of a course tho.

especially so on introductory course

like idt id get a better understanding if they were like lets apply hilberts nullstellensatz first on these things, then prove it, than the other way around

[dim blade]

I think definitions shouldn't lack rigor. But proving theorems in class might often be counterproductive. In your example I think it makes sense to prove a special case or the weak nullstellensatz

[brazen pendant]

stoopid woog

[true bone]

What's this channel for

[weary ferry]

😂

there ya go @brazen pendant

[turbid zenith]

Thank you 😃

[wet marten]

For a teacher maybe.

[civic tree]

it's for ppl that want to understand the art of teaching math correctly

[sweet swan]

nice

[weary ferry]

put your description in

[turbid zenith]

Yay

[civic tree]

yay

[weary ferry]

👍

[brazen pendant]

[civic tree]

ok now wat do we talk about first

l0l

[supple remnant]

I found this article awhile ago http://scholarship.claremont.edu/cgi/viewcontent.cgi?article=1003&context=jhm

[weary ferry]

whatever motivated this channel's creation

[brazen pendant]

help how do I teach numerical methods

[supple remnant]

hire a CS tutor

xd

[weary ferry]

could just shift general discussion here, or add whatever (relevant) stuff u wanna discuss

[brazen pendant]

no I'm the TA

^^

[supple remnant]

i still stand by my statement

[brazen pendant]

it's for physicists, too

[supple remnant]

[civic tree]

[cold fable]

wait

can i ask a question here

[civic tree]

relating to teaching of some kind sure

[cold fable]

oh wait

ok

[brazen pendant]

if it's on topic

[cold fable]

i mean

can i ask a meta question

because like

[civic tree]

uh

okay

i guess?

[cold fable]

it's not technically a math question

idk

ok like

[civic tree]

???

[cold fable]

i'm a high schooler senior and i took bc calc two years ago and multi last year

but slept through class

and don't remember any of it

[brazen pendant]

is starting to get relevant

[cold fable]

despite doing well in the courses

so like

what are some good textbooks

that i can use

to relearn calculus and multi

because i remember hating the ones we used in school

[brazen pendant]

yep, wrong channel indeed

[cold fable]

ah ok

which one

sorry i just read the rules

[brazen pendant]

/shrug

[supple remnant]

maybe just #math-discussion?

[cold fable]

ok

[brazen pendant]

I mean if someone hae an answer might as well give it

but i don't

[civic tree]

me neither

[sweet swan]

@cold fable https://www.amazon.com/Calculus-Intuitive-Physical-Approach-Mathematics/dp/0486404536

[supple remnant]

Apostle or Spivak are good options

[sweet swan]

one of my favorites

[supple remnant]

they cover classic calculus topics but also let the reader dabble in proofs

[cold fable]

uh

i have significant proof experience too

idk like

i want a relatively high powered textbook

[civic tree]

b a b y r u d i n ?

[sweet swan]

s t e w a r t s

[supple remnant]

if you want to review, then you can't go wrong with http://tutorial.math.lamar.edu

[cold fable]

what are those texts

o

[supple remnant]

some people dislike these notes, but i find them to be quite good

[cold fable]

idk this feels a lot like school

like i want school+++

if that makes any sense

[brazen pendant]

do you want calculus or analysis

[supple remnant]

idk if there's such a textbook that can do that

that too

[cold fable]

i mean, i think i remember like some calculus

[brazen pendant]

ir sounds like you want analysis

[cold fable]

would it even be useful

for me to like

try and relearn this sort of stuff

if i knew it two years ago

[brazen pendant]

I mean analysis is just calc in rigorous

[cold fable]

o

ok

well, that, then

[supple remnant]

i'd still review some basic calc stuff before going into analysis

[brazen pendant]

it's a damn shame no one seems to speak german cause I have fantastic analysis lecture notes in german. 800 pages, perfectly suited for self-study over the course of a year

[supple remnant]

just put them through Google Translate

[wet marten]

Six pages of references 👀 .

