study-discussion

[viscid zenith]

what is the most efficient way to study for test

[cunning totem]

Cheating on the test by learning or memorizing all the material so you know all the answers

[safe harbor]

The most efficient method is to not study. This is by far not the most effective method though.

In seriousness, what works for some people won't necessarily work for you and vice versa

You need to try different things and figure out what works for you

[unkempt quarry]

the space is just the 1 point space cuz it represents the identity functor

All spaces obtained by pulling back the point

😱

[safe harbor]

the wedgie is the pullback of pants

[viscid zenith]

You ain't sleeping well tonight

[viscid zenith]

Good Capybara 👍🏻

[cunning totem]

I don't sleep well most nights!

[viscid zenith]

i can see

[swift tartan]

nG, do you teach classes yet?

Prof nG would be goated

I guess to make this relevant, is there something you see amongst the ugs that you recognize or wish they knew sooner @cunning totem

[cunning totem]

I have taught classes before yes

[viscid zenith]

Professor nG

[rocky terrace]

Advocating for cheating?! Mods ban this man

[viscid zenith]

i agree with Neamesis

[vernal forge]

Hello. Is it possible to release a scientific paper without a degree?

[viral osprey]

You can put any papers you like into the world. Whether or not it will be correct, interesting or taken seriously is a different matter.

[coral acorn]

post it to tiktok and ull get the most conversation about it

[limpid sinew]

Hey dooter!!

[swift tartan]

Yeah i’ve seen and heard of it happening amongst a lot of different levels but you basically would need someone to vouch for your work by the end of the day

[swift tartan]

hs students usually work in labs or at those math camps or with a professor through chance sometimes; otherwise undergrads have chances to be published through REUs or labs as well

Some universités also have in-house research opportunities which also have a chance to be published

What’s most important to note is that you nor the professor choose what gets published on a journal by the end of the day though; it’s really up to the journals and the reviewers themselves

so i guess you can write a paper and send it over but it probs won’t even be looked at if you didn’t have some background or credible vouch bc who knows how many other people are doing that

[limpid sinew]

I'm studying a stats and probability textbook. I have my notes from a stats class that I've taken in the past.

The variance of a population equation in the book does not have a square root sign around the entire equation but my printed teacher's notes do. I'm confused.

I can post pics if needed. Help!!

[rocky mauve]

The book is correct; your teacher probably was referring to the population standard deviation

[limpid sinew]

I think I got it now. I haven't done this in awhile and am reviewing the basics again. I'm having a hard time calculating sample variance correctly. It's fun and interesting but tough.

Are you a math major?

[rocky mauve]

I was a math and economics major in undergrad, now a statistics masters student

[limpid sinew]

Oh that's cool. I'm struggling with this basic stuff but I'm learning it just for fun.

What do you want to do with a masters in stats?

[torn olive]

You'll probably get better help in the future in a probability channel like #probability-statistics + also posting specific pictures of the equations from the two sources in question

[rocky mauve]

Mostly to get a job as a statistician, but also dip my toes into academia

[limpid sinew]

Oh that's cool. I think I'd like to be a statistician too.

[verbal wyvern]

What type of math is good if I want to be an investment banker

I want to study accounting in college

[near timber]

i mean, isnt the college supposed to teach you? i guess it depends on the country and college specifically but for me i think you basically didnt need any experience with math to start the bsc, not even high school math really

[verbal wyvern]

Im pretty sure it is

It depends on what you do but some of them manage money for companies

One small mistake and you’re gone

Im not really an expert on business yet

I want to learn before going into college so I can have some experience

Im still debating if i should be an investment banker or a different business route

I want to get a degree in accounting

Not really

My dad is a facilities health manager or smth

I don’t remember what he told me

No, but he’s friends with the owner of Willis lease finance corporation

Alright

Thanks for the advice

[tacit sapphire]

For studying finance related mathematics like stochastics, beyond measure theory what else is needed

Stochastic process? Is it to do it immediately after a measure course?

I kinda see past exam quite different than the notions I learned from measure theory though. Or maybe they’re weird radon derivatives 😵‍💫

[steady wharf]

just to clarify: investment banking and investment banks are two different things. investment banks do have operations facing the market (for example sales and trading or asset management) and you may need math there, but in "investment banking", or IBD (investment banking division), you don't.

