study-discussion

[glacial raven]

Yeah i get you

[flint bobcat]

i saw a video on various ways to stop doing nothing

https://youtu.be/2IV3bZUk8p8?si=N7ym8xA_H7a8zAOi

this

it's about procrastination

but tbh it works for just getting into work you know

[glacial raven]

By the way how old are you?

[flint bobcat]

i feel like it should work for it too

[flint bobcat]

same as you but born in january

[glacial raven]

Oh nice.

[glacial raven]

Let me see this video first.

@flint bobcat good night man.!

[flint bobcat]

good night to u too mate

[coral sleet]

[heavy rock]

#chill

[reef ocean]

memes go in #chill

[unkempt quarry]

You should differentiate yourself, NOW

[solar cipher]

yes

[unkempt quarry]

Wow. So true. I await your ban 🙏

[solar cipher]

why?

Why should I get banned?

Im just stating that harvey shrek is beatiful in its own way

[crimson elm]

what did I come to

[solar cipher]

Is free speech banned?

[crimson elm]

it's just disturbing

[solar cipher]

I read your rules

*the rules

[crimson elm]

You apparently didn't read that this channel is called #study-discussion

[solar cipher]

"discussion"

[crimson elm]

[heavy rock]

<@&268886789983436800>

[heavy rock]

imagine thinking this server is the american govt.

please submit your taxes to me

[wanton cradle]

@solar cipher go shitpost in #chill

actually no u were already warned a few hrs ago. take a day off

[urban copper]

like 6 hours? But diff textbooks tho

[dim dirge]

but what if I live and work in Europe?

-# America: "nah, I need ur taxes anyway"

[rocky terrace]

This is true, famously Europe does not have freedom of speech

[proven lynx]

hello, if i want to learn how to do tasks like these, where should i learn from? Or what exactly to look for because i didn't find anything similar anywhere so far

The task is to simplify them, yet whenever i do that i end up making them even more complicated 🥲

[reef ocean]

There's some useful things in Paul's notes https://tutorial.math.lamar.edu/Classes/Alg/Radicals.aspx particularly the last few examples and the practice/assignment problems, though these are a bit too basic and what you really want to learn is how to multiply and divide fractions with radical expressions. (A quick search for "fractions with radical expressions" doesn't seem to immediately return problems like these though)

The key here is to recall the properties of the square root and common algebraic identities like (a+b)(a-b)=a²-b² to simplify, or rationalize the denominator and numerator as you evaluate the expression, so you could also look into online resources that teach rationalization of fractions involving radicals

[cyan dawn]

How do we ace our maths test

[torn olive]

gotta do practice problems

from the homework, the textbook, any exercises given in lecture, etc etc

and you have to actually understand all the definitions and results, be able to give examples and counterexamples where necessary

even if you won't be asked "give an example of this result," thinking of such examples helps build intuition and understanding

and then of course if you can't do homework and textbook problems while you have time and leisure at home, you won't be able to do them under a time pressure

any more specific advice would need more information from you as to what you specifically struggle with

[fervent summit]

Knowing your teacher helps too. At least, my college math professors either hinted or fairly blunt what type of problems were on the tests themselves. So you can usually practice those to guarentee a passing grade

[storm tide]

I wouldn't count on it.

[unkempt quarry]

I remember after my honors analysis class in UG I found an old AMC 10 and self administered it to just see how I’d have done. I think I just barely did well enough to have qualified for AIME that year.

I was not “an average pure math student say who just graduated”, I was still in my degree, but I did have zero Olympiad experience

[rocky terrace]

Chmonkey, the above average pure math student

[unkempt quarry]

Neamesis, the eternal cat gamer pfp

[glacial raven]

Hello peeps, i am preparing for jee advanced, and i need help with maths, its taking a toll on me, right now I dont have any specific questions, but if you could guide me how to study maths, i would be grateful for your help, i can say its difficulty is around Bsc level

[main trail]

As someone who has written JEE adv and is perusing a BSc degree, I can say that last bit is false

[fathom wyvern]

the right word would be "competition math", which is different from the math you may encounter in a degree. you cant really compare their "difficulties" (whatever that means)

[glacial raven]

Idk, when my coaching teachers explained the difficulty they said its bsc level

[glacial raven]

Oh, i dont know if i could define that way

[glacial raven]

How do i prepare for maths? Please any advice

[main trail]

Focus on concepts

practice a lot

[glacial raven]

Will coaching modules suffice?

Because whenever i encounter a new problem, i cannot solve it, i am unable to build concept and problem solving skills

[main trail]

Mostly should, if they are good

[glacial raven]

I am studying in allen

[main trail]

In 11th I pressume

[glacial raven]

I am in 12th, i keep shifting between Bitsat and jee advanced

[main trail]

One thing you should know is BITSAT is a speed game

JEE adv isn't

[glacial raven]

I have been practicing a lot for that

[glacial raven]

I feel i can crack jee but i am not utilising my potential

[main trail]

So practice, not under time pressure at first

later under time pressure

I have to prove something, will just prove that, and be back

[main lodge]

Ugh i need to get better at finishing exams fast

[young cobalt]

BSc is a bit complicated than jee maths imo

[young cobalt]

Ayo what?

[glacial raven]

no idea

[young cobalt]

I gave this years advance

Which is why I can say BSc level math is a bit complicated

[scarlet arrow]

it's not

that's kinda obvious no

less questions= more time to each

[main trail]

Yea

[errant hamlet]

Is bsc maths difficult than jee adv math ?

It should be

[young cobalt]

That is very much a misconception here
Normally less questions = more time yes, but jee advanced questions are never meant to be solved in a specific time
Chemistry is acceptable (30-45 minutes) but if the paper is very lengthy like 2022, your doomed.
Physics is again moderate (1 hour)
Maths is where most ppl fuck up tbh. It is very tough, and almost all questions need atleast 4 minutes (certain exceptions are there)
Time management is very essential for this, since losing time in one subject means you have to compromise in another

[main trail]

Not as much

you atleast get time to think a bit

[young cobalt]

Which is of no point unless you getthe exact idea

Many questions are very specific in the concepts they use, even if its taken from multiple topics

[main trail]

I know

[vernal sky]

<@&268886789983436800>

[stable valve]

I apologize for bothering the chat again but could anyone who completed a bachelors in pure math at an american university weigh in on how this curriculum, specifically following the 0.2 Field of study, compares to the average pure math degree from an american univerisity https://en.math.uoa.gr/fileadmin/depts/math.uoa.gr/uploads/Archeia_Proptychiakoy_Programmatos/Course_List_2019-20.pdf

[olive geode]

Don't post the same message to every channel

[stable valve]

Yes lord discord mod Sir!

[green terrace]

that person is not a mod

and considering that you apparently did post the same msg to every channel

<@&268886789983436800>

[stable valve]

😹

I posted it to 2 channels are was recommended here instead

[small salmon]

Please be understanding of those who are new to the server.

[small salmon]

or at least, new-ish

and don't post a lot

[subtle crown]

Ppl getting so pissed for what

[stable valve]

Makes them feel powerful for half a second on discord

[small salmon]

let's not snipe back and forth either.

[stable valve]

👍🏿

😹 😹 😹

[olive geode]

I respectfully asked you to not post the same question to 5 different channels - it's against the rules, and it's annoying as heck. If you're new here the least you could do is look into the rules and not get all defensive when people try to remind you of them

[stable valve]

😹 👍🏿

👑

[small salmon]

@stable valve the rules are the rules for a reason. And other users are trying to help you. Please be respectful. While it's not a big deal that you posted a question in multiple locations if you didn't know any better. I would ask that you keep your questions to a single channel in the future.

[stable valve]

👍🏿

[small salmon]

Blowing them off with laughing emojis isn't a good way to win friends and influence people who you are asking for help

[stable valve]

I understood the first time

[stable valve]

I don’t know what else you want me to say

I explain that I posted it in 2 channels and was redirected here

Do I beg to their ancestors for to graciously accept my apology

[small salmon]

yes, I understand that. Just no reason to engage with people prodding.

