study-discussion

[paper loom]

I dont quite get the idea of using such techniques. If you want to increase attention span, you kind of have to brute force it

[hexed shuttle]

Ok

[fleet hill]

Eliminate all possible distractions

Close all other tabs, move yor phone to another room, etc

[hexed shuttle]

Ok, thank you!

[coral sleet]

@hexed shuttle welcome to the mathcord

[gaunt ruin]

welcome to mathcord swarde!

[uncut turtle]

if u are addicted to games/ reels then just try keeping ur games on ONE device only not both. then when ur tryna study tell ur self that for every three hours of study u get 1hr 30 mins of games/ free time. it works for me ! 🙂

[storm jasper]

Unironically what’s your brawl stars account fr

very cool

[rocky terrace]

What da hailll!!?!! more than 600K games and 1300 elo... 💀 bro plateaued

it's funny you how you can see the variation in the rating literally pleateau over the years

Yea I've been meaning to read it when I got the time

perhaps it is now

[fleet hill]

I've never read it I just occasionally quote the Wikipedia summary of it

I'm ngl

[rocky terrace]

Meanwhile Feynman: "step 1: write down the problem, step 2: think very hard about the problem, step 3: write down the solution"

Solving a simpler version of a problem or a special case of the problem is a good strat

also drawing a picture, it's crazy how many times I've struggled with a problem but once I drew just one picture it instantly gave me the solution

On a related note, this is a really nice video from 3Blue1Brown on the topic

https://www.youtube.com/watch?v=ltLUadnCyi0

Interesting problem too!

@fleet hill Btw Eric, there are a few things in https://discord.com/channels/268882317391429632/1353730564712038471 to be pinned in this channel, could you pin those when you are free?

[fleet hill]

Can you put them in the channel

[rocky terrace]

1 sec

[rocky terrace]

https://youtu.be/9qlqVEUgdgo

https://terrytao.wordpress.com/career-advice/theres-more-to-mathematics-than-rigour-and-proofs/

[rocky terrace]

https://terrytao.wordpress.com/career-advice/

Sour drop's suggestions: https://www.youtube.com/watch?v=cRQqH18wJgw

[fleet hill]

Okay I'll watch some stuff then decide

[fleet hill]

https://arxiv.org/abs/math/9404236 I think Thurston's article here captures really well the process of developing intuition while learning mathematics

[rocky terrace]

Thurston!

[fleet hill]

I don't really see how this post is helpful to people, it seems like a complaint, maybe there's something with suggestions that you could link instead?

[rocky terrace]

True

[rocky terrace]

This is great though

[fleet hill]

Okay pinned

[rocky terrace]

This is nice too, it's basically part 2 of this TED talk you pinned

[short dirge]

amazing

[mental tinsel]

This was a very insightful reading. Thank You so much for sharing ❤️

[glacial raven]

A big part of my thought process explained by a meme:

Please help me tho with this

Genuinely

[junior dagger]

?

[slow yew]

Sounds heuristic

If you find yourself going back and forth on ideas and not progressing, it might mean you need to chunk the problem out into smaller parts and solve them piecemeal

[glacial raven]

Like, the miner here thinks of another miner, mining who thinks of being close to hitting diamonds but another miner quitting right before so they continue, but in reality that miner is mining into nothing, so the original miner doesn't even try.

[rocky terrace]

Are you saying you don't even try because you think you're going to be just mining into nothing while thinking you're close the the diamonds?

[rocky terrace]

Moral of the story: Keep moving forward, until all your enemies are destroyed.

[glacial raven]

bruh

[glacial raven]

I couldn't try because i know thinking i am close is false

[rocky terrace]

How do you know?

[glacial raven]

I am stupid af that's why

[slow yew]

Being stupid or smart has nothing to do with whether a thought you have is correct.

[rocky terrace]

You can tell yourself you can do it a 1000 times but you will only really believe you can do it, when you actually do it once. So show yourself that you can do it, show yourself that you can try and succeed

[olive geode]

I don't understand what the diamonds are supposed to represent. It's not like you will suddenly get to a point where you now understand everything. It's more like there are small diamonds at every step of the way

[rocky terrace]

Yea looking back, I often understand earlier material better and deeper now that I've gone through more advanced material

[glacial raven]

Kinda unrelated but it's even mentioned in Atomic Habits that we tend to expect big results with big inputs which is not always the case, and is also one of the reasons for creating a mental barrier of not giving a try at all. Culmination of small inputs every day can also lead to big results

You just have to give it a go

[glacial raven]

That's how real mines are anyways, also, if you use a real mine, it's a better analogy because you also have to refine the ores just like refining the knowledge.

[glacial raven]

When real life stops being tiring, i get out of the time loop, and i beat ADHD, i will try.

[glacial raven]

there is a Turkish proverb for this.

"drop by drop becomes a lake" But it's apparently ripped from some other proverb but at least this one is better.

I am Turkish btw that's why i know.

[rocky terrace]

Are you getting medication for ADHD?

[raw tinsel]

over 20 years i lived with it, only in the last few i knew i lived with it.

i dont think ill ever beat it, at best work with it

[glacial raven]

Yes, it doesn't do shit.

[glacial raven]

My ADHD is extremely strong.

One good thing is, i used to scroll for hours at a time, but i installed a special patch, that completely removes youtube shorts, so there is nothing to scroll.

[rocky terrace]

But you're stronger🗿

[glacial raven]

I haven't doomscrolled since, because i can't.

Thank you, revanced.

[rocky terrace]

I don't have ADHD but I have the "mindlessly consuming online content" problem as well

[rocky terrace]

right now I'm controlling it by not watching youtube videos while having food

[glacial raven]

Thanks... I try, but i think i can't try my best.

[rocky terrace]

You can

I believe in you!

[rocky terrace]

if I did watch youtube, I'd just sit there watching youtube even after I'm done eating

[glacial raven]

I do always watch while eating.

I even sometimes have a podcast on the background while playing games.

And game audio is muted.

[glacial raven]

It's mostly psychological health stuff

But many people have said i learn very fast, irl and online, as well as some psychiatrics while diagnosing me with autism.

[rocky terrace]

I learn very slowly... maybe the problem is that I don't have autism

[glacial raven]

My problem is that i BARELY EVER study.

Spend most of my time wasting it.

[rocky terrace]

same...

[glacial raven]

And while in school, i just sleep.

[rocky terrace]

That's the most difficult thing to deal with, you can't just "I'm gonna push through and just get over it!" But I do believe you can come up with effective strategies to deal with your problems

perhaps this can help you

and most importantly this

[glacial raven]

But currently everything is going downhill.

Nothing has gotten better for many months

[glacial raven]

Yeah, my attention span is cooked, but, sometimes, i can just focus on a long video and watch the entire thing or read some long stuff, but, those are rare.

[storm jasper]

Wait how do you do that

Like not doomscrolling

[gaunt ruin]

she removed youtube shorts using revanced

mine is in spanish tho

i have exam tomorrow for this philosophy exam i need to pass

i just want for exams to end so I can stop studying for a bit

monday I had chemistry exam, tuesday algebra, and friday philosophy

[glacial raven]

You won't doomscrolled if you literally can't.

[rocky terrace]

We can tell.

[glacial raven]

It also has a lot of other cool stuff, adblock, dislike counter, playing outside app, all for free and easy.

[glacial raven]

To be realistic it's not about quitting = killing your addiction. I had tried that in the past, but the thing is that there are some genuinely good things about this platform as well like the availability of Latex bot (because I'm too lazy to download Obsidian/use Overleaf), alongside the availability of such academic servers and more, that would be lost when you quit, increasing the urge to come back again and completely ruining the point of quitting itself. If this is the case, using discord in moderation only for academic purposes, via the help of app blockers is more helpful in my experience

And I'm thankful for the existence of studying/perma-studying roles here for that

[rocky terrace]

🫡 I'm sure you will achieve great things

I myself am planning on taking a break from discord for 1 or 2 weeks

[gaunt ruin]

i think in ios you can try uYouPlus

[glacial raven]

Who is "on reply" and why should i ping them.

[thorny girder]

how to approach studying calculus? how to know I'm ready with algebra+trig+precalc concepts? how to structure and spread out study sessions if I'm studying on my own? how many and which problem sets should I work on? should I focus more on problem sets or concepts at this point, or both? how to know I'm making progress with it?