[cyan marsh]

How long are y'all able to focus for until you get distracted?

[glacial raven]

15 min, 30 min, 45 min, or 1 hr on a good day

[tacit sapphire]

Usually an hour?

I study everyday for an hour or so and then probably just on social media already 🫣

[cunning totem]

sometimes like 30 minutes sometimes like 12 hours

[stoic meadow]

Dépends on the subject

Random uniteresting calculus 30 min, things like algebraic topology about 4-5 hrs

[limpid sinew]

I studied stats the other day for a few hours. 🤓

[swift tartan]

i spent 10 minutes studying and i switched to discord to converse...

i guess thats how long my attention span is oh god

this is why i dont have social media on my phone except discord, but i dont even have youtube. if i needed to that bad, just watch it on my laptop

its helped me be more productive esp in the morning; i watched this video which is kinda explicative at points, but it was basically describing what i was doing to a degree, but the youtuber had like science and research tied into it to min max productivity

actually changed my life

if you want to find it search ||dopamine loading by matthew smith|| but be warned he does talk about explicit content but its a pg video of him drawing graphs on a whiteboard. so doesnt show anything explicit

also on youtube

If it isnt obvious, i try to wake up early in the day so I can do whatever studies i want to do in the morning before I go to work or if i have classes etc etc. once media gets involved, its hard to switch back

[main cliff]

I am the same depending on my mood and state of mind

[odd parcel]

Im preparing for JEE Mains+Advanced
recommend me a physics book by analyzing me from the following

I love maths and so on problem solving
I scored 93% in GSEB 10
Book --- Advanced + Mains
I have a teacher that can help me solve the problems and questions

Book can be-
Physics Galaxy
DC Pandey
IRODOV(i dont think im capable of)
HC Verma

i care about questions not concept in book
only 1 book
im in 11th grade

[cyan marsh]

Tao's Analysis I book is fun because I've never felt so satisfied proving multiplication on N is commutative

[raven kindle]

agree

[tacit sapphire]

For math major’s study presumably first year undergraduate (they allow me to do third year if I complete everything included in the syllabus of 1 and 2) is their proof’s rigor as high as the measure theory course?

I only had done measure theory before at an actual math department but things change… I kinda want to finish everything? However we have selection system so we choose course… what course to pick to ensure the whole joy of it

Tasks are not heavy but curious which is more interesting way to pick courses.

• introductory analysis
• Complex analysis
  -Abstract algebra- Linear algebra (abstract algebra lasts for half a year)
  -Elementary combinatorics
  -Measure theoretic probability (not sure if they allow to enroll since I would be assumed as first year and requirement for this is being at least 2nd year. though but I have grade sheet for measure theory which satisfies their requirements)
  Fourier analysis?
  Kinda want to do a bit more abstract stuff to see big picture like functional analysis? but this is 500 course and measure already nearly impossible for me last semester but I turned out quite beneficial in general way of thinking abstractly.
  Or maybe topology? (General won’t dive anything into metric)

I have also very weak foundation in computational skill too in particular evaluating integrals (non-symbolic) and massive matrix operations too.

I really find it fun to do something maybe just one subject super abstract so I can ehhh soak into my brain 🫣 so I kinda want to do a functional analysis (this course uses functional analysis authored by Rudin) course it would start in spring and I wonder what other knowledge I would need beforehand and I have approximately half a year for prep, since other subjects aren’t heavy and intro analysis is probably gonna be fine
Wow I actually got in… the measure theory course most of the analysis stuff I have already developed only need to revise and refine.. so maybe I’ll dedicate to this one instead of ultra harsh study like functional analysis. So I actually can master the measure theory instead of only knowing theory.

[swift tartan]

i took abstract alg before lin alg, its not unheard of but def not common. i just kinda wanted to get ahead, and tbf algebra doesnt really intensively need too much lin alg because you learn the concepts anyway. when it comes to groups (i did rings and fields first sem, then groups and galois). Id saying having that taken abs alg class first, really made me feel like i had a better understanding and intuition for concepts in lin alg which was really nice. I assume youve taken a proof class because no abs alg class goes through the basics as ive ever heard. take this

Complex analysis and real analysis are both swappable. Id say for grad schools ive been told real analysis is more of a priority for pure maths, and the former for applied. A good friend of mine got rejected from some grad schools due to not taking real analysis. And another for not completing both semesters of algebra. can take this.