@olive geode please don't prod.

[stable valve]

I’m not engaging

If they choose to get mad over 😹 👍🏿

Their problem

I won’t do it again

Don’t know why it’s been half an hour and anyone is still on this

[olive geode]

Yeah sorry, I just got a bit pissed by the response, but I'm over it now 👍

[small salmon]

@stable valve to answer your direct question though, I'll have to pose another question, do the numbers in the document correspond to course numbers that are similar in form to US course numbers, where the first digit corresponds to the year that the material will be taken?

So 400 level courses are for seniors?

300 are for juniors, etc?

[stable valve]

It’s semester based

It goes in order of Greek alphabet

Alpha/Beta are first year

[small salmon]

So 800 for 2nd semester seniors, 700 for 1st semester, etc?

[stable valve]

Ect

Oh

I thought it was the physics one

It seems so but I can probably place out by the time I go

I don’t know how much they are willing to place me out

I will have calc 1/2/3 along with ODE PDE Lin Alg Point Set Topology and diff geo

Possibly an algebra class

[stable valve]

I’m just asking if overall the content covered is more or less the same

[stable valve]

• anal 1/2

[small salmon]

So if what I said above is true, this is somewhat more advanced than a standard pure mathematics course curriculum in the united states at a "normal" (not pure math focused) college. I selected my alma mater for the comparison, which is Georgia Tech, an engineering college.

It's not a super highly ranked college in mathematics.

[stable valve]

That’s what I thought

[small salmon]

https://catalog.gatech.edu/programs/mathematics-pure-bs/

[stable valve]

My other options are stony brook or city college

It does appear to me to be more advanced

[small salmon]

anyway, I need to get back to work. 👋

[stable valve]

Thank you

[glad zenith]

SPIKE!

[compact river]

How would you prepare yourself for an exam at the level of JEE, if you were starting from scratch?

I'm actually prepping for MEXT but if I prepare for something harder then I'll undoubtedly pass

I think

[scarlet arrow]

Talking strictly about mains:
Well the portion for jee is large, so you'll need to set a structured course, especially if you have no one to teach you in that order. For Chemistry there's a book called NCERT in ind, that's what most Jee mains questions are from, see if you can get that wherever you are. For math you're just gonna need to develop speed, I don't really think it matters where you study it from, and prioritise getting faster each time you solve a specific thing. Physics hm, there's two books by HC Varma, or you can get DC Pandey (i prefer HC Verma cause it's more in-depth). Also, find some way to get pyqs, and solve them after you're done with each chapter- either a pdf from somewhere or a site like room.examgoal.com(tbf, this is paid, and idk if its available outside ind, but its extremely cheap). You should solve topicwise/chapterwise part tests about once or twice a month of everything you've done until then. I'd say for actually starting to grind full pyq papers you should start about 3-4 months before whatever exam you're giving. And always try to first understand the concept and solve the problems without a time limit, and then move on to solving questions by timing yourself. There's a lot of other stuff you could think about, but ig this is sufficient.

Of course, all this is kinda like the dream, most important of all is that you need consistency, even if your studying hours per day drop, you shouldn't stop and do a little bit everyday cause once you stop you'll just get into a rut.

[compact river]

Compared to JEE those questions aren't hard tho

[compact river]

[scarlet arrow]

What are these

[compact river]

Question from the mext scholarship exam

U have to fill in the blanks the answer

[scarlet arrow]

Ic

Btw set a clear goal either prepare solely for mext or do jee and study those topics which are in mext but not in jee

Don't keep switching targets

[compact river]

Maybe JEE doesn't demand calculus knowledge?

Or it does?

[scarlet arrow]

It does

Jee has calc 1+2 both

[compact river]

Same stuff, different levels ig then

[compact river]

Calc 2?💀

[scarlet arrow]

Idk what mext is so cant comment on that

[compact river]

Do kiddos there finish high school at 30 yo?

[scarlet arrow]

Yeah we complete i think half calc 2

[compact river]

Calc 2 for undergrad applications or for grad only? 💀

[scarlet arrow]

What

For highschool

[compact river]

WHAT

u guys are crazy

[scarlet arrow]

Calc 2 is not actually full nm

I think like

Half

Dont sweat it tho its easy if taught by the right people

[hoary kindle]

I swear this is common in most places, isn’t calc 2 just like integration and extremely ODEs

[scarlet arrow]

Yh

I think

[compact river]

Most of what I've seen is derivatives and integration

[raven kindle]

yeah that's basically all there is to calc2

[scarlet arrow]

Is it

What abt the polar coordinates stuff and taylor series

Isnt that calc 2 as well

Wherever i go to look it up people give different answers

[wispy zephyr]

i can't speak from personal experience bc my school was on the quarter system but i think the topics covered in https://tutorial.math.lamar.edu/ are typical

[scarlet arrow]

O nice

[raven kindle]

Yes

That isn't much material though

[tacit sapphire]

Is it possible to study the exam I am curious

[glacial raven]

[glacial raven]

heyyyyyyy

mann i am pleading , like can anyone have me to understand integrals and derivatives with just the bases of them and also how to make use of them. We are required to use that presently in physics but knowing how vast a topic it is i often times need confrontation on doubts i have like , "yeah you'd study up that later "or ," theres a reasoning behind it too" , and "thats wut it does"

[rocky terrace]

Have you checked out this https://www.khanacademy.org/math/calculus-1

and this https://www.youtube.com/playlist?list=PLZHQObOWTQDMsr9K-rj53DwVRMYO3t5Yr

[main trail]

what do I do when I lose motivation

like RA is becoming so hard for me I'm starting to regret chosing maths

[glacial raven]

Discipline. Pushing through with or without motivation; whether you like it or not.

Of course I am not saying that you have to keep pushing through math even if you have other viable options such as changing streams that could be more beneficial to you in the long run. That's up to you to properly reflect upon and decide.

[sage seal]

So uhm, where do y'all get your problems to solve? I have to study a lot of mathematics to get into uni and need practice. I currently use chatgpt, is that fine?

[glacial raven]

no

[sage seal]

Ok so where do I find them?

[rocky terrace]

Why has it become more difficult perhaps addressing the core issue directly might help you get better at real analysis and eventually become an analysis god

[rocky terrace]

But yes ^ don't rely on motivation, develop discipline

[mental tinsel]

Analysis God

[wispy zephyr]

textbooks

[hoary kindle]

This is a pretty common problem, it’s well acknowledged in research and you simply just have to push through. Real analysis is typically the first major hurdle people encounter and learning to deal with that is an important skill to learn

You’ll also find the rest of maths “easier” because you will be more comfortable with 1) what proof based mathematics looks like 2) being stuck and lost and powering through anyway

[rocky terrace]

In my personal experience, no particular field of math has been a hurdle, everything I've learned/am learning, real analysis, group theory, linear algebra have been equally challenging and fun

The major and only hurdle I ever encounter is myself

[sage seal]

thank you

[hoary kindle]

I mean you’re an adult so

[agile fable]

Uh

I'd rather we don't even joke about that kinda thing please

[muted wigeon]

seems legit

especially with that week old account .___.

[reef ocean]

please don't post unsolicited forms in this server

[mossy shadow]

Zan (鹿乃 #1 Fan)

[green terrace]

wedge

hell yeah

[brazen mist]

(unsolicited form)

[green terrace]

OHHHHHHH

I'm a bit oopid

[rocky terrace]

A good way for reading books I have found is to read the books instead of being on discord all day long

[scarlet arrow]

Fr

[crimson elm]

Gal

[short anvil]

Hello everyone i need some help.

am a grade 8 that can do grade 3 math, I have dyscalculia and dyslexia so it makes math quite difficult, I need continuous help in math as I try to understand, I don’t understand anything further than average addition and subtraction, it’s quite embarrassing.

[muted obsidian]

that’s not embarrassing at all, everyone has their own level they work at and their own pace that they improve at, always feel free to ask for help in the server

[rocky terrace]

That reaction emoji, is that from a Detroit Become Human server?

Connor and Hank hugging?