[supple remnant]

ez

[cold fable]

oh sad

[brazen pendant]

at least use deepl

[cold fable]

what's a good introductory analysis text then

i guess i'll review some of the things on that website

that i completely forgot about

[supple remnant]

inb4 baby rudin

uh Abbott is beloved

https://www.amazon.com/Understanding-Analysis-Undergraduate-Texts-Mathematics/dp/1493927116

[cold fable]

https://www.amazon.com/Understanding-Analysis-Undergraduate-Texts-Mathematics/dp/1493927116

ah

ok

[supple remnant]

lul

[cold fable]

good

we're on the same page

ok tytyty

big appreciate 😃

[supple remnant]

figuratively and literally

[cold fable]

xD

[turbid zenith]

Okay so for LEARNING Analysis for the first time

Lay's book is probably the simplest, though its topics are occasionally limited

It reads more like a high school textbook, has lots of worked examples, and has some answers

A more thorough one I'd recommend is Elementary Analysis - The Theory of Calculus, by Kenneth A. Ross

And one more really good one is A Radical Approach to Real Analysis by David Bressoud

[hot storm]

🆙 | DMAshura leveled up!

[turbid zenith]

That one is interesting because it gives a lot of the historical background and has a high emphasis on infinite series, and why people like Fourier triggered the need for real analysis by doing things with series that shouldn't have worked 😛

There really needs to be more historical context given when teaching math I think

[supple remnant]

do you have any recommended math history texts?

[turbid zenith]

I personally enjoyed Katz's text

But also reading popular mathematics authors is a great way to learn math history

Mario Livio for example -- I read through Is God a Mathematician? and The Equation that Couldn't be Solved a while ago and learned a whole lot through those

[supple remnant]

huh, my roommate has Is God a Mathematician? on his shelf

[civic tree]

steal it and read it

[supple remnant]

o7

something to go through after I look at some nice books on soft skills

[turbid zenith]

So how many of y'all reading this channel are TA's, etc?

[civic tree]

well im still yung

one day

as of rn im an informal tutor and i teach my frens for fun

obsessive over the right way to explain proofs in particular

[turbid zenith]

Oooh?

Proofs in what class context?

[civic tree]

well im in calculus rn and stuff like proving the chain rule and the product rule and the FTC and wotnot

[turbid zenith]

Ahh gotcha

[civic tree]

ya

[turbid zenith]

I'm a much bigger fan of using differentials to teach calculus instead of limits whenever possible

[civic tree]

ooh

how doe that work

[turbid zenith]

It's a little more "hand-wavy" but that's not bad for, say, intro students

[civic tree]

ah i see

but yeah

good for intro

[supple remnant]

the article I posted above elaborates on different interpretations on what is meant by a proof

[turbid zenith]

For example here's how I see the Product Rule:

[civic tree]

oH yeah that way yessss

i see

[supple remnant]

oh

[turbid zenith]

If you increase u by a little bit (du) and v by a little bit (dv), the amount you tack on is u dv + v du + du dv

[civic tree]

mhm

[turbid zenith]

So when you look at the ratio of that to dx, you end up getting u dv/dx + v du/dx + (du dv)/dx, but that last term is negligible

[civic tree]

right

[turbid zenith]

Because of ratios of infinitesimals

So I used to have my students imagine an "infinitesimal microscope" 😄

[civic tree]

aha i see :)

[turbid zenith]

"When we're on Zoom Level 1, we can see infinitesimals like du and dv, but not products like du and dv"

[civic tree]

mhm

[turbid zenith]

And that intuition really lends itself to what's actually going on

[civic tree]

that's actually pretty nice

gonna steal it

[turbid zenith]

Oh feel free

[civic tree]

ty hehe

[turbid zenith]

I would rather sacrifice a bit of rigor if it leads to a ton of understanding.

[civic tree]

yeah

[turbid zenith]

The rigor can always come back when it's developmentally appropriate.

[civic tree]

because starting is always the hardest part

yes

[turbid zenith]

Hot take: Algebra 2 and Precalculus should be renamed Precalculus 1 and Precalculus 2.