[storm tide]

how to approach studying calculus? how to know I'm ready with algebra+trig+precalc concepts?
If you don't have a school defined course structure of prerequisites to guide you, the natural approach would be to start reading a calculus text, and see if the algebraic manipulations etc. it expects you to understand are actually understandable to you. If you understand enough not to get stuck with all the exercises, then you were ready.

[gaunt ruin]

isn't most books meant to be used as a supplement of a course?

[flat ibex]

in math you can just work through most books, you dont necessarily need lectures. probably good to have someone to check your proofs though

[knotty linden]

I think this is correct. Reading isn't the same as attending a lecture. Given an appropriate level, attending a lecture, and having a chance to ask questions is one of the most expedient ways to gain insight from someone that is an expert in the field

[rocky terrace]

Andrew wiles said the same thing

something along the lines of "reading a book on your own is the worst/hardest way to learn math" and "having a one on one session with an expert in the field is the best way to learn math"

[storm tide]

Often enough reading a book is the best option actually available to you. Experts in the field tend to be reluctant to having one-on-one sessions with random strangers.

[rocky terrace]

This is true, but I assumed he was talking about a practicing mathematician

even then experts in the field will be too busy for one-on-one sessions, so the next best thing would be attending lectures given by said expert

regardless, just attending lectures won't help, you still have to actually do the math yourself to properly learn it, so books are still indispensable

[reef ocean]

and even with known acquaintances like their own grad students and collaborators time is scarce

[hearty oriole]

does anybody have any recommendations for self-studying real analysis?

I have pretty much no formal math background (Im a physicist, so ive touched plenty of math somewhat, but never a rigorous treatment)

I'm going through a old textbook "introductory real analysis", and some reviews say the questions are really difficult, but I've felt most of the problems were manageable

Nobody is reviewing my proofs, so how can I be sure I'm not just completely wrong?

[glacial raven]

Is it ok if i memorize the quadratic formula to solve quadratic equations because like i tried to learn to complete the square and i ended up deriving another formula.

@coral sleet

and this thing is a lot less easy to use

after plugging numbers in you do other stuff

[cunning totem]

memorizing it is fine and good

you don't want to go through the work of plugging everything in to the formula when easier methods work

if you pick coefficients at random it's usually hard to quickly see the factorization so you just apply formula

[storm tide]

If you multiply that through by (2sqrta)² = 4a, you get something pretty close to the usual quadratic formula.

(But yes, the quadratic formula is one of the things it is quite okay to memorize).

[glacial raven]

what is not ok to memorize and what is?

[storm tide]

Uhh ...

[glacial raven]

quartic formula

but i mean something actually useful

[storm tide]

I don't have a crisp distinction, much less one I can actually explain.

[glacial raven]

gaussian elemination for partial fraction decompression.

ဪ

[torn olive]

You memorize what you use alot

And don't memorize the rest

[wispy zephyr]

don't memorize on purpose, if you use something enough to be worth memorizing then you will remember it

[storm jasper]

I mean

Memorizing thereoms and important concepts are super important to move forward

But are you referring to just not memorizing intentionally?

Or

[wispy zephyr]

yeah and if you use them enough then they will get memorized

but trying to memorize something intentionally by staring at it enough just doesn't tend to work very well (and doesn't do the critical thing of associating it in your mind with the contexts you use it in)

[storm jasper]

I mean what I do

Is just look at definition

And I try to use the definition to prove something

For instance for proper induction

Uh I still don’t have a good grasp

But I practice problems to indirectly get better at said thereom

[rocky terrace]

You dont have to explicitly sit down and memorize it

just understand the ideas

and the ideas used in the proof of the theorem

[rocky terrace]

and yea any book you're following will have problems related to the theorems in any particular section

Like in analysis books problems in the derivative chapter are just MVT spam

(or Generalized MVT)

[rocky terrace]

Book recommendations?

[rocky terrace]

same

[rocky terrace]

use this server! There is #real-complex-analysis. I think you can also use the Q&A website Math Stack Exchange

Also you slowly get better at gauging whether your proofs are correct or not

[rocky terrace]

"Introductory real analysis" by Kolmogorov and Formin? Looks to be a measure theory and "advanced analysis" book

[gaunt ruin]

are people Willing to read other proofs?

[storm jasper]

Lebl and the book of proofs is peak

[rocky terrace]

Yes

[storm jasper]

Probably not

[gaunt ruin]

math.SE i think deliberately says they are not a proof checking machine

maybe I'm just misinterpreting what i read

"For posts looking for feedback or verification of a proposed solution. "Is this proof correct?" or "where is the mistake?" is too broad or missing context. Instead, the question must identify precisely which step in the proof is in doubt, and why so. This should not be the only tag for a question, and should not be used to circumvent site policies regarding duplication."

[gaunt ruin]

is that so? maybe i have hope!

[rocky terrace]

Yea you check your own proof, if you are unsure about a particular step then you can ask on MSE. This is my interpretation

[rocky terrace]

Never give up!

[gaunt ruin]

quick question do you guys know any proof checking software, or proof assistant that checks if proofs are correct?

[rocky terrace]

go back, lock in, grind

[eager halo]

:notthis: check your own proofs. No proof checking software is advanced enough for general use

[raw fox]

,iam studying

[mossy shadow]

Gave you the studying! selfrole.

[raw fox]

@unkempt gorge

It will hide all talking channels from you

So you will see only study channels

If you take that role

[raw fox]

With this command

,iamnot studying

[mossy shadow]

Removed the studying! role from you.

No selfroles matching a potato.
See ,selfroles --list for the list of valid selfroles.

May 31, 2025, 6:37 AM

[raw fox]

,selfroles --list

[mossy shadow]

Self assignable roles for this guild:

Helpers, studying!, Not Very Ppl, Talks, Role that does nothing, she/her, he/him, they/them, any pronouns, ask pronouns
```Use `,iam role1, role2, ...` to assign yourself roles.
Use `,iamnot role1, role2, ...` to remove the roles.

[rocky terrace]

There is also the perma study role

which is assignable by the moderators

which might be more useful if you struggle with self-control...like me

[mossy shadow]

Gave you the studying! selfrole.

[raw fox]

Yes

[rocky terrace]

#bots

[raw fox]

#bots

[rocky terrace]

sniped

[wispy zephyr]

you can also select the "hide discussion channels" option in id:customize

or manage roles in #info

[rocky terrace]

You can also click on

I'm only half kidding, I used to do this when I was particularly distracted

You seem to be only in #book-recommendations

[raw fox]

Wtf

Oh

Ahh nothing

Misinterpreted

[rocky terrace]

who cares
Your future self

both is good

[rocky terrace]

You have the studying role

[vapid kiln]

mb i stupid

[cunning totem]

no and almost nobody will until it becomes easier and faster to write proofs in software like this compared to writing them by hand

the only main use cases for software like this presently are for proofs that are genuinely too complicated for anyone to understand where checking the correctness is really important, but this is really rare

and usually if a proof like this is too complicated to understand it's too complicated for a single person to understand it's also too complicated for a single person to write a formal proof, it takes a pretty large team of people a long time

[glacial raven]

if anyone is down to study basic maths (geometry/pre-algebra/algebra) im down, just DM me

[glacial raven]

We need that bleak catking here
Oh nvm

[storm jasper]

[near dragon]

what theme ( or chapter) r u studying rn?

[glacial raven]

Geometry

[hearty oriole]

im slightly too far down the rabbit hole with this book unfortunately

[hearty oriole]

ahh thank you for this suggestion

I do worry sometimes if my proofs border on insane but hopefully so long as im respectful people will be kind about correcting my mistakes

[rocky terrace]

yes they will

[hearty oriole]

yes! I was told to read it because I needed measure theory for some stuff in statistical mechanics

[rocky terrace]

Interesting

I thought measure theory was mostly only needed for QM

[hearty oriole]

I think the formulation of statistical mechanics I was trying to learn was a bit silly

it defined entropy in terms of the measure

apparently its useful in certain fields but its definitely not useful for the kinds of physics I want to do

also the author seems to have an aversion to proving statements

its very funny the book was originally in french, but itll be like "see bourbaki [9] for proof" without a page number and then the entire thing is in french

[rocky terrace]

well it's physics after all

[hearty oriole]

no no it was written by a mathematician but its more of a monograph

[rocky terrace]

Oh I see

[hearty oriole]

at least for a significant portion of the book

eh its 50 years old maybe he wanted to save money on ink idk

[glacial raven]

[gaunt ruin]

which resource explains affine subspaces?

[vernal sky]

linear algebra books do, look for the ones with geometry in their title like kostrikin-manin or shafarevich-remizov

[gaunt ruin]

but an affine subspace does not pass through the origin

it is not a vector space, so they explain the geometric intuition?

or wdym?

i will check them out tho

[eager halo]

Its not that complicated: an affine subspace is just some subspace displaced by some vector v

[tardy relic]

hi chat 😄

[fleet hill]

Another way to think about it is that a vector space is just like an affine space but you choose one point to be the "origin"

[fleet hill]

Hey!

[tardy relic]

do y'all have any tips for self studying,specifically how to schedule yourself and what to do when you're stuck on a topic

[fleet hill]

Unironically ChatGPT is kinda good for generating schedules lol, at least for getting a starting point

[tardy relic]

nice,ima do that this week

[fleet hill]

I wouldn't stress too much about sticking to a schedule tho except as a rough guide bc it's gonna be really hard to predict how much time you need for each thing

and it's also gonna depend on how deep you wanna learn it

[tardy relic]

i need to prep for AMC 10 and do all 3 calculus's,I MIGHT be screwed

[fleet hill]

Oh wow

You're planning to learn three semesters of calculus? By when? And why

[tardy relic]

by end of summer,because i want to do a discord integration bee

[fleet hill]

Lol

[tardy relic]

and i need calculus in physics,so best to finish it all at once

[fleet hill]

I would probably figure out what your priorities are first and stick to picking one thing up, if you have more time you can pick another thing up at the same time

Usually it's nice to have long uninterrupted stretches of time to think about math tho

Long-term speaking, studying for calculus will be more useful

[storm jasper]

You got it bro

I mean to me it doesn’t seem that far fetched

[subtle crown]

If you wanna be very good at it, it's pretty far fetched

But if you just want to know some tricks then it's fine

[maiden jungle]

Hi

[ruby basalt]

yo

how do u guys study

[silent apex]

Any tips for memorizing abt 70pgs word for word

[scenic shuttle]

depends on what you want to study

[ruby basalt]

math

[scenic shuttle]

your key is to practice a lot

and if you get stuck on something, try looking for same problem from textbook or online resources

or class notes

[fleet hill]

what level of math are you on rn?

for high school math, I think a lot of practice problems is the way to go, targeted towards a topic that you struggle on

[shadow storm]

hi hope y’all don’t mind me pasting my yap from #discussion here

just wondering how y’all study maths, I’ve never really studied for anything before because I just understood it but now in my first year of university I’ve failed 2 of the 4 calculus exams and their respective resits, now the last exam I have to pass for a positive BSA and I feel kinda stuck because I just look at it (probability theory), watch TOCT videos etc but I just can’t seem to make exercises on my own

[ruby basalt]

highschool

[fleet hill]

Oh okay yeah KhanAcademy is a great resource for practice problems

[fleet hill]

One thing you could try is posting exercises in the help channels and having someone walk you through it. Another thing is, try taking a blank paper and writing down everything you remember learning about onto the paper in some organized fashion. That way, when you compare it with the lecture notes, it'll be easy to spot where your gaps are.

You definitely have to keep doing exercises though because it forces you to engage with the material beyond a superficial manner, and once you start breaking through them, it'll also help build your confidence.

Does your class have office hours? If so, I would highly recommend going to them as often as possible.

[fleet hill]

Wait you don't have any office hours for any of your classes after the first semester??? That makes no sense wow

What country is this?

[hexed musk]

How do I study math to remember everything.

Like in school the teachers make few samples and such and the test is the same almost with different numbers.
And this is 0 compared to what i will need to know at a job.

Like this is so low level, how could I learn differential equations properly (I know integration / derivation)
But i dont really get the concept of diff equations at all.

I can solve them but I dont understand

[subtle crown]

understanding is the key to really remembering something

i would look at math texts that go into detail about why it is that something is true

rather than just being told it is

[summer pine]

hi

[rocky terrace]

Also it's okay to forget stuff

just relearn it

[brazen mist]

[tacit glen]

if you have enough skills, you can derive out some (un)necessary things even if you have not memorized it

[vernal sky]

spammer

oh

oh wait the ping didnt go off

[little smelt]

who

tf

is

spamming

bruh

i

don't

see

it

[unkempt quarry]

Sybau

[little smelt]

Chmunc

[vernal sky]

unblocking you was the wrong decision

[green terrace]

Buh

[little smelt]

i didn't notice u blocked me to begin with lil vro 🥀

[short dirge]

https://tenor.com/view/lie-lies-liar-bullshit-so-that-was-gif-15334130

[storm tide]

More time-consuming but likely to lead to a better understanding.

[olive geode]

It can be good, but I think you should choose one as your main book, then just look up certain sections in the other as needed. If you read both page to page then you're gonna read a lot of the same stuff twice

[dire matrix]

Yo guys, I think I'll be taking calculus 2 in college, since I got a 4 on ap calc AB. However, problem is, that was when I was a junior, and since they didn't have calc BC senior year, I had to take AP stats instead. Because of this, I don't remember much of the calc content at all, so I'm worried if I'll be prepared in college. I want to review with khan academy but I'm unsure if I should do the calc AB course again or the differential calculus course to brush up, or any other suggestions, or maybe not focus on either of them at all and prep by doing the BC or integral courses

[storm jasper]

I mean I learned calc 2 and 3 on khan so I would say it’s good

[wild badger]

any recommendations for arithmitic and geometric series and anything else on this topic of series . (Yt videos, books, pdfs)??

[thick ermine]

seconded: khan academy for any maths you'd do in university kind of sucks

khan academy often ends up being very computationy

which doesn't cut it at that point

[torn olive]

why wouldn't you be able to study the in college?

I would be surprised if you couldn't fit in a physics and/or math minor

especially since as an engineering major, you would probably take a number of courses in both fields so to get a minor in either would probably only require 2-3 additional classes

Alot of the engineering students at my undergrad added on math and physics minors