[short anvil]

YES

OMGOHS

YOU KNOW THEM TOO

DBSKKDBSKSKDI

sorry- I don’t find many fans out in the wild

[short anvil]

It’s actually from Bryan decharts official server! (He’s the one that acted Connor)

[rocky terrace]

Oh nice

[rocky terrace]

Detroit Become Human is so peak 🗣️

ye I know Dechart acted as Connor that's why I asked since the name of the emoji was "Dechart Hug"

[short anvil]

Hehehe

[rocky terrace]

But anyway yes I think you will find this server quite helpful

[short anvil]

I hope so

[rocky terrace]

#❓how-to-get-help

[short anvil]

Nothing has been able to help me

[rocky terrace]

especially this

[short anvil]

I can’t use that bc I don’t have a specific question

[rocky terrace]

No, I mean

When you are learning math and face issues due to dyscalculia and dyslexia

[short anvil]

Trash

Yeash*😭

[rocky terrace]

"Trash" 💀

[short anvil]

💔

[quasi oriole]

We are never instructed problem solving and neither I'm good at it. Following OSSU curriculum of CS and mathematics courses come with word problems. Can't help myself with those and see the solutions is only I can do. Ain't confident enough. Any advice from where to start and whether should I still continue the course provided no problem solving background?

[green terrace]

Show an example of the types of word problems you are stuck on

[quasi oriole]

May be basic but as I mentioned we ain't taught here. I don't know if regional background must be taken into account but it's a fact, even a CS graduate as I asked some failed to understand this.

[rocky terrace]

I think the correct answer is "eieieo!"

[quasi oriole]

I may complete the course like traditionally we do here. Just see the solution and try to understand it.

[coral sleet]

a question for you all: when you're writing a test, do you completely solve a problem before moving on to another one, or do you have a different method?

my method as of rn is to pick a problem, solve as much of it or make as much progress as I can on it until I get stuck for over 2 to 3 minutes, then select another one and repeat

and do this until most to every problem is partially solved

and then come back to finish off whatever I can

I think it helps me pick up partial marks a lot, but I also think it throws me off balance

as in, I have too many problems on my mind to think of at once, and also makes it hard for me to keep track of where I was on each problem

does anybody else do this? if so, any advice?

if not, what methods do you employ for test-taking, and what makes them work for you?

[muted obsidian]

i am a big fan of starting from the back and then making my way to the beginning (if it’s meant to get harder from start to end), it’s something my chemistry teacher told me to do in high school and i’ve been doing it since

it means the test gets progressively easier and even though the beginning is tough, it means you’re not scrambling for marks on difficult questions when your time is nearly up

[coral sleet]

the problems on the tests I write have, in my experience, not been in any order of difficulty

[muted obsidian]

oh really?? every one i’ve done so far has been structured like that

[muted obsidian]

well i guess even then just start with the ones that look the most difficult, and then move on to the easier ones

[coral sleet]

sure, but I almost never solve them in a timely manner

so I move onto other problems, but then I have all the issues I mentioned earlier

[muted obsidian]

ahh right yah i see the problem

[coral acorn]

mine r usually strucuted in order of difficulty somehwat

but

earlier questions do catch me out more than the harder ones sometimes

never ask me "why the model wont work" for 1mark, i wont get the mark 😂😂😂

[viral osprey]

I do basically exactly what you described but after I've seen every problem I don't keep cycling through. Once I've seen them all I tend to put my focus on the one that seems most easy to crack.

From there I just kind of alot time based on whether or not I feel like I'm going to make progress.

If I get stuck too long I'll poke at whatever seems next easiest and so on.

If they all seem hard I'll just cycle through them cyclically I guess.

It's kind of a shitshow no matter what you do on hard tests.

[coral sleet]

I'll try this next time

[viral osprey]

I think one thing I try to avoid is getting caught in that trap where you're just staring at the paper scratching your head.

It still happens but I'm always looking for something to tangibly try or to calculate.

[coral sleet]

thanks Doot c:

[rocky terrace]

Bro? Re:Zero enjoyer in the math server?! Based

[urban copper]

If we get partial points I do this, if we don't get partial points(which is literally half of the time lmao) I try to finish all the exercises I know as carefully as possible and then for the other exercises I just write as many things as I can :|

[coral acorn]

🙏🙏🙏

[coral acorn]

oh i js realsied u know icarus too

[rocky terrace]

@brittle falcon #❓how-to-get-help

You can read about it here

[brittle falcon]

Yoooo

[brittle falcon]

Okay let me see

[coral acorn]

yoooo

[rocky terrace]

Re:Zero gang represent!

[coral acorn]

real

[main trail]

does this look nice a time time table for next sem ( courses I'm planning to take)

like am I taking on too much

[rocky terrace]

you need at least twice as many courses (maybe even thrice)

[main trail]

my credit limit is 25, this is 23 credits

[main trail]

you're /j or /srs

[coral acorn]

bro the fuck u learning on friday

😂😂😂😂

and monday

[rocky terrace]

Are you talking about RA1? I would assume it stands for Real Analysis 1

[coral acorn]

no bro

the

folk music in india/ climate change/ game theory

😭😭😭

what an absolute lineup of classes

[scarlet arrow]

[scarlet arrow]

add your tutoring hours

[rocky terrace]

I didn't even notice

[main trail]

That's a 1.5 credit course

[rocky terrace]

still that's quite a title

[scarlet arrow]

it's 3 courses kek

[coral acorn]

no clue what a credit is

[rocky terrace]

Oh I see okay

[main trail]

those are 3 options lol

I'm not sure which one I'll get

[rocky terrace]

Folk music in India

is my prediction

[main trail]

Offered by a sociology prof

[main trail]

yes

hoping for evolutionary game theory though

[past totem]

how do you get rid of study role 😭

[coral sleet]

go to id:customize and unselect the role

this one in particular

[cobalt sun]

or do ,iamnot studying!

it won't work in onboarding if you did it through ,iam

unless you select it and then deselect it

[past totem]

thank you thank you THANK YOU!!!!!

[scarlet arrow]

You'll be cursing them soon after being fed up with the discussy brainrot

Btw, welcome to the server!

[past totem]

thank you!!!!!

i hope you’re having a great day

[crimson elm]

Seems good to me. I'd replace differential geometry with algebraic geometry and maybe macroecon with ring theory idk

[quaint viper]

i don't think algebra 1 means what you think it does..

[light talon]

Can someone give me a youtube playlist that covers all of factoring please

[main trail]

I am planning to replace macroeconomics with operator theory

If I'm able to get the time table fixed

[crimson elm]

based

Yeah engineers know wtf is a pro-Galois group

[safe harbor]

Egg in ear

[main trail]

If I can get some time table issues sorted out

[main trail]

I hope you realise this is for a 2nd year math major

[crimson elm]

You can't take ring theory as a 2nd year?

[main trail]

that's in my 4th semester

this is my 3rd

[crimson elm]

hmm okay

Idk how it is there tbh

I took a graduate course in my 2nd year

[cursive oracle]

~~ terrible if you are not doing topos theory on 1st year of undergrad you're cooked~~

[main trail]

I'm planning to do a PhD course in year 3

just that I don't have the pre-reqs rn

[safe harbor]

i took your mom in my first year

oh this is study-discussion

but honestly i dont think its constructive to be like "I did X when I was only Y years old", it just makes things seem unnecessarily competitive. And no one's in a rush here either

(I took a PhD course when I was 2 years old)

[crimson elm]

Oh sorry I didn't mean it this way

I was just curious about how is it like in other institutions

Some do let you take courses even if you don't have prereqs

[rocky terrace]

I finished my PhD when I was 1 btw (using Arch)

[rocky terrace]

I think it varies from "There are no electives, you're gonna shut up and take the courses we tell you to take" to "Do whatever you want, take whatever courses you want"

[worn wharf]

https://www.youtube.com/watch?v=1YRvXpLOft8

[rocky terrace]

what

[worn wharf]

I have to respond with something just as outrageous

[main trail]

I'm just so tired of home 😔

NEED UNIVERSITY

but at the same time I feel this atutude will lead to burn out

[deep inlet]

What's the motivation for replacing diff geo with alg geo without further knowing what the person wants to study?