Topology can generally be taken with some introductory analysis course, but ive seen some do some analysis proofs in our intro to proofs class and they went straight to topology. it just depends on how good your knowledge of basic analysis proofs are. It isnt required to take full real analysis for this. up to you; skill dependent.

Elementary combinatorics, idk what your uni is to qualify that and what the syllabus contains. if it says elementary, maybe its meant for first and second years id think. so maybe?

For Measure Theory, we actually have a grad student in the dept who took measure theory in their ug before ug analysis. imo i think thats kinda insane. generally measure theory is built ontop of analysis, and ofc it does extend into probability as you have mentioned. It sounds more of a 4th year course for a ug and even that is pushing it. Its generally a grad course in most unis but i understand some unis do also bring it down a lot of notches for that. Example being in my uni diff geo without analysis. tl;dr dont take measure theoretic probability.

Fourier analysis is generally built ontop of analysis and PDEs.... so if you have that then thats good to go. dont recommend it early on.

Functional Analysis, ive heard it more from the applied maths students and they were only able to take it after taking grad real analysis. I assume 500s+ is grad courses so id say no. tl;dr hell no.

[swift tartan]

I say all of this to also explicitely state. No one can stop you from doing what you want in uni, esp if its a relaxed math dept like mine where there isnt really a lot of measures to prevent taking upper level classes. Ive just waltzed into taking grad classes even bc we dont even really check for permission of dept here, its crazy compared to other depts and majors.

But, burnout is real. And I personally was really ambitious too when I first started which I sometimes wish I could have taken it slower. I worked throughout uni, did research, and also still in a relationship since first year ontop of my math courses and gen eds. Yeah I actually do have a social life, but once burnout hits.... it hits like a truck. My dept has professor mentoring program and my mentor was just like "meh i dont recommend it but thats up to you and your abilities". and having done exactly what you did, sure i did fine and great in my classes, but i did eventually go through hell during burnout.

Also many math majors are computationally weak in the pure math field (as ive seen). Its kinda a running joke in our dept (maybe beyond). "Im good at math, not arithmetic." Yes, im still a math major still taking math courses but I slowed down considerably. I also added a second major in CS after a convo with Loch here, led me to reconsider my goals and ambitions and also considerations for grad school

Also the person who took everything grad lvl as a ug is insanely brilliant, and his notes also get shared around in this discord pretty often from what I see. https://dzackgarza.com/

If you want to follow through your ambitions and be successful, you need this haha, but also having a good work ethic and setting priorities. I went out on regular dates, partied with friends, jobs and research, ontop of all of this

so thats that

[swift tartan]

@worldly rune cc the last part of that block. hope you dont mind the tag, but you did really change my perspective for what I wanted to really pursue in life due to being narrow-sighted/tunnelvisioned. helped recognize many more paths to get to my goals as well, ofc still in research lol

if you dont recall, we talked about pqc

[worldly rune]

isnt this your friend @cunning totem ?

[swift tartan]

i was called a friend by nG?

[worldly rune]

are you zack garza

[swift tartan]

Oh no lol

I wish

Hes from my uni

he just graduated from his phd

[worldly rune]

sure, hope it works out for you!
this isnt too dissimilar from my own path and im now a researcher in cryptography so 🤷

(on reading more than the last paragraph, i wasnt this cracked lmao)

[swift tartan]

honestly i am so thankful for my partner for actually helping me do this. they are older but also pretty studious ofc not to the same extent as me. if it weren’t for them i probs would have crashed and burned by the end of my first year or second at the most

kept me sane enough

[cunning totem]

lol lmao

[cunning totem]

Ah glad to hear that he graduated we both started the same time and I graduated a year earlier

[swift tartan]

Yeah it was nice and i’d pop by Boyd occasionally at like 1/2 or even 3 am and he’d be there

it freaked out the first couple of times

[cunning totem]

Oh jeez

[swift tartan]

i’m waiting for the preprint still tho

[cunning totem]

Lmao I once slept in Boyd because I locked myself out of my office

Say hi to Gary for me if you know him I roomed with him the last year I was there and I miss the cats very much

[tacit sapphire]

Thanks I should be more cautious with the choice though the transfer actually might delay my graduation for a year that’s why I felt I want to make it very busy 🫣

Let me read it thoroughly

[swift tartan]

Gary? Idk if we are thinking of the same person

iliev?