Hm ok in any case, self study is hard (but you already probably knew this) but it's definitely doable. I guess a first step would be you saying what math you've already learned and perhaps what math you're interested in so that people can recommend things to study.

The best source 9/10 times would be a textbook, not youtube lectures or whatever

well you aren't going to actually learn anything if you aren't doing problems

and textbooks are a source of problems, and they'll pull from knowledge and notation and ideas given in the textbook

depends on the book, the playlist may or may not exist, and again you need to be doing problems (most of your time will be spent trying to work on problems, not just consuming information)

not that I'm aware of

I get that learning from textbooks seems scary, but it really isn't that bad (especially since you can use this server to ask questions and get help) and learning how to learn from more sources can only help you

[pulsar forge]

How do I figure out what we be doing on a test when our teacher hasn't told us anything and wont tell us anything (as far as i remember we have done angles on triangles and transversal whatever it is) 😭
It chooses what set im in next year and I wanna be quite good yk

Any advice in general for studying is helpful since I've never studied before, like no joke but now I've decided I want to be successful in life someday soo

[scarlet sequoia]

When is the test?

[pulsar forge]

I think sometime between 17th-28th, so pretty soon

[scarlet sequoia]

Well congrats on getting the mindset that's a great step already and I hope you be consistent with it, most likely your teacher won't give anything except what they have taught so I would suggest looking through your classwork and hw as well and if you're lacking with all that ask for help to your classmates, additionally you can google the topics and there are various good sources of information to get a good understading of what you have been taught. If you ever have any problem with questions you can also ask it in the help channels, getting started with it is the hardest thing. So my advice will be to stick with it even if it feels boring at first and when you start understanding it you'll have a lot of fun studying, I hope this helps.

[pulsar forge]

Thank you! I'll look more on whatever these are called ⁵ ⁶ ⁷ as well as the negatives because I was not paying attention when we were learning these, whoops (even though it's super basic)

[scarlet sequoia]

They're called exponents

[pulsar forge]

Thanks lol

[scarlet sequoia]

How old are you?

[pulsar forge]

14 but my class is far behind and I don't go to school and lot

[rocky terrace]

imo calc 3 in Khan Academy is great

I mean if you supplement it with a textbook and do the textbook exercises

[gaunt ruin]

im eating croissant while preparing to my intro to basic python exam

good morning yall

[ancient dagger]

python?

let me help you bro

[gaunt ruin]

well most specifically is about using this libraries matplotlib and pandas

[ancient dagger]

epic. ask on.

[gaunt ruin]

what would be the main difference between iloc and loc for pandas

what is a legend in matplotlib

[green terrace]

loc uses labels for accessing, iloc uses indices

[fleet hill]

Do y'all feel like you get whiplash when you switch between reading math textbooks and textbooks for any other subject

The style is so vastly different

[rocky terrace]

When I'd switch between physics and math textbooks I don't think I felt that sort of whiplash

perhaps it was because I'd gotten used to both styles

man I miss physics I need to stop procrasintinating, finish Abbott and restart classical mechanics

[fleet hill]

Hm physics is pretty similar to math in culture/style

What about other subjects

[green terrace]

yes

[subtle crown]

https://tenor.com/view/whiplash-not-my-tempo-jk-simmons-gif-9593874262333532084

[coral sleet]

I struggle to read physics books these days

the writing is just so different

[upbeat veldt]

social science and philosophy textbooks after going through proofs from math ones

trying not to also tackle problems in social science in a positivistic way like math does, does seem to require some effort when changing subjects

[quick elk]

Which books

[coral sleet]

the last ones I read were Morin and Griffiths' E&M

[quick elk]

Physics epubs on a phone seems like a nightmare

[quick elk]

oh, I thought you were farther along
didn't you say it's a physics program you're doing technically

I just assumed since you're farther in math

[coral sleet]

I don't ever recall saying that I'm in a physics program

[quick elk]

hmmm
I thought you said it was a math and phys program
my bad

I think you were saying a specific course last week and I misinterpreted that it was your program

[rocky terrace]

I like both physics and math books since I can more easily understand how the stuff proceeds into each other

The duality of man

[green terrace]

<@&268886789983436800> scam

thx

[coral sleet]

[fiery iron]

So we practice to reduce mind calculation?

[quick ferry]

i havent had to read a single book for chem

[devout sun]

i agree with higher

[rocky terrace]

You'll get used to it

Like how you got used to math books

[devout sun]

Well math books are better 🗿

[glacial raven]

Nah I'd poetry

[brazen mist]

https://tenor.com/view/nah-id-win-gojo-nah-id-win-gojo-satoru-gojo-jujutsu-kaisen-gif-722934852497975468

[unkempt quarry]

<@&268886789983436800>

GG Zanarcane, your time on this planet will soon come to an end, just as soon as the mods see the horrors you posted

[rocky terrace]

fool, Zarcane IS the mod

secret mod

[torn olive]

<@&268886789983436800> (in multiple channels btw)

[brisk heath]

Has this been dealt with?

I think the user has been banned

[torn olive]

As far as I can tell yea. It was some dude spamming pictures of some scam

[brisk heath]

They were in discussion too?

Ok great thanks

Gonna thumbs up, but any smods that see this can review

[reef ocean]

yeah likely been dealt with by now

()

[rocky terrace]

Woah seniors mods are RGB now sick!

[reef ocean]

gamer mods

gamer role

[rocky terrace]

is it supposed to resemble the colors in the trans flag?

[reef ocean]

yes nami made it like that to try out the feature lol

[rocky terrace]

ew

jk

that's pretty cool

[rocky terrace]

Oh is this a new feature? dynamic role colors

[reef ocean]

cf. #discussion message

[wispy zephyr]

yeah it's a thing you can buy with nitro boosts

alongside server tags

apparently the boosts used for buying fancy role colors and server tags also don't count towards the traditional nitro boost perks (more emoji slots etc)

(not that it's a problem with like the 60ish boosts we have)

[rocky terrace]

nah wth the senior mod role dynamic colors actually look super cool especially with the bloom effects and stuff

[main trail]

is it normal for a RA proof to take forever

even relatively simple ones

Like proving an unbounded seqeunce diverges( no hints pls)

[worldly rune]

juggling epsilons and deltas is quite hard if you arent used to it yet

takes a while

[fleet hill]

^^

[zinc shore]

how to learn math, I'm interested but I dont have any starting point, I studied history, geography, & politics before, and then tried to learn advanced math in Desmos, but without a starting point, my mind couldn't comprehend anything at all

[main trail]

the funny thing is this proof has neither of those

[worldly rune]

that doesnt seem correct

[main trail]

I mean the easy part does

but we have for some n, a_n>M for all reals

I have to show this n is less than the least N after which |a_n-L|<\varepsilon

[wanton cradle]

u should expect it bc every epsilon definition has a million quantifiers

[rocky terrace]

I have noticed though, intro algebra is usually easier/simpler than intro analysis

I would attribute this to the fact that you're usually dealing with simple algebraic structures in algebra, such as groups or rings. They are simple compared to what you work with in analysis "a complete, totally ordered Archimedean field". You play with not only the algebraic and order structure but also the metric and topology induced by this order.

[rocky terrace]

Desmos is a graphing calculator, usually one does not begin learning math there , but it certainly can help. I've used Desmos a lot to get an intuition about what different functions look like when graphed.

But learning math is akin to climbing a ladder, without the bottom rungs, you cannot reach the higher rungs. So you will need to begin at the beginning

I don't know how much mathematics you already know, but I'd reckon Khan Academy is a good starting point.

https://www.khanacademy.org/math

[mossy juniper]

Any channel for set theory

I can't find it if u know plz send it's link here

[vernal sky]

#proofs-and-logic and #foundations

[mossy juniper]

Thanks

[glacial raven]

Can a person study TCS in depth without really doing analysis?

Or at least skip some parts of analysis? Because I don't really know what intersections it has with TCS except the big-O stuff

[green terrace]

I mean, most CS departments will teach the basics up to turing machines to undergrads with almost no real analysis experience just fine

[green terrace]

Even big O isn't all too difficult imho

One should be able to read a text like sipser or CLRS with no more than basic calculus and some notion of graphs (and possibly basic knowledge of data structure implementation)

[glacial raven]

Thank you

[storm tide]

No.

[green terrace]

No, that's literally what I just said

Maybe to them calculus = analysis? Or they saw the wikipedia article on big O notation 😭

[olive geode]

Do any of you often make up/compute concrete examples while reading? I'm reading Lee's ISM currently, and some of the concepts, like derivations and tangent spaces, are pretty hard to get used to, so I'm thinking I need to go through some concrete examples. The exercises in Lee are usually proofs/theory, so I have to come up with my own examples if I want any

[torn olive]