(Maybe they mentioned it before, idk)

[rocky terrace]

Deltoid hates diff geo and wants to make sure diff geo never sees the light of day

[agile fable]

Replacing macroeconomics with ring theory indicates that it's just a shitpost lol

[crimson elm]

Not sure if they mentioned it before

[crimson elm]

I feel like you'd benefit more from AG. That was the case in my experience

[runic crest]

I wish I took AG instead of DG

[crimson elm]

Burnout sucks

[crimson elm]

I wouldn't say easier. It's more enjoyable

[olive geode]

The content gets harder, but you get better at learning - like how to spend your time reading, taking notes, doing exercises - plus you have more experience to draw on, so it's easier to put what you learn in context

[deep inlet]

Wouldn't that be heavily dependent on what the person wants to do?

[crimson elm]

Sure

I'm just biased towards AG

[deep inlet]

😂

[crimson elm]

Even with stuff like lie theory

[deep inlet]

Im currently going through Hartshorne myself actually

[crimson elm]

Learning it the algebraic way was more helpful

Which chapter?

[deep inlet]

On Sheaf Cohomology

[crimson elm]

Chapter 3

Nice

[deep inlet]

Yea

First time I am actually doing coho via derived functors

Very cool

[crimson elm]

Yeah it's really fun

[deep inlet]

Also it's finally super elegant to prove De Rhams theorem with sheaf cohomology

[deep inlet]

I do agree that learning it algebraically is super nice, but a lot of my working intuition for this algebraic stuff works so well because I learned smooth manifolds before hand

I eventually want to get to moduli space stuff tho

[olive geode]

Hmm, maybe you'll be more productive, but if so the workload increases proportionally, because I think very few people spend less time studying as they progress. But it's hard to define workload objectively, so I don't think I have a definite answer

[rocky terrace]

What if you could be biased towards both AG and DG

[crimson elm]

I wish

AG has so many good stuff it makes it hard

[runic crest]

Deltoid is not a hater of DG lol

I AM the hater of DG

[slow yew]

What did DG do to you

[unkempt quarry]

Drainnnnn ganggggg

[slow yew]

?

[main trail]

I don't even think AG is being offerd RN

I don't have the pre-reqs and there's no demand rn, though I could get it offerd soon

Fractal geometry sounds fun lol

[storm jasper]

Yes study fractal geo

[main trail]

Let's see, been 5 years since it was offered

[storm jasper]

Well self study it

Looks cool

[main trail]

last offered

I can get it offered IMO

[main trail]

honestly, should I take diff geo or operator theory

LA2 is an option too

just so confused

[safe harbor]

How would you do either of those without linalg2?

[main trail]

idk, it will either be made simpler or they'll teach whatever's required

like we've done linear maps, inner product spaces, eigenspaces and the spectral theorm ( this without proof) in LA1 amongst other things

shoulnd't that be enough

[ornate wind]

honestly it might be

My linear algebra class didnt even talk about spectral theorms i had to learn that shi in functional analysis

[main trail]

In that case what do you suggest I take

both sound fun

just so confused

[ornate wind]

Any of the two is good i dont think it matters

i encourage breadth in undergrad

U can try diff geo maybe and see how geometry feels

Operator theory is more analysis + linear algebra

[main trail]

hmm

[cyan dawn]

hey guys

[main trail]

hi

[main trail]

would doing both be taking too much upon myself

[ornate wind]

idk

Maybe

[main trail]

I also do RA1 next sem

[ornate wind]

Ohh

i would wait until after real analysis to do operator theory things

[main trail]

okie

thanks

[ornate wind]

also what is this channel 😭

I never seen this shi till today

Worst mod award goes to

[main trail]

@mooderators

[glacial raven]

Happy birthday

[main trail]

do you know of politico?

[ornate wind]

Ty

[ornate wind]

Maybe. is it the thread in somewhere i forgot where

For political discussion or sth

i never go in there

[cyan dawn]

how do we get better at maths

I wanna be fast like my professor

[glacial raven]

Practice

Your professor may have taught that course/topics in the field many times to get comfortable with the types of questions in it, which in turn was practice for them

[storm jasper]

Diff geo

[cyan dawn]

Damn

[cyan dawn]

could I see

your guys math notes

for inspiration

[odd parcel]

Any ISI student (Indian Statistical Institute) here🤞
i need guide and help
pls contact me if possible
Pleased to connect

[scenic shuttle]

which one do you want? i have both written in latex(latex is tiring btw) and handwritten on ipad

some samples

[rocky terrace]

hand drawn diagrams in LaTeX, absolutely based

instead of trying to TikZ everything @eager halo

[scenic shuttle]

yeah tikz is annoying lol

too much work

[rocky terrace]

way too much work and way too little gains

TikZ: annoying and unatural
hand drawn: beautiful and has a certain vibe to it

Do you have a drawing tablet?

[scenic shuttle]

yes i got an ipad for a reason

[rocky terrace]

Oh you have an ipad okay

[iron orchid]

Hi

I got sent here

[royal spindle]

[iron orchid]

I need help, who's willing only because I dont have a small favor,

Anyone here?

[candid berry]

OK. So, you can use Khan Academy and start where you're at. Just grind, do a lot of practice problems (like on AoPS's alcumus), and if you have any specific math questions, you can open a help channel.

[iron orchid]

Tried lmoa

My brain just shuts down

Prob since I moved to homeschool

[candid berry]

Well, in what way?

[candid berry]

I'm homeschooled too

and I have no idea why you're experiencing this

[iron orchid]

I've started homeschool since 6th, whenever I didnt understand smth in public, I would've needed a teacher to explain it to me so I would understand logically

[candid berry]

mhm, ok. So, if you don't understand a specific thing, you can open a help channel here.

There will be people who are very happy to help.

[iron orchid]

I've met a person here my age who's helping me rn, but she has a different time zone

[candid berry]

Whenever you have specific questions, you can ask on here. Many people are online, especially during this time.

[iron orchid]

Must be embarrassing to say, but I finnaly understood rearanging formula last week

Being in 11th 😭

[candid berry]

That is OK, if you work hard, you'll be able to do it.

Again, you just need to grind, and by that, I mean a lot.

[iron orchid]

Idk even know what im supposedly to learn to get back

[candid berry]

You said you tried Khan academy. They have a curriculum there, no?

[iron orchid]

They dont have a testing area to check your knowledge to set

[royal spindle]

do you do gcse or wht?

[iron orchid]

What is gcse

[royal spindle]

ok nvm sry

[candid berry]

By what you're saying, I think you should start by looking at the 6th grade section. (no offense btw)

[iron orchid]

💀

[candid berry]

you can see what you know and don't know; if there are too many things you don't understand, you can go back one grade; if you understand everything, you can go up one grade.

[candid berry]

and just grind from there

[candid berry]

I'm sorry, but this is really the only way.

[rocky terrace]

Bro I finished undergrad and I still don't understand it

[candid berry]

I think it's just cuz you never heard of it mentioned this way

I think you understand

[candid berry]

Anyway, does that make sense?

[iron orchid]

But im going to public in 2 months

[rocky terrace]

tbh yea I don't know what the "rearranging formula" is

[candid berry]

iirc it's just adding the same thing to both sides / multiplying the same thing to both sides

[iron orchid]

Ik what you mean and im not trying to be rude, but I need someone who can help me along the way, like I said it isnt a small thing im asking

[rocky terrace]

Oh yea that's trivial

shame on you for not understanding

[candid berry]

There are many people who can help you here

[rocky terrace]

jk

[rocky terrace]

and they'd be glad to help you Wonder, because they simply like math and helping other people

[candid berry]

You can open a help channel like you just did if you don't understand a concept

[candid berry]

And good luck!

[iron orchid]

😭

[candid berry]

I'm sorry, but again, that's the only thing you can do. I wish it wasn't.

[iron orchid]

So there isnt a person here, who can guide/teach me along the way, "no offence btw appreciate all of yall advices"

[candid berry]

There are many!