[supple remnant]

Based on the idea of the death march to calculus, just rename everything as Precalculus n

[turbid zenith]

Lol

[civic tree]

or algebra 3

l0l

well

okay

[supple remnant]

ohgodwhy

[civic tree]

precal material involves some limits

so

uh

ehhHHhh

[supple remnant]

oh I was asking that as a joke

[warm lintel]

addition = precalc 1

:/

[supple remnant]

precalc 0

0-indexing baby

[civic tree]

everything is precalculus

then calculus

then postcalculus

[supple remnant]

xD

[round heart]

🤔

[supple remnant]

Group Theory is Postcalculus: Algebra Edition I

[civic tree]

Postcalculus 5: topology

[supple remnant]

Applied Postcalculus

Dynamical Systems

[turbid zenith]

cf. Horseshoe Integration

We actually used to have Algebra 3 at the school I used to teach at

It was basically a slower precalculus

[civic tree]

ah

[turbid zenith]

I would rather the big three mandatory math classes be one year each of Algebra, Geometry, and Statistics

[silver ravine]

This may seem like a random question

but assuming I'm done learning the Algebra II curriculum in June, how can I prepare for the exam in mid August?

just search Algebra II Regents and go to old New York State exams

it's probably like middle school math but still

[brazen pendant]

@turbid zenith I like your approach to calc

and I totally agree, in high school, intuition beats rigor without question

most people there don't care about the rigor

but you might be able to convince them that understanding it intuitively will help them pass the course

[boreal sentinel]

Oh it's a Sascha

[brazen pendant]

and whoops now they get it

[boreal sentinel]

Long time no see dude

[brazen pendant]

hi i've been back for a few days now

[boreal sentinel]

How's the exam period?

[brazen pendant]

but yes, not been around for a while

over

finally

[boreal sentinel]

Oh, early for you then

[brazen pendant]

the exams went, in order, okay, good, good and wtf

[boreal sentinel]

I remember having an exam on like, Feb 16th last year

Kind of a shitty schedule

[brazen pendant]

isn't that like, two days before the next semester

[boreal sentinel]

Yeah LOL

So you had 5 exams?

[brazen pendant]

four

[boreal sentinel]

Glad you don't feel bad about any one of them

[brazen pendant]

"wtf" is not a good feeling

however, everyone felt that way

fucking mmp

[boreal sentinel]

mmp?

[brazen pendant]

methods of mathematical physics

topics were like, fourier stuff, PDEs and distributions

and the exam was just about as hard as it could've been

based on what we were told about the format

didn't meet one person who thought they did well

[boreal sentinel]

Anything with PDEs in it is hard at ETH

[brazen pendant]

every old exam had like two easy PDE exercises on it that I could solve blind

[boreal sentinel]

Throwback to that one time when I learned about stochastic ODEs and barely passed

[brazen pendant]

this one... had two too, one I could solve the homogenous part, but not inhom (which we never did before), the other I just couldn't

[boreal sentinel]

Seems like they like to put up the students with some nice surprises, as usual

Was it the same professor as last year?

[brazen pendant]

nope

[boreal sentinel]

That might be why

[brazen pendant]

willwacher, who never held that class before

I mean he promised to keep it similar to previous years

[boreal sentinel]

Name doesn't sound familiar

[brazen pendant]

but he has a distorted sense of difficulty cause the man's a bit of a genious

he's like 30 and has a fuckload of publications and is a full professor

[boreal sentinel]

My friend who studies Data Science at the ETH now has a prof with a similar problem lol

Distorted sense of how much the students can take

But your prof doesn't seem to have lived up to his promises

[brazen pendant]

not as a professor, no

I mean all in all, the class was alright, it definitely had its issues but i've had worse

it did necessitate doing a semesterfeedback and talking to him tho

[boreal sentinel]

Is it a big class?

Also which year are you in rn lol

[brazen pendant]

2nd year mandatory class for phys and math, so around 250 students?

[boreal sentinel]

Oh 2nd year

Big class

At least compared to Master classes

[brazen pendant]

well yea

[boreal sentinel]

Hopefully he will realize what he's done when the assistants finished grading

[brazen pendant]

it turns out mandatory classes are pretty well-visited

[boreal sentinel]

And curve it

[brazen pendant]

probably gonna happen

though last year linalg 1 had a non-passing average

as in, 3.5

[boreal sentinel]

Like graph theory last semester LOL

Damn

[brazen pendant]

though imo the exam itself wasn't actually that bad, I found it quite comparable to the year before, and easier than the summer exam before ours

[boreal sentinel]

Did you pass?