You don't need analysis for a large portion of it. Perhaps if you get deep enough to start looking at some more modern areas of TCS (especially those with heavier overlap with mathematics) you may need to learn real analysis but that's highly dependant on the topic

I think you are very much at just the start of studying TCS so worrying about this is putting the cart before the horse

[torn olive]

everyone could spend more time computing examples IMO

(myself included)

[olive geode]

Yep, I'm slowly realizing how important it is! I have to get used to textbooks not supplying me with all the examples I need

[unkempt quarry]

<@&268886789983436800>

This one doesn’t even have the 4th pic smh

[wispy zephyr]

is it always that same mr beast scam atm

[unkempt quarry]

Yeah but one I saw before had 4 pics

[wispy zephyr]

they're getting lazy

[lucid glacier]

Has anyone here taken or planning to take the GRE subject math exam this year?

[fleet hill]

@buoyant root Okay so maybe I can give a more detailed description here

I don't think I really had a "system" but there was stuff that helped

Pretty much all my engagements were somewhere on my Google Calendar, mostly stuff like classes, club stuff, job stuff

and plans I made with friends

and then there was stuff like random talks going on on campus

I organized them all into different colors

[buoyant root]

ah i might try that

how time consuming is setting up something like google calendar

[fleet hill]

oh it took like no time

you just have to remember to add stuff to it when you plan something

that way I never had to keep anything in memory

Google Tasks is nice because you can make different categories of to-do lists, set reminders to do things by various dates, check stuff off, readjust dates, etc.

And it's integrated into Google Calendar

[buoyant root]

yeah i found that to no longer work as optimally as it did in high school

or even fall semester

[fleet hill]

Yeah no, keep as few things on your mind as possible at all times

[buoyant root]

would just forget 🥀

[fleet hill]

Write stuff down even if you think you'll remember

[buoyant root]

no thoughts, head empty

[fleet hill]

Lol

I mean realistically your brain is not good at multitasking

So I would aim to do like

[buoyant root]

Yeah I can see that working

[fleet hill]

Maybe 1 or 2 things each day

Besides going to classes and stuff

Things will probably take more time than you expect them to, so you have to account for that too

Plus there's the motivational thing of like

[buoyant root]

That's facts as hell

[fleet hill]

If you have a huge to-do list and you finish one item of it, it's really demotivating

[buoyant root]

The dumb python class was like that

[fleet hill]

So IMO it helps to have some metric of success, like hey I want to have this thing done for today and then I can do whatever I want

Oh and set a consistent sleep schedule for the love of god

[buoyant root]

The time the HW took would vary so much on a week to week basis that it lowkey made planning around it hard

[fleet hill]

right

[buoyant root]

and sucked away time from math

[fleet hill]

that's annoying but if you set some buffer time, it'll work out

[buoyant root]

hmm did you self study a bunch during school?

[fleet hill]

yeah a lot

[buoyant root]

like other math

ah i c

[fleet hill]

I didn't really plan that out

but I get a lot of energy from reading math

it's just exciting

(I'm reading math as we talk instead of doing more important things )

[buoyant root]

Ye same, but the problem is I'll fall down random rabbit holes and not really majorly engage with the material sometimes to the detriment of actual pending tasks

[fleet hill]

yeah I think that's kind of natural

[buoyant root]

But I think I can remedy this if I plan my days out better

[fleet hill]

if you sort of nudge yourself to go down the right rabbitholes it'll work out

[buoyant root]

and slowly but surely work through some text

[fleet hill]

you'll probably find that it all comes together somehow in the future anyways

[buoyant root]

🔥

[fleet hill]

so I would say like having free time is really important

[buoyant root]

I'm just kinda worried about next semester with physics 2 on top of my classes

[fleet hill]

yeah

[buoyant root]

Granted you don't go to my uni so you don't have reference for this probably, but people say it's kinda hard

and like not really "hard"

but annoying hard

[fleet hill]

generally I would aim to finish assignments the day they were assigned and then I would never have to worry about anything

in terms of time management

obviously this isn't always practical but it's a good goal

[buoyant root]

Ye I gotta get back to that

In HS I would do it

However, sometimes I am majorly skill issued

[fleet hill]

xD

[buoyant root]

some algebra problem sets that seem trivial now took me so much of the day to do

do you ever have stopping points for such scenarios

[fleet hill]

You mean like, take a break, work on something later?

Yeah I would do that all the time whenever I got pretty stuck on a problem

I'd knock out all the trivial stuff first

[buoyant root]

Yeah, just a signal that you should do something else

[fleet hill]

And then like yeah I'd just leave that problem in the back of my mind

You sorta naturally think about a problem you're interested in at the back of your mind even if you're taking a break from it

And then like I'd go to bed and realize I had the answer lol

[buoyant root]

Fire fire

[fleet hill]

Obviously like

You should also get in the habit of working with other people

[buoyant root]

and then office hours if you're hopelessly stuck?

[fleet hill]

Yeah

[buoyant root]

oh yeah i don't do that

[fleet hill]

But also make friends

[buoyant root]

i think ive mostly just talked on groupmes in dire moments but i think i gotta make study groups

[fleet hill]

Now the downside of doing stuff early is that no one else will probably have looked at the problems yet when you get stuck but that's fine, you can wait until they look at it and ask them to tell you when they do

[buoyant root]

or join them

[fleet hill]

I don't think I had any official like study groups but I would text people

It helps to try to know like at least one person in each class

[buoyant root]

ah i see

ok yeah text might be more realistic

i lowkey like hanging out with my gf a lot and we study together but she's in totally different classes

and i dont want to neglect her to just study with a group of people

[fleet hill]

That's totally healthy haha

Yeah

The ideal situation is that you make friends with other people and your gf also likes those people

[buoyant root]

Damn that's some einstein shit right there

[fleet hill]

May or may not be practical depending on the personalities of the people in your classes but eh

[buoyant root]

There might be some chillers

[fleet hill]

Yeah

[buoyant root]

But anyways, thank you a lot for this talk eric

[fleet hill]

Yeah nw good luck with the next semester I'm sure you'll do awesome :)

[buoyant root]

You're always helpful af

[fleet hill]

Ask me anytime

You're welcome!

[buoyant root]

back to discussy

[fleet hill]

I also have a vested interest in seeing this channel get active lol

[fleet hill]

Man I always hear the math GRE is hell and boring

Its subject areas are weirdly limited so it just comes down to doing like a whole bunch of calculus and linear algebra problems or whatever really fast

Luckily a lot of schools are going GRE optional now

[eager halo]

Downside? I see that as an absolute win. No one can spoil me.

[eager halo]

Duistermaat and Kolk might be able to provide you with some concrete examples (exercises)

I'm not 100% sure but check it out if you so wish.

https://share.google/w5crO8F9q9vaMDtHG

The link looks funny for some reason but it just goes to Cambridge's site.

[lucid glacier]

Boring? Yeah, I'd rather spend my time exploring other topics that I enjoy. I'm trying to score high in order to supplement my app.

I hate taking tests, but it is what it is.

Or at least timed tests like this one.

[fleet hill]

Yeah it sucks

[glacial raven]

Noted. Thank you

[olive geode]

Thanks for the recommendation, I'll check it out I have just ordered Analysis and Algebra on Differentiable Manifolds, which has loads of exercises with solutions, so I think that will help too

[tiny jolt]

Hello I wanna ask question
How do you guys deal with mental exhaustion while solving problems?

I am not even able to solve a lot of questions before I enter a state of not wanting to solve anymore, it feels like a mental barrier

[storm tide]

Take breaks. Go for walks.

[tiny jolt]

How many times
I see people around me studying 4 to 5 hours without taking break

Also I won't have the privilege of going for a walk during exam

I need to get to atleast 3 hours of constant studying
Because that's the duration of exam I 'm preparing for

Also pin me while replying 🙏

[green terrace]

Obviously, but you should take breaks between sessions when studying at home, study is not the exam

[tiny jolt]

I'm in a time constraint, isn't there a way to increase my capacity and a quick way to get rid of exhaustion

[green terrace]

No, you should have began studying earlier, excuse the harshness

[tiny jolt]

Well I know that, I could have done more earlier, but we can't change what's done so isn't there a solution of this problem

[green terrace]

No, you cannot change what has been done in the past, so at-least start now and take this as a lesson to do better in the future

[tiny jolt]

That is why I 'm asking for you guys to help me 🙏😭

[storm tide]

Your capacity will be optimized by taking appropriate breaks.

[tiny jolt]

How long should an ideal session be and how long should an ideal break

[green terrace]

If you take breaks you will be better able to focus during the times you do study

[green terrace]

This depends on you and your limits

[tacit glen]

there is no exact solution

you need to find yours

[tiny jolt]

Give me atleast a target

[green terrace]

Does not exist, depends on your subject, proficiency, how much you need to revise, etc...