However, most of us probably can't teach every concept to you (because honestly, we aren't professional teachers)

But if you have any questions you are more than welcome to open a help channel or DM me.

[iron orchid]

Ty, for that appreciate all the help I can get

[eager halo]

Yeah no

I'm pretty sure that mixing hand drawn diagrams in TeX is considered bad typography

[cunning totem]

hand drawn is fine if you are actually good at art, otherwise learn to tikzpicture and quit bitching

[safe harbor]

Or inkscape

[glad zenith]

tikz is king

I'm a huge tikz fan for its conditionals and loops

[unkempt quarry]

I’m in the process of painfully learning tikzpicture since I’m writing notes for my calc 3 class

Pain

[glad zenith]

tikz is good for the soul

[unkempt quarry]

I’m eating my veggies

[glad zenith]

time to eat my veggies (=sleep)

good night everyone

got push day tomorrow

[cyan dawn]

how do you format it

and your hand writing is super neat

[eager halo]

Yeah well-drawn inkscape looks as good as TikZ, at least to my layman eyes.

[scenic shuttle]

format what? in latex it should fine but for handwritten takes a little bit time but it could be also easy

[scenic shuttle]

thanks

[cyan dawn]

How do u do latex

[cyan dawn]

np

[scenic shuttle]

pinned messages in #latex-help

you can get started with these resources

[cyan dawn]

Nvm it’s alright I’ll stick to iPad notes but like i don’t have any structure

[scenic shuttle]

there are good apps i wanted to try but most of them are paid

so far i use freenotes and note+

those might be great ones imo

[cyan dawn]

have u tried Microsoft one note

[scenic shuttle]

yes but personally I dont like it

[cyan dawn]

why not

[scenic shuttle]

because i hate microsoft

[cyan dawn]

why do u hate Microsoft

[scenic shuttle]

its shit and always have problems if it makes sense im a linux user

but i wouldn't say onenote is too bad its up to you

seems fine

[cyan dawn]

what is Linux

[cyan dawn]

fair point

[scenic shuttle]

google exists

[cyan dawn]

you are google

[scenic shuttle]

linux is just an os

[cyan dawn]

Oh

makes sense

do you guys think mind mapping notes is good for maths

[scenic shuttle]

if it helps you then sure

[shell wasp]

hello eveyrone

i graduated highschool in june 2022 only VERY recently have i decided to go back to school im attending the university of washington now but between those years ive obviously have not done any math

i was just wondering if doing algebra 1 geometry algebra 2 trigonometry precalculus ap calculus ab & bc multivariable calculus and differential e quations and liner algebra is good enough

to get prepared

literally starting from level 1

so basically

doing everything from that screenshot but skipping integrated math series statistics college algebra

[thick ermine]

the three at the bottom aren't well handled by khan academy

[rocky terrace]

Khan Academy's Multivariable Calculus course is GOATED 🔥

Most of the videos (and articles too I think?) are done by Grant Sanderson (3Blue1Brown guy), they're super useful

[fast remnant]

is khan academy really that good? for following the path of learning math without skipping smth etc

[haughty parrot]

khan is quite bad imo

pick up an analysis textbook

[fast remnant]

a what

[safe harbor]

What math are you studying?

For high school level math it's fine iirc

[fast remnant]

yes yes high school level

[safe harbor]

Then yeah you should be fine

[fast remnant]

“proving inequalities” rn

[safe harbor]

Though I think it's a bit lacking in later highschool material

Could be wrong though

[fast remnant]

idk i just made an account 2 days ago

[safe harbor]

You won't lose anything from doing it, you'll definitely gain a bunch

But I don't know if it can replace a full highschool curriculum

[fast remnant]

also need to work on my factorising

[safe harbor]

For that it should be fine

[fast remnant]

murica is really advanced

[safe harbor]

Is it?

Idk it's been a few years since I've done highschool math

[fast remnant]

idk i live somewhere else

[safe harbor]

Same

[glacial raven]

how do you guys stay motivated? i found this video already https://www.youtube.com/watch?v=8ZhoeSaPF-k

i think that i do best when people validate my efforts / reward me anyone else studying maybe we can encourage each other

[glacial raven]

also found this video, seems like this is a really effective way to study https://www.youtube.com/watch?v=4WHbaEQZ6pU

[crimson elm]

Anki for math?

I only used it for language learning

[solid venture]

I used it for intro to abstract algebra. Pretty good, but it takes a lot of overhead to do good slides.

[glacial raven]

it'd be kind of neat if a teacher added to a deck as students learned and then had the students take turns answering the slides so that they socially could see how others answer questions and learn together

[coral acorn]

is this not js class

mb if that was rude, it js sounds like regular teaching

[tacit sapphire]

Study is so hard

Life is so depressing

😭

[solid venture]

Take a break and reevaluate your life circumstances.

You will not be productive if you are in a bad mental state.

@tacit sapphire

[tacit sapphire]

very true, I actually made very awful life choice for being addicted to math.. and whenever I look at my current grade sheets I just want to curse

And it actually is harder than I expected in many ways😢

Though I am thinking of studyint quantitive finance or something to utilize my learned skill if I can’t manage to study math however I don’t think if they actually need such knowledge I learned… almost completely out of real life applications

[left edge]

Guys can i ask a question? why AM-GM so hard?

[whole wing]

Idk, why is it hard for you?

[ionic dew]

You're addicted to math , i badly want that

[young cobalt]

boy if you think thats hard

also wait are you talking about inequality or just arithmetic mean and geometric mean

[mental tinsel]

is there a way you folks orient yourself to be able to sit down to do math? I know this sounds like a very odd question but I basically do this as a hobby and sometimes I become a bit too complacent to be able to follow up to whatsoever progress that I have made

In essence, I am struggling with commitment and consistency and was wondering if there are any ways to mitigate the issue

I have a part time job which isn't too intense, so idk if I could shift the blame to any form of excuses like exhaustion or being overwhelmed by work

in any case, I'd love to hear yall's inputs

[storm jasper]

I kinda just forced myself to sit down

That was a joke

But

I kinda just

Shift my minsset

Especially on some annoying and hard topics

I usually focus on something cool

Whether it be trivial like integrals

Or advanced as manifolds and general topological shapes

[mental tinsel]

mathematics comes across rarely as "cool" to me

to me it's just definitions, theorems/lemmas, proofs and exercises

[storm jasper]

Well, are you really learning math correctly?

What math do you study

[mental tinsel]

rn I am trying to do Number Theory and Real Analysis

[storm jasper]

Hm

Real analysis is like

Studying calc stuff

In an analytical way

[mental tinsel]

Yeah it's a more proof oriented course

[rocky terrace]

But if you look at what those definitions and theorems are saying, it's so PEAK though 🗣️🔥🔥🔥

and quite beautiful

[storm jasper]

Yes

[main lodge]

Finance is such a joke of a field, holy shift

Especially the beginner stuff. Trying to calculate some WACC nonsense that is literally wack and I am 99% sure there is some circular reasoning going on here

Maybe it is just gpt (o3 latest model) screwing up, but at least it managed to be somewhat precise. The school book's 600 pages is basically just a handwaving marathon

[storm jasper]

Try doing cfa

[slow yew]

Is that to say CFA is better or worse?

[limpid sinew]

I'm starting to read through an Intro to Stats and Probability textbook. I want to review some concepts and learn others. I will work on some problems from each chapter. Should I focus on the odd numbered ones so I can check my answers in the back? Maybe complete the even numbered ones for extra practice?

Should I take detailed notes on each chapter? What about the definitions and terms explained in each chapter?

[glacial raven]

The thing is to sit down and crunch through at least some problems daily in your free time, whether you feel the motivation or not. You may take a few days rest if you are not feeling productive at all while doing math. I personally take at least one rest day per week.

One can memorize/prove the definitions/theorems, but how to apply them and reason comes from problem crunching. Do at least one problem a day, or you may even extend the duration of solving that problem to many days till you understand the underlying concept(s) in your free time. You're doing math as a hobby, so don't take much pressure.