[brazen pendant]

I've had only good grades so far

[boreal sentinel]

Good boi

Keep it up

[brazen pendant]

no grade below 5 yet, but MMP might be

probably will be

[boreal sentinel]

Nice dude

[brazen pendant]

can't judge it

[boreal sentinel]

I wish my grades list could've been like that

[brazen pendant]

Of course except for TAing, they don't care about your first grade grades

but since I want to (and will!) TA, I won't complain

got a job!

[boreal sentinel]

Which course will you TA?

[brazen pendant]

Numerical Methods for Physicists

which is mostly easy stuff, but there's some two topics i'll have to do reading when it gets to that point

namely ausgleichsrechnung (dunno the english name) and eigenvalue approximations

those are both topics I... could do but didn't really understand well

[boreal sentinel]

I'm sure you'll do just fine :3

[brazen pendant]

for the most part, I hope so too

[boreal sentinel]

I'm curious about the ausgleichsrechnung now

[brazen pendant]

it's uh, like, finding a linear combination of functions which minimizes the distance to data points

[boreal sentinel]

Wikipedia says curve fitting

[brazen pendant]

yea

[boreal sentinel]

Yep, seems about right

[brazen pendant]

that sounds right

[boreal sentinel]

Did I tell you I graduated

Moved back

[brazen pendant]

it was one of those topics we kinda rushed through

[boreal sentinel]

And now I have a full time job

[brazen pendant]

nope, nice!

(well, hopefully nice)

[boreal sentinel]

It's alright so far

Software dev trainee

[brazen pendant]

missing school life?

[boreal sentinel]

Not a lot of responsibilities (yet)

Well now that you mentioned TAing I'm toying with the thought of how it would've been if I stayed for another semester and just did nothing but TA

Would've been chill

But I kinda just rushed back home lol

Feel like most master students like to take their sweet time

[brazen pendant]

i'm already intending on taking my sweet time in the bachelor"s

[boreal sentinel]

You should

It's over in an instant

[brazen pendant]

I wrote the study advisor and he actually advised against it but I think i'm still gonna do an extra year

to take more foundational classes before specializing

[boreal sentinel]

Do you have a clue where you're gonna go next?

[brazen pendant]

msc math or applied math at eth, then the teachers diploma so I have it, and then probably look if I wanna do a phd or become a teacher straight away

[boreal sentinel]

When my job starts to become boring I'll try for a PhD

[wicked minnow]

grumbles did you make sure to turn off tatsu persistence in here? @weary ferry

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

[wispy slate]

why are you grumbling

[turbid zenith]

Tatsu persistence?

[supple remnant]

I think they're mod options for tatsumaki

[civic tree]

bro my math teacher decided it would be a good idea to teach antidifferentiation techniques before riemann sums

which is interesting

i think the reasoning was like

we had been doing differentiation so it makes sense to keep on the same track and immediately go to the idea of "reversing" the processes we know

instead of sidetracking to accumulation of area under curves because that might take several classes and could possibly make us lose sight of what we had been doing

idk

how do u feel of this teaching

[dim pewter]

I think that would work better

imo

riemann sums had me going "why does this matter rn?"

then i learned integrals and it worked out

[civic tree]

yeah im leaning towards this as being better too

bc it's a swift transition

that doesnt immediately confuse the student with "new" stuff

because it's "just the reverse, innit"

[turbid zenith]

I like that a lot

So what I did when I taught AP Calc

I did anti differentiation right at the end of derivatives

So it was still very tied together - hey you're just doing it backwards

Then I introduced integrals as a completely new concept

But once we did some computations with then, some basic Power Rule stuff... the students were like "heeeeeeywaitaminit"

So FTC was actually significant -- holy cow, we can find areas by doing derivatives backwards!