For example, last month we pulled a near 14 hour study session with two 1hr breaks in between as we wanted to cover all the material from the term prior to an exam the next morning

(Yes we'd studied the whole term)

[storm tide]

A typical choice is something like 15 minutes every one or two hours, but you may have better results placing your breaks when you feel you're running into something impossible rather than on a predetermined schedule.

[tiny jolt]

Ok

How should I solve a problem
Some people say give it only 5 minutes and then check the solution and remember the approach in it while some other say give a lot more time and try to come up with your own approach and only check the solution when you have tried everything

Also should I write down all the approaches and try to organize my mind

But I think there can be an infinite number of approaches

How exactly do you train your brain for math?

Pin me when you reply 🙏

[storm tide]

There's no magic trick.

[green terrace]

You find what works for you

[fleet hill]

If you're struggling to focus for long periods of time, you can try working your way up to it maybe

Like do 15 minutes then a break then 15 minutes again

And then the next day do like 30 minutes or something

Generally being able to focus for long uninterrupted periods of time (e.g. multiple hours) is a good thing because switching between tasks gives your brain cognitive overhead

I assume that's a choice that each individual European needs to ponder themselves

I will say the political climate does not look good for international students especially with what happened with Harvard...

Funding is cut for all PhDs, not just international

Also visa issues are tenuous

I think there's a pretty good chance nothing happens to you on that front, but if the government decides for whatever reason that they don't like you, it seems like you're just screwed

[rocky terrace]

it depends, if you really enjoy the material then you may study for hours without even realizing it

but sometimes you may struggle to make any progress, in which case it might be wise to take breaks regularly

[fleet hill]

As far as I'm aware but I'm not directly involved in any PhD admissions stuff so I only have secondhand info

I'm sure someone in this server does but I don't know personally any details

Maybe ask in #advanced-lounge too

[lucid glacier]

For what course/exam was this?

[green terrace]

Systems arch

[rocky terrace]

This is true, I've encountered this

[tiny jolt]

I'm doing pre university trigonometry , the problems might be some complex expression which you have to simplify or have to manipulate it in some way to get the value of another expression. Any tips for this?

[tiny jolt]

It's when I'm not able to make any progress I get frustrated and start to get exhausted, generally happens when I start to reach final few questions

[rocky terrace]

yea same

@fleet hill

I think these videos could be pinned as well

https://www.youtube.com/watch?v=zHU1xH6Ogs4&pp=ygUVbWF0aGVtYXRpY2FsIG1hdHVyaXR5

https://www.youtube.com/watch?v=4HFyWC-YtIk&pp=ygUVbWF0aGVtYXRpY2FsIG1hdHVyaXR50gcJCd4JAYcqIYzv

they were very good

[fleet hill]

okay

[tiny jolt]

I'm trying to solve this problem
Haven't checked the solution yet

Can you give me a hint

[worldly rune]

wrong channel, you want to read #❓how-to-get-help

[tiny jolt]

How do I reopen?

[vernal sky]

you can open another channel and ask again

[eager halo]

!noWorddocument

[neat terrace]

hey guys i am a freshman at college who din't take math course any idea how i can learn it along with my college

[vapid kiln]

k h a n academy if that helps

[main trail]

chat, need help deciding what to do next in RA:

1. Equivalent characterisations of completeness
   2)General problems in RA

[rocky terrace]

Why not both?

by both I mean

1. then 2.

[main trail]

I do plan on doing that eventually

[rocky terrace]

In fact you can turn 1. into 2. by proving that different characterizations are equivalent yourself

[main trail]

Lemme find a list of them stated clearly

thanks

[rocky terrace]

The two main ones are Axiom of completeness (every bounded above set has a supermum) and cauchy completeness

There are also a few more iirc, like nested interval property?

[main trail]

There are around 7 I think

[rocky terrace]

Abbott talks about this at the end of section 2.6

you can check that out, that's nice

[main trail]

Thanks

[mental tinsel]

any suggestions on planning out the study sessions?

I often find that I can do the first 2 hours rather well but after that I tend to fizzle out.

Setting up timers have helped to some extent

but I would love to know how you folks go about it

I am on a gap year with no constant course pressure or the likes, so it has been kinda hard to stay consistent haha

[royal ice]

is this the right place to ask if you can trim a b-spline?

[inland talon]

hey everyone I am looking for a study buddy who wants to study IA Maron's Problems in Calculus of one variable. If anyone's interested, DM me. We will discuss some really fun problems from the book.

[fleet hill]

No, you probably want to ask in the help channels or in one of the math topic channels

#❓how-to-get-help

[fleet hill]

Do you mean like planning out a schedule for what topics when or like planning out one study session

[mental tinsel]

the latter

[fleet hill]

Oh okay I think for me it helps to have some specific goal I want to achieve for that day

Like I want to learn about X and do a couple problems related to it

That way I have some sort of forward vision which gives motivation

[mental tinsel]

sorry I was afk

That sounds reasonable. I will try that.

[lavish breach]

Is it possible to jump from only knowing Algebra 1, Geometry, and Calculus 1 to learning complex analysis?

I’m really interesting in many of the topics I’ve heard are in the course and I don’t wanna learn linear algebra and real analysis or calculus 2 or whatever as of rn.

Understood Calc only knowing Algebra 1 and Geometry, just learning prerequisites as I went but idk if complex analysis is gonna be too hard for that

[agile fable]

The first question about two numbers having the same value is not advanced enough for that channel

And then when we just talked about how it's not a good idea to talk about being < 13 and on instinct, in a serious channel, you were like "Ah I'm 3"

That just seems unserious

The question you asked did not seem at all like "advanced algebra"

What's the syllabus for the class?

Alright, I'll take off the -- but I'm gonna expect that you maintain seriousness going forward in the serious channels

Or else you'll lose access and that includes to the channels you need

I'm not gonna give specified access

It's your responsibility to control yourself

[viral osprey]

I do not know what alg 1 means to you. "Knowing" complex analysis is a pretty broad target. Complex is one of those topics that has actual applications to fields outside of just math. What this means is that there are books (Brown and Churchill for example) that would be accessible to a typical engineering/physics student. Ime these kinds of courses usually expect a bit more than just calc 1, typically multivar, but not a ton of extra knowledge.

But you could also go a lot further with things and study out of a more in depth book like Ahlfors, Saeed/Zakeri, Bak/Newman or Conway.

Those kinds of books would expect you to be pretty comfortable with more topics like basic real analysis.

[radiant turret]

I’m trying to learn to memorize verbatim text…and why is it so difficult?

I know about mnemonic, spaced repetition, and active recall but forming mnemonics quickly and or recalling the text fast enough is super hard for some reason

My conscious thought seems too slow…

and trying to do so instinctively doesn’t recall verbatim text but whatever images/feeling it causes

There has to be a way…

[rocky terrace]

For what purpose are you trying to memorize text verbatim?

For some memory competition?

I hope it's not for learning math/physics...or even chemistry/biology...or anything for that matter

Damn beef between mq and mods?

[raw tinsel]

give it to yourself

[agile fable]

I took off the -- role but you need to give yourself the necessary academic role. Read the server instructions

[kind kernel]

does anyone know how to study combinatorics? i understand the basic theory behind it but when i try to apply it i never know what i should use

im talking 1st college year combinatorics, like counting possible maps, partitions, subsets...

[fleet hill]

Honestly combinatorics is one of those things that does feel like a big bag of tricks sometimes. I'd keep in mind the following core principles: counting the same thing in two different ways, addressing double-counting

[desert meteor]

i struggle with weak central coherence and i wanted to ask if theres even any point in trying to learn math because everytime i want to learn something new in math i have to know every detail about the calculation first and things like why how what (things that might not even be related to it) and i just lose the whole overview of everything so does anyone have advice

[fleet hill]

For example you can count the number of subsets of a set in two different ways to prove the identity 2^n = sum nCk (for the left-hand side, each element of the set is either in the set or not in the set; for the right-hand side, the number of subsets of size k is nCk, then sum over every possible value of k). If you keep those two principles in mind while you learn details, it might help you organize things in your mind.

[fleet hill]

1. Yes there's definitely a point to learning math.
2. Would you say the problem is that you struggle learning math or that you struggle to learn it according to your school's timeframe?

[desert meteor]

Well both but i haven't had math at school for like 2 years now because i had to drop it because i felt that if i kept the subject i wouldnt be able to finish school and now i just feel so stupid because im still so bad at math and everyone seems to understand it so much better and faster so its a combination of both probably