As for progress, select some small questions that serve as a revision of the previous topic(s) whenever you get back doing math, and gloss through them if you want. But solve, that is very important. And go through a variety of questions, not just crunch on the same type. It's training one's mind to think about a problem in multiple ways and finding the best/reasonable solution, in my opinion.

And, if this helps, form a small habit of appreciating the upsides/advantages of the theorem(s) you have learned about. This in turn may help you to get an idea where the theorem(s) can be applicable.

[rocky mauve]

As a general caveat, everyone learns differently and learns at different paces. Part of developing as a student/researcher in any field is to find what works best for you.

With that out of the way, i would suggest that (depending on the amount of time/patience you have) you try to work through as many problems as you can after reading a chapter. This is really the single best way to learn and gain intuition for what you are reading. If you only really have time to do half of the problems then sticking with the odd problems in the beginning may be useful insofar as to make sure you are understanding the core concepts. As you progress, you should be able to pick out problems that you feel will help you the most.

If there are things you are reviewing, simply rereading the material is often sufficient. For new material, I would suggest writing down the big theorems/lemmas and then adding your own personal notes on specific points which give you the most trouble. Ideally you will revisit these notes. Writing down definitions is often tedious, but may again be helpful in the beginning to get used to the material/concepts. Lastly, consider what you want to get out of the book. Textbooks are hundreds of pages long and unless you have hours and hours of time to study the material, you really should skim the next chapter’s material to see if it is worth pursuing. That said, if you are new to probability/statistics you may not know what to exclude. In that case, you should consult a syllabus or ask someone before you just skip a chapter. Best of luck!

[limpid sinew]

Thank you!!!

[left edge]

im talking about AM-GM that usually show up in math competition

[rocky terrace]

Same

[mental tinsel]

🫂

[young cobalt]

Yes I understand

It makes up a lot of questions in imo

They pull out some bs inequality

[main lodge]

My approach has been to first try to understand why I want to be better at math and why it feels important to me. Then I try to create a routine for it. I try to also pay attention to what distracts me and is of less importance and also try to figure out how I can remain focused. So far having a screen time limit on my phone has helped with a lot of the distractions and physical exercise helps a lot with focus

It is a struggle tho and i do have setbacks from time to time, but having a very concrete routine on things is of great help for me

[main lodge]

often times people being bad at math is because they are trying to learn higher level stuff without having fully mastered the basics. If you try to learn odes without having a good understanding of derivatives and integrals first then it is going to be harder and a whole lot less fun

[rocky terrace]

And sometimes people are bad at math because they spend more time asking for book recommendations than actually reading the books

[main lodge]

It does take courage to slow things down and go at your own pace, but if you rush things then you will end up just memorizing the method and that knowledge wont stick around with you for much longer than 6 months (at least in my experience that is). The ideal thing would be to find some problem you want to solve and see if you can break it down into smaller problems and you dont move on to the next problem before you have fully understood the solution of the current one

[rocky terrace]

It does take courage to slow things down and go at your own pace

This must mean I have the most courage in the world

not me taking 2+ years to learn basic analysis

[main lodge]

but i do get that academia often doesn't allow you to spend this much time on one single problem

that is often the case for me

[rocky terrace]

You can ask for hints if you are spending too much time on a single problem

[main lodge]

yeah you can, but i really dislike asking for help. That's my issue

I prefer to figure out what kind of problem it is, check if it is a well researched one and see if there are solutions out there of similar problems that I can use as hints

[main lodge]

what kind of analysis you learning btw?

[rocky terrace]

#1059828221887135774 introductory real analysis

[main lodge]

looks like measure theory to me

[rocky terrace]

Lol there was just a conversation about the Lebesgue integral, I myself haven't yet started MT

[glacial raven]

insert catking

[left edge]

I see, that's explain everything

Thank you

[mental tinsel]

Thank You @glacial raven @main lodge for the suggestions. I appreciate it ❤️

I actually went out of my way and rented out a Library space where they allot you a cabin where you can work.

It has helped tremendously, I must say!

[rocky terrace]

Can I join you in that space

[fringe sage]

I have a question regarding those who are studying math in university. What math should i study to make myself ready?

I've already studied linear Alagebra and multivariable calculus.

should i study anything more?

[storm tide]

Those are typically subjects you're supposed to learn at university ...

[fringe sage]

oh

would studying proofs be good

since i do not how to prove shit

[storm tide]

"Proofs" is what all of mathematics is about.

[junior dagger]

what about having fun 🥺

[storm tide]

That's an excellent idea. Pick some math you have fun with, and play around with that.

[junior dagger]

if you have alr done a course in LA

its prob the best place to learn proofs imo

loook [here](#book-recommendations message) for some books on a second course

[cyan marsh]

The hardest thing about shaking off my math rust (for context, I'm going back to school after dropping out for 3+ years) is that I have a natural tendency to speed through everything. Feeling like I need to play catch-up isn't helping either

[glacial raven]

i'm in a similar position, i'm starting with the aops prealgebra book

it's nice cause the challenge problems are hard

i'm using anki to schedule reviewing the problems. so far it's effective but i've only gotten the problems from the first section in anki so far

‏Hi everyone! 👋
‏I’m interested in learning some essential math concepts that are useful for executive-level decision-making, especially in fields like finance, strategy, and analysis.
‏Here’s a list of what I want to learn:
‏ • Ratios and Proportions
‏ • Percentages
‏ • Basic Algebra
‏ • Fractions and Decimals
‏ • Mean, Median, Mode
‏ • Standard Deviation
‏ • Variance Analysis
‏ • Probability
‏ • Time Value of Money
‏ • Simple and Compound Interest
‏ • Rate of Return
‏ • Discounting
‏ • Net Present Value (NPV)
‏ • Internal Rate of Return (IRR)
‏ • Sensitivity Analysis
‏ • Scenario Analysis
‏ • Linear Programming
‏ • Mathematical Modeling
‏ • Area, Volume, Graph Interpretation

‏If anyone is teaching this or has resources, please let me know! I’d love to join a study group or get some guidance. 😊
I’m 14.8 years old girl and I want to learn thus Because I want to become an executive leader at Aramco. , im new

[cyan marsh]

My advice is to just cut down the number of subjects you want to learn into something that you can actually juggle in the short term, in the meantime, as for resources, Khan Academy (to my knowledge) covers almost every single one of these, anything you can't look for there, Google is your friend

[amber pier]

Heyy, should I learn how to use theorems in statistics or should I also learn how to rigorously proof them?

[cyan marsh]

https://tenor.com/view/principal-skinner-yes-seymour-skinner-the-simpsons-enthusiastic-yes-gif-15806751

[jade furnace]

I'm so close to completing all of High School Geometry on Khan Academy.

After this, it's time to learn Algebra 2 again.

[candid berry]

nice

[jade furnace]

Does anyone else get surprised when they finally learn something they never thought they could do before?

[jade furnace]

Thank you!

[candid berry]

me

[limpid sinew]

Is anyone studying stats, probability, or calc just for fun? 🙂

[stray zodiac]

Hi

[scenic shuttle]

I barely started with stats cause I might need it to my degree just in case don't wanna get cooked

as for calc, which one are you referring to?

[sinful plank]

hey guys, are there any recommendations for someone in middle school who wants to get into college with like a math major? i literally don't know anything about college and stuff but I wanna start off early.

[agile hollow]

maybe you can start with calculus or linear algebra

[sinful plank]

alright! im not sure if its a start but I've been practicing matrices

[agile hollow]

I am cooked, the uni i wanna apply for master requires basic knowledge in probability. I have to revisit it ahhh

[agile hollow]

idk what exactly you are practicing in matrices.
But in order to have a clear path it is recommended to have a textbook

[sinful plank]

gulp... do you have any textbook recommendations? im going into 8th grade in August btw if that helps. I'm practicing multiplication of two matrices

[agile hollow]

since i have never studied any calculus book properly so i cannot recommend any \

[agile hollow]

oh, sorry i thought you were talking about university

[sinful plank]

real

[sinful plank]

OH

[agile hollow]

mb

[sinful plank]

its alright

[agile hollow]

well, i guess using math textbook for next class (grade) would work

idk if there are fixed books

[sinful plank]

no clue 😵‍💫

[agile hollow]

in our country, from grade 1 -- 12 the books are fixed. So everything comes from there, exams lectures etc

[sinful plank]

ohh

my teachers do follow a book, so perhaps...