[civic tree]

yah

[pearl dust]

oh that's interesting

[brazen pendant]

I find it very interesting how this stuff was handled in my analysis class

we did riemann integrals before limits

(well, darboux integrals)

using pretty much only supremum

then we did limits, series, sequences etc

and only then differentiation

and then the fundamental theorem

however, it was expected that everyone had already seen both integration and differentiation in high school

so it wasn’t a first intro

for those who can read german, here’s the reasoning (tl;dr incoming):

you may wonder why we do integrals now, even though we haven’t done differentiation. here’s three reasons:
-areas have been studied since ancient history and are significantly easier to reason about
-integration has a lot of very nice properties (e.g. monotony, triangle inequality), differentiation does not, but we can use some of these properties to show things about differentiation later. since we want to build up from foundations, it makes sense to start where there’s more structure
-the connection between differentiation and integration is one of the major goals of Analysis I. we hope to further emphasize this by introducing integration early

[supple remnant]

How prominent is abductive reasoning in learning mathematics and doing proofs?

[wispy slate]

Abductive reasoning?

[unreal ledge]

Definitely not something I constantly think about, but the process of generalizing ideas is rather abductive. "This is true when I do this, is it also true in this broader sense?"

"What can I change, and does this result change with it?"

You follow up with deductive reasoning for proofs though

[civic tree]

yea

[wispy slate]

Even though I'm only in my first year of my four year plan of getting out there and teaching and helping inspiring students to learn
(I'm still in college pursuing)
One troubling idea has always come to mind.... if I teach at a high school level....there will always be those kinds of students who 'have' to be there and don't want to do anything
Is there anyway I can help them get involved or help them appreciate what they are doing?

[turbid zenith]

I've never heard of abductive reasoning

@wispy slate I think you will always get those kinds of students yes. But that doesn't mean they're all lost causes.

You'll occasionally get one or two who are ... but you have amazing power in being able to make math come alive for them if you do it right. 😃

[wispy slate]

I was a TA for a freshman level math class my senior year of HS and there was some sophomores and juniors in there who just didn't care.... hold on... like 99% of the class did not care for what was going on and I just felt powerless to get them to pay attention or...well ask for help or even attempt it....

[brazen pendant]

honestly for TAing I would probably actually tell them to leave. not angry-in-front-of-the-class but like, tell them after the class that they don't have to be here and if they think it's boring they should spend their time in a better way

[wispy slate]

In high school though, I was not allowed to do that, plus they kinda had to be there for graduation requirements

[brazen pendant]

ah our classes are all optional

especially the tutorials

like, you have to write the exams, everything else is your problem

but in high school that was different

we didn’t have TAs in highschool though

[wispy slate]

In my community college we have SIs which get paid and work directly with the professor and get copies of practice exams on that, but I currently don't have time as I already work part time somewhere else

[weak rampart]

@weak rampart

[wicked minnow]

@weary ferry since this isn't a channel to ask for math help, why not put it below #math-discussion?

Also think the channel should be extended to everything academia, not necessarily just teaching math.

[sterile wren]

I am not a teacher but I just wanted to say good luck to everyone wanting to be one 🙂🙂

[wispy slate]

It could also be for better learning techniques

[wispy slate]

Any of you plan to teach in community colleges?

[wispy slate]

Not sure. I’m thinking high school level atm but anything can change

[fathom vessel]

Hi, folks! I'm a private math tutor (not affiliated with any university). I'm teaching a review of / second course in linear algebra to a few people right now, all of whom are used to working in coordinates (they are mostly computer scientists and engineers). Any advice on how best to motivate the coordinate-free / basis-independent perspective, or show that it's useful?

[wispy slate]

find real life instances in which these situations work, don't only be a tutor to them, but also connect with them and have a positive atmosphere with them.

[novel ruin]

you could try working in n dimensions instead of having a fixed dimension, and showing that it's possible to deal with vectors as purely algebraic entities not composed of numbers

[halcyon tapir]

Today I learned something so simple but I never noticed

The first 6 primes add up to give 41, the 13th prime.

I know, it's really simple but I thought it was cool how they worked like that.

Sad as it is, this only works because 2 is an even number. Otherwise adding an even number of primes gets you to an even number.

Interestingly, if you add 3 5 7 11 13 17 19 you get 73, the 21st prime. Maybe some sort of pattern exists there.

[hasty widget]

Well a lot of mathematicians have been trying to find out if there's some pattern with primes

None have managed so far

Think the most famous of them is Paul Erdos

[wicked minnow]

Why post here?