And i dont know where the dip came from because i had always been pretty good at calculating things when i was younger like multiplication subtraction n stuff was never a problem for me but then we went over to math and i just couldnt keep track

[fleet hill]

math is an endurance game, don't be discouraged by people around you learning faster because thinking deeply is going to be more important in the long run

also everything in math takes multiple exposures, sometimes things just won't click until the 100th time you see them, does your school have office hours or something similar where you can talk to a professor/ta and get more detailed help?

there are people that were scared of math all their life, failed calculus two times, etc., and then go back to uni later in life and end up passing, so you're definitely not alone in this

having someone to support you through it definitely helps

[kind kernel]

thanks!

[plain gale]

,iamnotstudying

[mossy shadow]

Removed the studying! role from you.

[glacial raven]

How frequently does combinatorics pop up in higher levels of math?

[rocky terrace]

Which field of math?

it pops up a lot in combinatorical commutative algebra, but it doesn't pop up very much in functional analysis

[glacial raven]

I guess TCS, statistics, probability, graph theory which it obviously seems to pop up from time to time

What about lin algebra?

[viral osprey]

There are intersections between lin alg and combo for sure.

A sorta nifty one is using dot diagrams for the jcf (fis does this)

Some more obvious ones are assigning matrices to graphs

Things like adjacency matrices and so on

And then trying to use those matrices to find new details about your graphs.

I guess some basis/dimension counting trickery is sometimes also basic combo.

[rocky terrace]

I always thought that was more of "Applying linear algebra in combinatorics"

but I guess the question could be interpreted as "what are all the places where combinatorics intersects with other fields of math"

[viral osprey]

I don't think it's a super clean cut distinction.

Combo itself is kind of squishy even.

[rocky terrace]

True

[viral osprey]

I can assure you people do sometimes count stuff in lin alg.

[raw tinsel]

did someone mention rep theory

[desert meteor]

im almost done with school so i wouldnt rlly be able to ask for help since i dont even need help with school anymore its just something personal i wanted to learn

[torn olive]

I ask questions all the time in this server I'm learning that isn't for school!

self study is one of the most important parts of mathematics IMO (and in general being able to learn something on your own is a useful skill)

[torn olive]

There's an area of mathematics that I'm interested in called Schubert Calculus. One of the predominant geometric objects is this object called the Grassmannian of $k$-planes in $\mathbb{C}^n$, $G(k, n)$, which is the set of all $k$-dimensional linear subspaces of $\mathbb{C}^n$. This is a useful tool for answering questions in algebraic geometry about counting intersections of surfaces and curves (at a high level). But that's literally just a collection of linear subspaces and alot of results on Grassmannian are proved using linear algebra. But these objects are combinatorially very interesting as well. There's a way to assign polynomials to certain subspaces of the Grassmannian, so we get some algebraic tools, but then these polynomials can also be described and labeled via combinatorial objects. Then you can describe some of these geometric interactions between subspaces of the Grassmannian (which is hard to do) via algebraic and combinatorial arguments (which IMO is easier to do).

[mossy shadow]

Spamakin🎷

[torn olive]

The go to book for this IMO would be Fulton's Young Tableaux

It's split into 3 parts, Calculus of Tableaux, Representation Theory, and Geometry

the first part is quite approachable with little background

the second and third parts definitely need some more algebra and geometry background to get all the information out of them

but the second and third parts will apply the combinatorics of the first part to many things with a linear algebraic flavor

[glacial raven]

Thanks everyone for the responses.

And I'll try to check those books out as well (fis and Fulton's)

[desert meteor]

Idk if anyone would have the patience for it tho most people find the questions i ask
stupid 😅

[torn olive]

I ask tons of stupid questions

Don't be afraid to ask questions

[desert meteor]

Ok because when i want to solve a math question i want to fully understand it and why everything is the way it is i cant just memorize how solving something goes

[fleet hill]

That's very natural

Most mathematicians are like that

[desert meteor]

Oh cause most people in my class didnt rlly have that they just learnt it with no problem

[fleet hill]

I think that sort of thing is encouraged by how math is taught in grade school but it's not inherently how math is

[dim dirge]

this channel has existed for more than 17 days and I discovered it only now

[glacial raven]

Ggs on discovering

[rocky terrace]

You were too focused on Typst

[ivory plover]

I’d actually argue it’s the most important

[fleet hill]

I'm glad we made it!

[hushed latch]

anyone's listening to justin sung? I'm not paying for his course but his studying tips seem on point

[cyan dawn]

how do I study for maths?

[worldly rune]

doing exercises

[signal imp]

hello :)

,iamstudying

[mossy shadow]

Gave you the studying! selfrole.

[signal imp]

read book -> understand topic -> do problems -> fail -> review solution and understand where you went wrong

[cyan dawn]

what about in lecture

during lecture or in class

what should you be doing

?

[signal imp]

Honestly, just listen and take notes

thats it

For me, I don't take notes because I self study haha

(please dont be like me)

[olive geode]

I don't take notes during lectures either. For me this is the best strategy, since I can't focus on listening/understanding if I take notes, and I can usually find what I need written down in textbooks or online notes later anyways. I think asking good questions during a lecture can be a good idea

[swift tartan]

Yeah and it also depends per learning style

I take paper notes pretty much blindly. But sometimes if I do have a question, I write down my thoughts and put a box around it to ask the professor during or after class. When im transcribing my notes onto latex, but also like trying to go through the proofs again I usually would also get more questions that way and also jot them down. Office hours is the way to go for all of this

Im that person that tries to make it to every office hour every semester

Because professors who cant teach the best exists (distinguishing between teaching as a tenured prof and lecturer vs their research(optional)), i usually read through the text or find supplementary material of my own

this approach is pretty arduous and extensive tho, i def agree with most ppl who think that, but i still have a social life lol

[swift tartan]

also definitely this, ive seen a lot more success when i actually try putting effort in a class and keep doing the exercises and practice exercises vs not at all (im definitely not consistent enough tho but trying to be)

exercises usually lets you find gaps in your understanding which is why people in math always say to practice or do exercises

you may think you got it, only to find a problem dealing with the limit of the sequence of partial sums, averaged, and converging and i thought i knew how to do epsilon-delta pretty well (ug real analysis)

that was a personal catastrophe on that test

[swift tartan]

i still think this was a dubious question, but i recognize it was still fair game

[whole wing]

You mean Cesaro?

[swift tartan]

? i havent taken grad analysis, i dont know who that is tbh

https://en.wikipedia.org/wiki/Cesàro_summation ?

[whole wing]

https://en.wikipedia.org/wiki/Cesàro_summation

[whole wing]

Yep

[swift tartan]

Yeah, i didnt know this had a name lol

literally this was the question, but i think there was also a sqrt involved for the sum itself

$\lim\limits_{n\to\infty} \dfrac{\sqrt{\sum\limits_{k=1}^n s_k}}{n}$

[mossy shadow]

Zyphen

[swift tartan]

iirc that was the question, this was last fall tho

haunted my dreams

[whole wing]

Wouldn't that go to zero? For s_n convervent

Since it's 1/sqrt n * sqrt(avge)

And sqrt avge -> sqrt lim s_n

[swift tartan]

You were right there wasnt a sqrt

I just pulled up the profs solutions for that test

[swift tartan]

So it was a true Cesáro

[whole wing]

But yeah personally my prof showed this in class and emphasised it waw important to understand the proof to master epsilon-delta ideas

And then one exercise on the hw used a similar idea

[swift tartan]

yeah even his proof was a whole 2 pages, given that there were like 2 parts and he spaced it out decently for clarity but thats a lot compared to the soltn's for the other problems

[whole wing]

Let $y_n = 2 x_{n + 1} + x_n$
Show that $(x_n)$ converges iff $(y_n)$ does,

[mossy shadow]

afqt

[swift tartan]

the second part of that question was i think comparison for lower and upper bounding the cesaro itself

[whole wing]

With the hint: for the more difficult implication, reduce the pbm to the case of cvgce to zero and express x_n in terms of the y_k

[whole wing]

That's kind of weird, since the proof should be reasonably short

Like less than a page

[swift tartan]

I can screenshot this to you if youd like in dms?

maybe you can make more sense of this than i can lol

i dont have the original test saved sadly

[whole wing]

Sure, if you want

[digital yarrow]

What teacher Spanish/English do yall reccomend me if i wanna study like a hobby

on youtube

[fleet hill]

Wdym? Like you want to learn Spanish?

[digital yarrow]

i speak spanish and english so im trying to find a good maths teacher

[fleet hill]

Oh

What level of math?

KhanAcademy is good

[swift tartan]

tbh, duolingo sucks for almost every single language except spanish