[agile hollow]

maybe

btw you also can follows Khan academy's videos on YT

[tacit sapphire]

Is it better to train one self to write slicker proof when it does not obscure the main logic?

How to write proofs that are self contained? Like if I study algebra then I can write proofs using algebraic method instead of other not that painfully?

[minor depot]

I would suggest you give an example to illustrate this, if you can...

[tacit sapphire]

Sure

[tacit sapphire]

Here are two examples, one is similar ball arguments, one proof I did with every detail spelled out another I just did symbolic manipulation though I don’t find black box but it’s harder to decode? I don’t know the math departments’ standard

Another is on page 3

One question I proved it twice, one with formal induction long and hard to write (you need to type) but details are spelled out, the alternative proof is one liners

The way to achieve the slickness is always through symbolic manipulation than explaining because if you explain you have to illustrate the inequality with more inequality despite its basic fact and more words too

[minor depot]

[so, just to point out - there are proofs for three separate things here]

[tacit sapphire]

Yes but barely I’ll do twice. For the first proof I can actually make it more slick but I felt since it is my note I need it comprehensive

[minor depot]

[But assuming your question is whether to use different algebraic approaches to simplify the logic]

That should be fine, as long as the logic remains sound

[minor depot]

I think I would need to see an example of what your slick version is to make a judgement call on it

By "formal induction" I assume you're referring to this section specifically?:

[tacit sapphire]

Another problem is some argument despite used as facts are hard to prove, sometimes I had to appeal to another branch of mathematics

[tacit sapphire]

Yes that’s a lot more wording

I kinda want my note to be self contained however this little lemma turns out way harder

[minor depot]

So they've written everything out to be very explicit; it's already self-contained to a point

[tacit sapphire]

The alternative proof is an example

[minor depot]

But essentially this boils down to "do you understand how to write an inductive proof?"

Oh, as in avoid induction altogether?

[tacit sapphire]

But the proof I wrote is exactly how the induction is done in basic analysis book define property basic case and hypothesis then implication

[minor depot]

In this case, yes you can, since you're actually using induction implicitly

Because the logic is sound for any given n, it will also work if I add another U in there

[tacit sapphire]

So the alternative is still induction?

[minor depot]

It's implicit, you wouldn't even have to state that that's what you're doing

[tacit sapphire]

Is the alternative proof for the third claim an actual example? Because I think iam quite in short of that logic

[minor depot]

Admittedly, that's me claiming that this is still induction; others may argue otherwise

[minor depot]

This, right?

[tacit sapphire]

Yes

[minor depot]

This is less about logic per se, and more about exploiting a definition

It's mentioned as much: "Then by definition of the open sets, for any arbitrary..."

If you want I can give a brief explanation of what that proof is actually doing

[tacit sapphire]

Is the second proof in this case considered better for math department or the fully spelled out induction?

[minor depot]

"better"?

If I were to write either of them I'd get full marks

It's worth trying to make sure you at least understand both

[tacit sapphire]

Because for every open set x in B we have epsilon > 0 such that B(x,epsilon) contained in B so if I take the minimal epsilon then immediately it contained in the intersection

[minor depot]

I'll briefly explain this one so it's a little clearer what's actually going on

[tacit sapphire]

Since it’s finite so it’s minimum no need to consider the infimum so the property of closed under intersection holds is the base logic

I think for the proof

The induction is essentially the same though

Only details spelled out?

[minor depot]

Take a point x in the intersection of these U-open-sets
As each U is open, I can draw a ball around x, say with radius epsilon_i that fits inside each U_i
Let's make a list of these epsilons

Now consider what would happen if I take the smallest epsilon_i (call this just epsilon) [this certainly exists if n is finite]
Then B(x,epsilon) is certainly inside B(x,epsilon_i) which is inside U_i, no matter what i I use
So in fact B(x,epsilon) is in all the U_i's
i.e. this ball is an open ball inside the intersection of the U_i's
i.e. we've just drawn an open ball in the intersection - so we've proven the intersection itself is an open set

The induction proof is a sure-fire way to approach this question if you don't come up with the above; the mechanism behind induction gives you the groundwork/requirements you need to formulate a proof

[tacit sapphire]

Yes! That’s my logic I think. Only it won’t hold if it’s not finitely many open sets, Becasue if we take infimum over epsilon it might as well reach 0

[minor depot]

But this proof also exists

[minor depot]

Correct; if n is infinite you might need a greater condition

[tacit sapphire]

I must say you’re right it’s actually very nice to draw I learned it from someone from this server

It helped me a lot with understanding this

Another issue I face currently is

[minor depot]

And in fact, it is not generally true, if n is infinite - as a counterexample, consider the sets U_i = (-1/i , 1/i )

Each U is open; yet the infinite intersection is {0}, which is non-open

[tacit sapphire]

Many basic facts used in my current subject, aren’t easy to prove this turned out to be very hard

In particular this

This seems to be very easy and elementary fact but it is completely different thing.. I tried many times I couldn’t prove it

At all

[minor depot]

You haven't come across Fubini or Tonelli?

[admittedly they're a little odd lol]

[tacit sapphire]

I know fubini tonelli but it’s not self contained anymore it’s my note for abstract algebra

I tried using basic argument and I just can’t prove it

And this tonelli fubini makes my note completely not self contained

[minor depot]

You can look these up

Specifically see if you can keep them in sigma notation rather than integrals, if that makes it easier to grasp

[tacit sapphire]

But that’s still measure theoretic

[minor depot]

True

But these index sets are finite, so they're Lebesgue integrable; that's all we need

[tacit sapphire]

I want an elementary proof, this fubini tonelli proof I wrote it myself I just find it too abrupt to my note

Since it’s quite elementary abstract algebra note and I bring in tonelli

And the elementary proof for the lemma is really hard actually

[minor depot]

Ah I see you're arguing that using Tonelli or Fubini is a little overkill

You can argue as much

[minor depot]

Specifically the sets I and J are finite; you could just make a counting argument

[tacit sapphire]

I just find it weird why those facts used almost routinely so hard to proof

[minor depot]

The more elementary something looks, the less clear it is how wild the proof is

Some things fall out as natural consequences

Others you have to go out of your way to demonstrate

It's why things like Fermat's Last Theorem having a proof hundreds of pages long are a thing

[tacit sapphire]

True, but it somehow makes me so annoyed especially I thought it would be an easy argument

And I spent an entire afternoon giving up on it and used tonelli

[minor depot]

Ah - have a look through
https://web.math.ucsb.edu/~cmart07/fubini.pdf

...It doesn't embed oops - but this is essentially what this is about: the Discrete version (discrete because we're counting discretely (Sigma), not continuously (integral)) of the Fubini Principle

This is the theorem in question

It doesn't list a proof, but you might recognise this as "adding up all the terms in a matrix"

[tacit sapphire]

Thanks so much though this lemma actually made me quite sad yesterday for that I couldn’t prove it

I just can’t accept it’s basic and assumed…

This proof in fact, was like a spiral somehow and it became more and more complicated. So but yesterday there was a person who mentioned double induction and I am gonna watch some vid to learn it

[minor depot]

Yeah it is just a counting argument

[main trail]

I know I've asked this before, but just want reassurance , is it normal for RA to absolutely destroy one

[storm tide]

Real analysis?

It's a common context for getting "proof shock", for sure.

[main trail]

yea

I've written proofs before

a lot of them ( I used axler for LA1)

I'm particularly having trouble with the huge number of defns I have to work with at once

[storm tide]

Well, there's a new source of proof shock in analysis, in that it becomes much more common just to pull estimates out of a hat, with no compelling reasons why those particular estimates.

[storm tide]

That could be a sign of having done too few exercises about the early definitions. Or a bad book that doesn't offer those exercises, Iunno.