[cunning totem]

One of the older topology students I assume you’re at UGA haha

[swift tartan]

oh i didn’t know there was a grad student named gary, i think i’ve seen them in passing

[swift tartan]

yeah i am

I stopped by your office once during my burnout 😂

that’s how i got introduced to this discord actually

[cunning totem]

Oh that’s right I remember you now

I am a postdoc in Stockholm Sweden now and am currently on the tail end of a Prague/Vienna/Budapest vacation

[tacit sapphire]

I did measure theory for many stupid reasons becasue I had a bet and I skim many textbooks book too. I wanted a study for measure theoretic probability is kinda that I wanted to preserve what I learned due to highly abstract nature of measure theory if I don’t apply it I will forget it (it’s hard after I passed the final to continue to do massive exercises since no tutorial anymore)

And I invested like massively into measure theory, for it I studied (fast forwarded) basic analysis 3 books of them and did (primarily) the problems

It would be very wasted if I actually forgot this.🫣

[swift tartan]

gotcha i had assumed you were a first year, was i mistaken?

[tacit sapphire]

Second year Econ but they probably assume me first year

[swift tartan]

ohhhh gotcha

Dang you left proper game theory

[tacit sapphire]

And if I accumulate enough points i graduate one year later instead of 2

I kinda don’t understand how hard will it be the measure probability it’s a 400 course like measure theory itself

Which was insanely painful already

[swift tartan]

our grad lvl probability class is measure theoretic iirc and i’ve heard it’s difficult but also a qual class which means it’s a lot of work

not as bad as real analysis tho

[tacit sapphire]

I took measure theory without prior enrollment of real analysis 🫣🫣but I kinda am good with calculus somehow

[swift tartan]

the math major is generally a really small major in terms of requirements

[tacit sapphire]

The book I read wasn’t profoundly complicated compared to concepts I learned from measure theory but the probability part is a bit alienating

[swift tartan]

you’d be able to finish the major in a year and half realistically after you got through the basics calc and diffeq

this is also by only taking 2-3 per semester

[tacit sapphire]

The prof and tutors took care of me since clearly I was clueless and not graduate 🫣🫣

There are other courses though

I struggle a lot with algebras..

[swift tartan]

i should ask for clarification on what kind of algebra do you struggle with?

[tacit sapphire]

I kinda felt bad somehow so was insisting on parallel transfer but it turned out to be too unrealistic since I am already second year into Econ

[swift tartan]

do you mean abstract algebra?

or just arithmetic

[tacit sapphire]

Linear algebra, I don’t know it felt not right

Like determinant formula it’s proof seem to me harder than dct

Probably as hard as fubini

[swift tartan]

a good gauge generally is how the other students felt about that class

[tacit sapphire]

I never took math major centered linear algebra though

[swift tartan]

if they felt good, then it’s likely you, mixed feelings means it wasn’t the right prof for you, and bad means sucky prof

i see

[tacit sapphire]

So I kinda studied myself

More study more confused and then I decided to do abstract algebra first hoping I can have some insight first

Still hard but not but not insanely hard

I mean I really don’t think I can understand that determinant still and massive normal equations computation, Svd

[swift tartan]

going from computational lin alg to abs alg is weird for me to hear; idk how that would turn out honestly so no advice there i can give

do you know how to do proofs from lin alg?

the main takeaways is really just knowing the diff matrix groups and homomorphisms

that’s basically it

[tacit sapphire]

Depends usually proof are easy but I don’t know much techniques and formalism since stuck by those computation concepts I didn’t dive deep into theory but inner product and norm are easy though I use extensively those representations theorem learned from other course

[swift tartan]

ofc you’d need to actually know lin alg for grad lvl but most ug texts don’t go into too much detail

[tacit sapphire]

Some formalism maybe hard but I don’t know like I barely had any motivation to look after all confusing concepts and I really do see any sense of determinant formula

[swift tartan]

maybe as a self study it would be good enough; i liked it better when i self studied between classes rather than breaks on my own unless it was something i was personally passionate or pursuing

[tacit sapphire]

I just hope I won’t get the progress so delayed

And I don’t actually forgot this measure I recently realized how detached this study from reality and if I actually forget it, my efforts of half year will be completely gone. But still I am a bit scared of measure probability it’s in first semester (it’s funny before I passed this I only thought it was a fancy study)

So coincide with other subjects I barely know difficulty

[swift tartan]

don’t mind the messy handwriting but when the professor lectures , i wrote notes or questions i had in mind that most of the time got answered but usually asked after class or in office hours if it wasn’t

that’s my best practice i can hand down

[tacit sapphire]

So to ask more questions will that help?