it was initially made for spanish

but given the "ai first" initiative thats up to you

[digital yarrow]

Erm @swift tartan

[swift tartan]

also really only relevant if you are a english speaker

Im lost?

oh

im blind

[swift tartan]

i second then @digital yarrow

[digital yarrow]

Pre uni

[swift tartan]

then yeah KhanAcademy would be good

[digital yarrow]

Im js trying to learn more because on school the teacher js yap about his wife 💔

[digital yarrow]

Ty

An ty too to ignorEric

[fleet hill]

Np

[green terrace]

we do, we've had little issue with it

[wispy zephyr]

it takes some amount of practice to be able to write without looking at your hand. just kind of have to stick with it

definitely make sure you're writing on a table in the same position as you would be writing on paper

[rocky terrace]

I write like a kindergartener even on paper

[crimson elm]

My prof tells me I should've become a doctor instead of a mathematician just cuz of how bad is my handwriting

Then I tell him I was premed before so you're not totally wrong

but yikes i didn't like premed

[crimson elm]

i was bio major

calculated my chances and likelyhood i'll like the journey and said no

[rocky terrace]

different kind of surgery theory

[crimson elm]

dont think it was crazy

i was already attending math seminars as a bio major

just wanted to see around before i made my final decision

[wispy zephyr]

you aren't allowed to automatically, there are hoops to jump through

but also the first year or so tends to mostly be bottle neck intro classes that would be covered by a levels in the uk

[compact river]

Hi

[brazen mist]

やあ

[hasty rune]

Hi everyone

Can you give me some tips to study the geometry in the space

Because for the shapes my mind can't analyze and see the 3D vesion

[reef ocean]

you could learn how to use GeoGebra 3D https://www.geogebra.org/3d or search online for resources people have made with it

in my experience plotting two-variable functions or regions of space defined by some equation is easy

to work with 3D vectors you need to learn GeoGebra's notation which is a bit weird, but once you've done that it's easy too

[solid cobalt]

Ello?

[green terrace]

hey

[solid cobalt]

Ohmaga I just turned on iam studying and got silenced

From using the discussions

Lol this is ingenious

[green terrace]

yes

when you're done just run ,iamnot studying

[brazen mist]

reduce your discord usage

[glacial raven]

Hello

[torn olive]

I really gotta do this

[ancient dagger]

,imnot Studying

,imnot Studying!

,imnot studying!

[short dirge]

fyi i believe it is ,iamnot studying
and a better place to do this is probably #bots

[quick tundra]

I am 8th grade.
(Dont worry I am 14 and havent broken any rules in this server)
I feel i am lacking.. Just in case, where do i study or get my resources?
Khan Academy?

I was looking at Algebra 1 should i do that first? then what do i do after?

[twin wraith]

start with algebra then trigonometry then complex no.s then geometry(straight lines, curves, parabola, circle, equations of curves, slope, etc) then calculus

[quick tundra]

algebra 1 right?

[twin wraith]

what does that include??

[quick tundra]

wait

i wills how you

[twin wraith]

okae

[quick tundra]

so like

what ones in order?

[twin wraith]

i really dont have such systems in my country but what i know algebra and trig set up the the base for complex no.s then start geometry beacuse this requires the three of them together and slowly through geometry when you reach slopes and stuff u will start getting into the part of calculus

@quick tundra can you send me the link which your refering to

[candid berry]

@quick tundra Perhaps you should also ask your teacher.

[nimble basin]

is there any small study group formed that hold a call often and cover topics in "advanced" mathematics
"advanced" categorized in accordance with server

[quick tundra]

The link of what?

[cyan dawn]

,iamstudying

[mossy shadow]

Gave you the studying! selfrole.

[twin wraith]

yess

[twin wraith]

the link of this @quick tundra

[fleet hill]

khanacademy is really great yeah, I think they specifically have an 8th grade section?

it's tailored to US curriculums though so it might not exactly fit if you're outside the US but it's still very well made content

[strange heron]

is anyone aware of similar channels in which i can ask people questions/code of competitive programming?

[torn olive]

there are probably other servers better than this one for competitive programming

I'm sure they exist but idk any off the top of my head

[grizzled hedge]

check out computer science server maybe

or a discord server of a youtuber

there was one i don't remember

[torn olive]

Yea I'm aware of programming discords (look up The Coding Den) but idk if they allow competitive programming questions or not

In any case they'd probably know of servers there

[solid venture]

Errichto server

[quaint viper]

doesn't even seem to be a real article

[strange heron]

could u pls share the link of the same

[strange heron]

could u pls share the link of the same

[torn olive]

If you Google "The Coding Den discord" you will find the link, like I said

[solid venture]

https://discord.gg/BpSdMJjW

[junior dagger]

dis feels like promo for visionask

[safe harbor]

It's their only post

Probably is an ad

[reef ocean]

yeah not even a real news article

sent an icbm to their location

yeah sometimes people may use LLMs to help them with homework much like you'd normally use math stackexchange or something pre-AI

as someone who hands out HW I don't really worry about whether my students hand over AI generated stuff, mostly because I've never noticed something like this and I suppose it would look kind of obvious given current models' tendency to fail at subtle stuff or to use fairly repetitive sentence structures

[main trail]

Advice on how to study RA

like I spend hours but at times I don't make any prgress

[fleet hill]

what do you do during the hours?

[solid cobalt]

How much time is the ideal time to study per day? (In yall's opinion)

[main trail]

Just thinking

[main trail]

Depends on the grade

[keen bridge]

hi I'm just gonna come out with my first post on this server and say I want to study basically everything I need to go from the undergrad math education I currently have (and probably need to brush up heavily on) from my CS bachelors so I can do theoretical physics

actually given that my undergrad GPA was awful I genuinely think the best track for me is to self-study basically everything a phd program would teach me anyway, publish a couple papers, and then give that as my application

I don't know how this is gonna come across, I'm quite confident I can do this though.

is there a roadmap I can find for this? I have a general idea what's needed but I want to check if I'm missing anything

I suppose I could just check a physics program courseload

[dim dirge]

[dire eagle]

the importance of learning vs learning retention

[whole wing]

I'm not sure the study method depicted is the most efficient

[dim dirge]

redbull cans are accurate at least

[storm jasper]

This is actually sort of my situation but I’m learning undergrad for fun

[storm jasper]

Yo

[main trail]

hi

[storm jasper]

I’m studying real analysis as well

I can offer you some recs

[main trail]

please do

[storm jasper]

Where are you now?

[main trail]

Seqeunces that tend to infty

I'm also quite bad at proof writing in RA

for instance

textbf{$a_n,b_n \to \infty \implies a_n \cdot b_n \to \infty:$} As $a_n ,b_n\to \infty \forall K_1 \exists M_1 \in N : a_n>K_1, \forall J_2 \exists M_2 \in \N: a_n>K_2$. Let $M= max{M_1,M_2}$, for a given $K_1=K_2=K$. We then have $a_nb_n>K^2>K$.

[mossy shadow]

wai

[fleet hill]

thinking about what?

[main trail]

the problem?

[whole wing]

You can't make progress by just "thinking about the problem"

You have to try things

Like with a pen and a piece of paper

Make a drawing. Try one approach/idea. Try limit/small cases. Play around with the objects...

[fleet hill]

what does your process of thinking look like?

[main trail]

Just sitting , maybe writing some ideas

[fleet hill]

I mean, depending on the problem, spending hours on an analysis problem is perfectly normal

If you're doing something for all those hours, like trying ideas out, then none of the time is wasted

[flint bobcat]

@glacial raven let's talk here to not bother anyone

[flint bobcat]

so, what are the things you need to know for your final exams

i could try to help you with that as we're the same age so we must have pretty simmilar things to do

[glacial raven]

Basically I have to get good marks in this exam (final exam of high school) to get a good university. I know what should i do to get good marks i am not able to do so.

[flint bobcat]

yeah but what are the maths concepts you need for your exam??

like if you look at the exams from the years before

what are in them

because it's important to know where to start off

[glacial raven]

No you are getting what i am trying to say I KNOW THOSE THINGS..

[flint bobcat]

oooh okay

so what's the problem

[glacial raven]

I know that but the problem is i am not able to study man

[flint bobcat]

hmmm

so you want some advices

to know how to start studying or how to study in general??

[glacial raven]

Yeah maybe

[flint bobcat]

like the problem is about re-starting studying or it's about how you dont remember what you studied after spending time on it??

[glacial raven]

The problem is these days when i study. Like i will study for sometime but after then i am not able to.

And also i am not able to remember also everything

[flint bobcat]

it's like you cant find the motivation to study???

[glacial raven]

I hate this word but kind of that

[flint bobcat]

hmmm

well idk i dont really get your problem

i saw something

if the problem is really to start getting into studying

[glacial raven]

Then?

[flint bobcat]

when you want to do something that isnt productive

idk what

you can like if it was code, tell yourself that to do this action

for example, playing

you need to

study