[main trail]

I'm basically self studying( using my prof's notes from my seniors) and having my friend who has done this course give me problems

[storm tide]

Hmm that might be a situation where you face a dearth of simple exercises (perhaps your friend is wary of boring you).

[main trail]

Perhaps, the exercise have mostly been interesting results.

I do have a copy of abbott, but I feel that too is mostly interesting exercises. Would Tao's analysis be a good book to supplement it?

[whole wing]

Fubini - Tonelli is waaay overkill for finite sums

Indeed it smells like induction of the size of I

[storm tide]

I'm not able to comment on particular books, unfortunately.

[main trail]

I'll ask in #book-recommendations , thanks for the help!

[whole wing]

Actually maybe even better and more general, you can prove that the double sum is equal to a single sum over the Cartesian product

[rocky terrace]

How many chapters of Abbott have you gone through?

[main trail]

~3

I've to do cantor's argument

and hiene borell

[rocky terrace]

You'll get there

You've barely just begun

So it's only normal to feel like analysis is destroying you

If you feel like you're not good enough, just do more exercises

use the theorems and lemmas in the book as exercises

[main trail]

Yea, which is why I was thinking I could get a copy of Tao

[main trail]

I do that

[rocky terrace]

Tao? Are you doing every single exercise in Abbott?

[main trail]

I try to ( If I've done the theory)

Like I have not done cantor's yet

so that leaves a few good problems

[rocky terrace]

Wait Cantor is chapter 1

[main trail]

yea

I skipped it

[rocky terrace]

Don't skip the project sections of Abbott(thr final section of every chapter), they're very good andn instructive and often contain very nice results

I'd recommend Rudin for more problems

[main trail]

My course hasn't started and I've probably done a month's content, I guess I could redo it from scratch

[main trail]

rudin is

I've seen it

[main trail]

Lilke I've done fields , sequences, and am currently doing toplogy of R

[storm jasper]

What happened

[rocky terrace]

Nah Rudin's problems are basically like Abbott's

just with more general metric space stuff

[storm jasper]

Just baby riding and Abbott for real anal

[rocky terrace]

so it seems difficult on the surface

[storm jasper]

Baby rudin*

[main trail]

should I do this?

[rocky terrace]

Nah

What exactly do you mean by Anal is kicking your ass?

[main trail]

Like even after working on a problem for a day, I can't solve it at times

[rocky terrace]

You say you're doing almost every problem in every section you do in Abbott, you seem to beb doingn fine

[main trail]

and at times I get a problem only after a final nudge

I'm missing something small but important

[rocky terrace]

that's normal especially at the beginning but try taking a break after a few hours, move on to the next problem, or take a walk, then come back to the problem you were working on. You can also re-read the section to get a better idea of what tools/ideas to use to solve the problem at hand

I remember spending several days on a single problem

[main trail]

This one problem is from a friend

[glacial raven]

The walk is the important part here

Give your subconscious mind some time on the problem

[rocky terrace]

True but temporarily moving onto another problem is also helpful

[glacial raven]

Indeed

[main trail]

Show $\overline{A^C}= (A^{\circ})^C$ was the problem

[mossy shadow]

wai

[main trail]

I'll do that

[rocky terrace]

Its okay to skip/ask for a hint if it's a problem from a friend, especially this early into learningn analysis

it took me around 1 year to finish 3 chapters of Abbott (mostly due to my own slothfulness )

[whole wing]

I believe this is mostly an exercise in unpacking definitions

[main trail]

It is

which I'm working on

I'll send this in a help channel with my current working?

[whole wing]

You can try #real-complex-analysis

[rocky terrace]

capital C for complement

[main trail]

complement

[whole wing]

No, comlement

[main trail]

bar for closure

[rocky terrace]

??

wdym?

[main trail]

yea

[glacial raven]

sotrue

[whole wing]

A^C = X \ A

[glacial raven]

Lma

[rocky terrace]

A^c

[whole wing]

Capital C is more common

[rocky terrace]

No way

it looks more like set of all functions from C to A

[whole wing]

Be sure to give the textbook's defs of closure and interior

[brazen mist]

[glacial raven]

Not that bad imo

[rocky terrace]

Me during May 2023: by January of 2024 I'll finish chapter 7 of Abbott and start learning measure theory

Me during Jan 2024: Doing chapter 4

Actually tragic

[main trail]

oh, just wanted to share this ( unrelated), I'm doing differential geo next sem

that is this coming sem

[glacial raven]

Good luck

[rocky terrace]

of curves and surfaces?

[main trail]

yea

[rocky terrace]

Based

[main trail]

The prof taking this studied at ISI, CMI, TIFR.
I'm cooked

[rocky terrace]

Oh you're from India as well

[main trail]

yea

[rocky terrace]

I keep forgetting

[rocky terrace]

Based

[rocky terrace]

Have you learnt multivariable calculus? That's quite important

for diff geo of curves and surfaces

[main trail]

yea, had 2 courses of it

[rocky terrace]

Nice

what did the 2nd course cover?

[main trail]

the first course covered sequences and multi var calc upto differentiation

the other course focused on space curves and integration

[rocky terrace]

Oh okay cool

[jade furnace]

Finished the Geometry section. Now it's time to move onto Algebra 2!

[main lodge]

congrats

[limpid sinew]

Just an intro for now. Reviewing a few things before I get into more advanced stuff.

[scenic shuttle]

oh i just barely started :D

which book are u using?

[limpid sinew]

I have this book:

https://www.amazon.com/Calculus-Early-Transcendentals-James-Stewart/dp/1305267265

I'm reading and working through an Intro to Probability and Stats book now. Haven't read the Calc book much yet. I want to very soon.

[scenic shuttle]

oh nice

[scenic shuttle]

I'm reading this book and skipped most of the sections I already know, except for statistics and other topics listed on the last page since they're new to me

this is just an introductory topics from 1st year bme they gave me, which I still don’t know well for upcoming years lmao

i probably wont doing advanced stuff who knows ¯_(ツ)_/¯

[limpid sinew]

Oohh that looks like a good book. Expensive! Do you have a hard copy or pdf?

[scenic shuttle]

I do have the pdf yeah and i can dm u if u want

[limpid sinew]

Sure if you want to.

[limpid sinew]

I tried to add you as a friend but I cant. Add me!

[scenic shuttle]

oh sorry I have these turned off

done

[thorny girder]

I wonder about thinking of mathematics not as beginning or advanced, but more like concrete versus abstract.

[tacit sapphire]

Yes

It’s from concrete to abstract

Inductive reasoning

[tacit sapphire]

You observe a phenomenon called it A
You observe the pattern of A
You make a conjecture about the pattern of A
You conclude by proving or disproving A

Though not necessarily, i think it’s also possible that
You know something called A
You extended A so there exists B
You study the nature of B and then make a conjecture
You conclude by proving or disproving B

Principle of mathematical induction
Is to see the base case
Make hypothesis
And the inductive step implied by hypothesis

However this is deductive reasoning

So Galois purposed the framework of group theory and later mathematician work on it to extend the theory into Galois theory and modern algebra. These are abstraction to abstraction that’s deductive reasoning (I personally think it this way)

[rocky terrace]

[analog lynx]

can someone pls explain this so i can solve it

[wide crypt]

To ask for mathematics help on this server, please open your own help channel or help thread. See #❓how-to-get-help for instructions.

[agile hollow]

What should i say

• Every discrete space is a Hausdorff ...
• Every discrete space is the Hausdorff...

this question is kinda related with english, rather than Math

[safe harbor]

first (you can remove the a though, like in the image, "every discrete space is Hausdorff", or "every discrete space is a Hausdorff space")

what would "the Hausdorff" mean?

There isn't a unique Hausdorff space

[unkempt quarry]

What is written is fine, Hausdorff is an adjective so you can just say the space is Hausdorff

[agile hollow]

This makes a lot of sense

[agile hollow]

Noted

Thank you Capybara and Chmonkey

[safe harbor]

chbara

[unkempt quarry]

Champybara

[agile hollow]

[cunning totem]

Thinking about the space