[hasty widget]

Why post what here?

[toxic spire]

Prime numbers are nice, connected to pi and natural numbers

[hardy solstice]

Pattern with primes ? I guess T.Tao published like a formulated general interval between two primes

[brazen pendant]

<@&268886789983436800> someone’s not reading #info and asking in multiple channels

[weary ferry]

dealt with.

[crude lava]

casher ?

[brazen pendant]

nah

the other one who posted at the same time

hey @weary ferry since you’re here and it’s topical did you see my suggestion to
-rolelock all channels except the read-only and the questions ones, and botchannel
-make a bot command that gives you a role which unlocks all channels and mention it in #info
-those who are capable of reading faq get access to the whole server

[weary ferry]

I saw.

[brazen pendant]

how stupid do you find it?

on a scale from “never talk to me again” to “hang on lemme just do it real quick”

[weary ferry]

well, I don't think anything goes at the "never talk to me again" side of the scale

I also don't think it's necessary

[brazen pendant]

it’s like an hourly annoyance

I don’t think I’ve held a conversation in #math-discussion without it being interrupted by a homework request

[weary ferry]

that reminds me, let's move this discussion to #math-discussion

[brazen pendant]

(wouldn’t #discussion be more on topic)

[weary ferry]

o ok

sure!!

[brazen pendant]

I feel like I should prep for the classes I’m gonna be holding but idk what to prep even

[meager bronze]

what class is it?

[brazen pendant]

numerical methods for physicists, as a TA

[meager bronze]

🤢

[brazen pendant]

so not holding the lecture, but I know for a fact the lecture will be garbage

and I’ll have to explain stuff

[meager bronze]

wait so what do you have to prep for?

[brazen pendant]

I have to hold tutorials

well, get to, really

I signed up for this

which are basically smaller classes

[meager bronze]

oh I see

[brazen pendant]

they don’t have a high expectation for us (they’d actually be fine if we were just there to provide help with homework) but I wanna do a good job and actually do useful stuff

since I know the prof I know that the thing students will be lacking most is knowing how tf to actually do stuff now

ie implementation

so I feel like I wanna mostly focus on that, plus some intuition in what we’re actually doing here

though the first class is just gonna be setting up and explaining python

[elfin tulip]

Trying to relearn Algebra, do any of you have an suggestions for online services for that?

[hasty widget]

khanacademy.org @elfin tulip

Or brilliant.org

@brazen pendant how many students are you going to be teaching?

[brazen pendant]

@hasty widget in the beginning prolly around 15-20, but they'll come and go since they get to change TAs more or less as they please. The good ones end up with classes of around 30, the bad ones more like five

we're around ten TAs for a class of idk two hundred?

[river steppe]

What class? @brazen pendant

[brazen pendant]

numerical methods

[elfin tulip]

Thanks!

[civic tree]

my frens abandoned my lessons i was giving then

didnt even get to clairaut’s thm:(((

[turbid zenith]

:<

That sucks

(That's the one about second partials right?)

[civic tree]

ya

[turbid zenith]

So, question for anyone who might be able to answer

If you teach, what's your process like for creating test questions and homework problems and such?

(Assuming you make your own)

[brazen pendant]

I’ll tell ya once I’ve done it a few times :P

[wispy slate]

Hey folks I'm new here
UK based Science/maths teacher ages 11-18
Also I make YouTube maths/science revision videos

[brazen pendant]

so today, we had our first meeting

almost all of us are second-years

(and in particular, doing this for the first time)

[wooden agate]

@turbid zenith I am not teaching just yet, though given that, possibly within a bit of a short period of time I may have at least more of a teaching role than I currently do, I am keeping an inventory of problems I particularly like

Among ones I've been assigned

Now, the thought process I'd have creating such problems varies a bit. If I'm doing your standard timed midterm or final, I'd probably principally try to design a test that relies both on insight that I've tried to convey in class and the content, but not rely too much on students being especially slick

For example, one meta-principle in analysis is that if you see an infimum, you should take a minimizing sequence. So I'd try to have a question in there which requires you to do that.