Like the questions I don’t know yes

That’s a good habit!

[swift tartan]

uni is kinda more of an investment into dedicated rotating tutors on specific material

[tacit sapphire]

I was almost thinking before the email that I was about to do quantities finance 😵‍💫😵‍💫

[swift tartan]

if you treat them like how you would a tutor, but ofc actually also making connections and having a meaningful relationship

i go to a profs office in my dept to gossip around every once a month

not going to say who 🫣

[tacit sapphire]

I actually don’t know course structure of math… I mean if it’s like that measure one where you have discussion session which is nice actually

That’s nice

[swift tartan]

wait what?

oh no i meant i got close with my profs and continued some of our conversations and engagements even if i didn’t have classes with them

[tacit sapphire]

You should see Econ Prof, they look like rich business man while teaching for little money.. which kinda find funny

[swift tartan]

but also they have office hours and they teach you for a reason and they get paid with your tution money

when you sign up for a class, that majority goes into their paycheck for lecturing

[tacit sapphire]

🫣 that’s so nice

I feel Econ profs are so different

[swift tartan]

i mean it’s usually because they are a business associated or related degree

[tacit sapphire]

They just pretending

If they re rich they’d be gone

We all agree that

[swift tartan]

all of the business college students here are seen as snobbish and stuck up and literally wear suits to class atleast once a month due to presentations; but they are in fact nice

our highest paying professor is in the college of business

[tacit sapphire]

Very very childish indeed

[swift tartan]

iirc they make 500k+

[tacit sapphire]

In particular when some people have unrealistic financial expectation of themselves

[swift tartan]

i’m so lost at where this conversation is leading to?

i’m saying the opposite of you

[tacit sapphire]

Study guide and complaint of economics

[swift tartan]

oh alright

[tacit sapphire]

I mean Econ students are nasty

The profs at my uni maybe have high salaries but if they re Simon’s rich

They’d be gone

If you actually studied economics you know a little how their theories are like

Literally A implies B if not then we add a condition so that A implies B

To be fair I only went to Econ because of money

Now I felt math could help me make more not to mention I like it more

[swift tartan]

i vehemently disagree? idk if you’ve ever read economic theory papers but they go pretty hard. not to mention having a close friend who did math and econ who also did pure math extensive research in the econ dept?

[tacit sapphire]

It depends, if it’s like quantitative theory like modeling or financial market then it’s basically math

But if you say about macroeconomics those opinions can even vary (in some sense)

[swift tartan]

it seems like a hasty generalization though

let’s move to #discussion since it’s not math or study related anymore

[tacit sapphire]

No access

[swift tartan]

You have the studying role so you may need to remove that

[agile hollow]

~~Discussion violets studying ~~

[tacit sapphire]

Is there any nice material to study a bit of measure theoretic probability beforehand? And is it actually doable? I felt so wasted of effort if I don’t constantly practice this measure stuff

[swift tartan]

when you eventually get to the graduate level, outside of the qual classes which are your core graduate studies, the grad electives are usually on a basis of the grad students needs and if someone can teach it. It is almost always irregular scheduling for electives. This is to say, there is no harm waiting a semester or even a year for it

bc of rate of new grad students, you have to wait for classes every other year practically because the new grad students have to finish their cores somewhat, and then they finally want to take the electives in their y2

[tacit sapphire]

It’s more likely I feel those knowledge too heavy to be retained for very long though maybe I will ask if I can take without accounting it to my grade list

I am undergraduate

Like 19 ish

[swift tartan]

if thats case; im going to be a little frank, and completely my opinion, if you are struggling to keep the knowledge then i dont think you learned it great

im 21, a fourth year now

in ug too

[tacit sapphire]