Another one is, if you have "soft" information (say, topological) about a linear operator and you want to show it's bounded, usually you want to use closed graph theorem

So I'd try to have a question where I give some soft info that doesn't "obviously" scream closed graph theorem (the conditions on the map won't just be the verbatim hypotheses), and students are supposed to notice that

An example of the infimum type question, which came up on my analysis midterm first quarter, was to find a necessary and sufficient condition on a set A\subset R^n such that d(x,A) is achieved for any x

(I don't remember exactly if it was just R^n or if it was in a metric space but I feel like you need local compactness so I'm gonna roll with R^n for now)

[burnt vessel]

Daminark:

[wooden agate]

I feel like problems of that form are probably optimal for tests, since the test becomes the kind of thing where you do well iff you learned

For homework, I may or may not borrow a hint from my algebra professor and have some problems that are more straightforward or of the above form, where you don't really need to come up with any real creative input to solve them

Just follow your nose and keep in mind the general practice principles

And have others which require ideas

[turbid zenith]

Hmm. Makes sense. 😮

[wooden agate]

The former are probably gonna be problems where the result is somehow important, since I'd rather make the homework problems mostly interesting. So at least if the solutions aren't necessarily all that satisfying, the results are nice

[turbid zenith]

The thing that always worries me is that when you're creating a timed test, there's not a lot of time for clever insightful flashes

And I can't stand when professors put clever insight problems on timed tests

Where you have to "see the trick" out of the blue to be able to answer the question

[wooden agate]

Yeah I don't think those are appropriate unless you've somehow hinted at that trick, sort of the way I mentioned above wrt knowing that somehow you should apply closed graph theorem, and now you have to find the way to include it

[turbid zenith]

On our second midterm in graduate Algebra I, one of the questions was "Assume that R is an integral domain with the property that every proper ideal in R is prime. Show that R is a field." And the trick to show that some a in R was invertible was to consider the ideal (a²). Easy once you've seen it but how are you going to come up with that on your own?

(Insert somebody who's already really good at abstract algebra saying "but it was so obvious") -ducks-

[wooden agate]

Hmm, okay this is kinda one of those things where I could buy that the professor didn't think this was especially clever insight. In your mind you can sorta justify this as, well we wanna say that a is invertible and we know we have an integral domain and proper ideals are prime

Somehow there are only a few ways one could even hope to prove it, you know?

[turbid zenith]

I guess. But I remember trying a bunch of things and nothing worked, and then when I saw (a²) I was like "well that was out of nowhere"

[wooden agate]

Some professors definitely gun for cleverness, others (my analysis professor third quarter) are just that smart

[turbid zenith]

I think when you're a professor it can be easy to forget how hard it is to learn the stuff

[wooden agate]

So, this is true for most people. My third quarter analysis professor was kind of a child prodigy so in her case I dunno if that even checks out

She told me once actually that there was a class for which she was the only undergrad, so she had a take home final (grad students didn't get graded at all) with 2 weeks to do it

She comes back in 2 weeks later and practically trembling from fear of failing because she could only solve a special case

That special case happened to be an open problem

[turbid zenith]

...wow

What was she supposed to do?

[wooden agate]

I mean the professor just wanted to see what she could pull off

[turbid zenith]

That's hella mean for a final but if that was just because he knew what he was dealing with then great

[wooden agate]

I imagine she was already known at that point to be pretty good

[turbid zenith]

Yeah makes sense

[wooden agate]

But yeah she has definitely given some tough homework problems. Tests weren't as bad my year because she gave really hard ones the year before thinking they were easy

And from the experience then she recalibrated

[turbid zenith]

Hopefully she curved the year before?

[wooden agate]

Oh absolutely, if anything she's too nice with grades

So what happened was she gave a midterm which really should've been a 2 hour test, but in one hour. And then she gave a fairly tough final but gave people unlimited time

My year the midterm was toned down a bit, the final didn't have unlimited time (we started 6:30PM instead of 10:30AM, and the year before someone took a full 8 hours, which was cruel to the TA, but we had until 10PM)

And over half the class got As I think

[toxic spire]

here's how to math

$[_{(1)}^{(2)} _{(-1)}^{(3)} ]$

[burnt vessel]

Yeat:
Compile Error! Click the reaction for details. (You may edit your message)

[civic tree]

what

[wicked minnow]

🤢

[rich rampart]

So, I've been teaching myself mathematics for the past 4 months and I've made quite a lot of progress as an autodidact.