That’s why I felt if I can make it a bit more concrete into my brain 🫣

[swift tartan]

i also dont mean this in a demeaning way, more of a reality check

[tacit sapphire]

That investment is huge in both frame of how long i spent and how much

[swift tartan]

having occasional practice is fine for after a class, or i usually study like maybe a month prior to my classes as a refresher and usually just skim through notes, dont even have to solve problems and then just take the next level

[tacit sapphire]

I just hope it won’t be very heavy so I can catch some measure course

Because I feel really bad I trashed my gpa for the measure theory

[swift tartan]

i mean take that risk as you will, you seem dead set on it; but i gave my warning as did my predecessors

[tacit sapphire]

But if it’s actually impossible

[swift tartan]

what???? idek why you would continue doing that then??

[tacit sapphire]

Then I move on

[tacit sapphire]

Like I got addicted to it

Not like trashing trashing

I was having very pretty grade as Econ student

[swift tartan]

this is also given that bc im ug, i dont have the pressures of actually having to know stuff for research and having to constantly practice it, which is the same boat for you; grad students usually have to upkeep their knowledge from what ive seen. so ug should purely be taking classes for fun with no pressure other than getting good grades

if you are trying to have knowledge for the next level class, its expected that you know the last class somewhat decently to begin with regardless of what class or major

[tacit sapphire]

Okay now i felt a bit more aware of dynamics 🫣🫣

[swift tartan]

that doesnt apply to just math?

dynamics?

like engineering?

[tacit sapphire]

Yes try to ease myself 🥰

So not having to keep something for the effort well maybe I already benefited from it enough

No need extra pressure?

[tacit sapphire]

I think you’re right

I shouldn’t preserve something for the sake of preserving it

[swift tartan]

if you plan on grad school, you will practically have to take these classes again anyways

[tacit sapphire]

I am not that clever for graduate school I think

I feel I am overall very slow and not fluent

Maybe teach at middle school is fun for me. I kinda want to be teachers for some reasons but kids are hard to mange

To be honest I am pretty much the most clueless person I feel there is 😭

All the new puzzles everything, just feel so trivial of myself whenever I see anything new completely destroying the hard built confidence

Imposter syndrome maybe I don’t know

I just kinda like those puzzles for that it’s quite fulfilling after failing like hundreds of times which is probably bad I think… I barely made thing correctly in one go

[swift tartan]

i think the best advice i can give you, is attain some mathematical maturity. Wiki Link https://youtu.be/zHU1xH6Ogs4?si=B0P4u4XCwe_LDfKj

This is a video ive seen in the past, idk who sent it in here, but its the best talk i have ever seen

its not boring at all

[tacit sapphire]

I’ll watch it after the puzzles and thanks so much 🥰

[dire eagle]

@tacit sapphire obligatory shill

[solid venture]

Yes I agree. This is my issue with my programs(CS) math classes. They leave out the proofs entirely and it feels like you don’t arrive at a deep understanding.

Ahem. I had a teacher which was an alumni of the same program. Dude barely understood algorithmic complexity. Vaguely remembering having done some Big O stuff.

[swift tartan]

dang

tbf, if they were a lecturer they usually dont touch the math side of it all after they finish their phd

professors are those that are intertwined with their fields and research and most unis and colleges only let professors teach the classes they are somewhat intimate about

on the otherhand, lecturers are usually given lower level classes and sometimes upper level to fill in if no professor is available

[solid venture]

Should have mentioned this was high school.

[swift tartan]

oh whoops

[solid venture]

How do you deal with burnout? Atp where your cognition declines.

[swift tartan]

cope

[tacit sapphire]

Though it’s actually nice to dive into abstract it’s making things natural more. Like phrase everything into topology (those from intro analysis) I took advice from ousider and I feel the new angle allows me to see many I couldn’t see so reading become more of a pleasure

And I kinda learned this skill of latex due to extensive homework

How to write proper mathematical proof in detail

So even i eventually forget I probably won’t find it wasted 🫣

[solid venture]

You mean latex formatting?

[tacit sapphire]

Everything inside the file is my own work

Independently done

You won’t find any duplicate since there are some mistakes

[swift tartan]

realistically, i largely think a huge part of my burnout was due to having unhealthy routines. once i started getting rid of those like doomscrolling or waking up an hour earlier to just doomscroll at 5 in the morning bc i technically didnt have work yet.

instead i could replace that with hobbies that are healthier. An example of one that is unhealthy: I stopped playing games like after first year bc i was addicted honestly, but occasionally on breaks id play videogames and then proceed to play them throughout the night. this is obv not healthy.