I'm wondering if there is any fast track test or exam I can take that would give me a qualification in mathematics so long as I know all the maths related to that particular qual.

[brazen pendant]

30 minutes till my first class hype

[hexed perch]

gl

[turbid zenith]

I wish, @rich rampart

If there were I would have done it 😛

I mean you can always sign up for the GRE Math Subject Test -- it's not a degree but doing well on it can certainly show people you know your math

[fading trail]

what do u guys think of professors purposely holding back past exams because of question reuse?

[grand laurel]

Depends on the subject

In some cases it makes sense, because there are only so many "good" questions you can ask

In most cases it's unnecessary though imo

[rich rampart]

@turbid zenith Hey, the GRE looks perfect. At least it's something to aim for. I can structure my learning around it and try to learn the content that will be on the test.

[turbid zenith]

That's what I did. 😃

[placid mantle]

Hey, I'm teaching fractions to students and I'm curious if anyone knows a good program to visualize fractions with shapes

So I can show 3/4 of a square, 2/3 of a circle, etc.

[shy lintel]

@placid mantle I would recommend taking a look at these links, hopefully they're sufficient enough for visualizing fractions.

https://www.visualfractions.com/

https://www.visualfractions.com/teachers/

https://www.mathwarehouse.com/fractions/manipulatives/fraction-maker-online.php

https://archive.cnx.org/contents/fe83677e-2580-44b5-8505-7ee2260a988d@2/visualize-fractions

[placid mantle]

Alright, thanks

[oak wraith]

do you guys get a lot of math whiners who bemoan having to take dry and desiccated math classes where teachers seem to only show a jumble of unrelated problems and a bunch of tricks, mnemonics, properties, and "math facts" to solve them rather than an overarching cohesive subject with just a tad of depth?

inb4 "no, just you"

[wise onyx]

Hmm

Tbh

You can't expect a highschool classroom to be perfect lessons every day

If you wanna learn cool stuff you gotta, as the student, invest in finding those cool things yourself

[ocean bobcat]

my recollection of high school is that even in the supposedly advanced classes nobody was there to learn or try

everyone just wanted to slack off in math and heckle the teacher

[wise onyx]

What can you do

It's a fact the average person is not interested In learning abstract ideas

[ocean bobcat]

i spent lecture time half paying attention and half trying to get a jumpstart on uni material

[wise onyx]

I would avoid doing the borring exercises sheets in class

[ocean bobcat]

it only partly worked because i was an idiot but i learned things that made first year easier so hey

[wise onyx]

And instead try to derive the formulas or create new ones

[turbid zenith]

@oak wraith All. The. Time.

The worst part was that it happened more in my honors classes than anything. :/

A number of those students had always done well with the usual "learn the formula, do 20 problems of the exact same type, lather rinse repeat"

So when I had them in my Honors Precalculus class and was expecting them to think more deeply about things, derive them, explain them ... some of them almost flat out rebelled

One sicked her mom on me

[meager pewter]

http://prntscr.com/mobf8a

Shouldn`t this come out as

http://prntscr.com/mobfwt

[warm lintel]

that's not really the chan where you should ask your q but w/e

How'd get +2?

[meager pewter]

my bad not 2

1

would be like this

http://prntscr.com/mobinr

[warm lintel]

It's exactly the same thing as on the right hand side tho

[meager pewter]

so the one the first img

just takes out 1/2n out front

and thats it right?

let me say that better sec

this

http://prntscr.com/mobinr

is the same as

http://prntscr.com/mobjon

[warm lintel]

das ist what I meant yes

[oak wraith]

That's just too bad. If I want to learn more math and enjoy it, I've got to learn it all on my own.

[brazen pendant]

it gets a lot better once you get to a point where everyone taking your classes is actually there to learn math and not just fulfill requirements

[oak wraith]

im not a teacher, if that was addressed to me. I'm the lazy student wanting less of a slapdash and disjointed curriculum.

[hasty widget]

yeah, i had the same, thing, lemetrix, class should've been named math facts instead of mathematics