Instead, I could be doing math, or working on my computer science portfolio, reading actual books (i got recommended a lot of russian literature for some reason and philosophers), or even math textbooks. you just have to go back to doing things that interest you while you still maintain life. in a way, i know this is def too far in the future, but for a general person reading this, you cant just crashout in your career sadly. you have to wake up and do your job by the end of the day regardless of what it is, (i absolutely hate those talks and personas of people saying "just step away and take a break").

[solid venture]

Yeah I can relate to that. Unhealthy routines or expectations can be detrimental. I think burnout instigates some kind of forced reset of said circumstances.

[tacit sapphire]

Almost never felt burnout though

[ruby wave]

interesting

[solid venture]

In some wierd way, stress accumulates, and at some point get burnout.

[ruby wave]

For me it's a combanation of laziness, comparison, and jealousy

[tacit sapphire]

Maybe I’m too clueless to feel stressed🫣🫣 I mean dumb people always feel happy

[ruby wave]

no matter how hard you work you see other peoples accomplishments, while you just barely miss your own, that can screw up your mentality

eventually you overwork yourself and fizzle out

[tacit sapphire]

I often felt the other way around I felt happy those did better than me kinda analyse their pattern and do

And be fair I am insanely lazy

[solid venture]

I think the trick here is to embrace a set of values/mentality that prompts you to be happy for their sake. Jealousy is after all considered a sin in Christianity.

[ruby wave]

well, then you are what I strive, I only see that it could have been me

[tacit sapphire]

After booming some Econ subjects I do feel insecure though

But that’s a bit different I just got more desperate so I tried to force myself a bit. I chose it so I fix it

I still do sports and different things

I felt some of my schoolmates are too cruel to themselves I couldn’t imagine that mindset..

[tacit sapphire]

Yes I mean if I don’t do well it’s not their fault, everyone has their imperfections so I will probably forgive myself first and see what I can do to improve, besides the success of other is always better the failure in anyway..

There isn’t anything that is more awful than failing but certainly not the success of other makes it worse.
It’s quite predatory to think the study is a zero sum game, people should be happy for the success of all including themselves and others and feel sad for failure for yourselves or others

[solid venture]

In some sense you do indeed compete with your peers. Who gets internships etc. But in a more grander scheme their success probably benefits you. Maybe they are fellow citizens paying taxes for the good of society. Or maybe they use their skills to improve the world. We all live on the same planet, what if aliens attack?

[tacit sapphire]

Yes, but competition is not that you should feel happy for other’s failure or vice versa. It’s more of how to think what fits you or what makes you better. Being blind never makes you better

Competition isn’t a zero sum game per say, we compete one fails, one feels sad one also learns how to improve, it’s meaningless to feel bad for other’s success or feel happy for other’s falling.

I genuinely find it okay if other calls me dumb or something, a bit rude but okay; since I genuinely find myself a trivial person among all the study or things I have seen. All the coursework. I would happily accept the loss from the exam despite feeling insecure

Again this is just my personal opinions

[main trail]

Is spending a. Day on a single Ra problem normal ?

[vocal sedge]

Random question:

Can someone explain the difference between f'(x) and \frac{dx}{dt}

[scarlet arrow]

#❓how-to-get-help

[vocal sedge]

Mb sorry

[scarlet arrow]

Nw, welcome to mathcord!

[tacit sapphire]

Really depends on the question

Just don’t waste all your time when clearly you mess up definitions

[swift tartan]

honestly depends on at what level

for a grad lvl RA class, yeah sadly (im not a fan of RA )

but ug, likely chance like how Emma stated, you missed some definitions

Most of the times with proofs, you could literally scroll back through the entire chapter and construct a proof using either the proofs used in the proofs of the thm, or used or make a proof that utilized the theorem (intentionally dense as a tongue tie)

but you get the idea

They do this intentionally to promote you reading through the proofs and theorems on your own to facilitate you learning content and actually remembering

because if i had to read the same proof 5 times for just one hw, or the thms again and again; i better remember that by heart by the end of it

[tacit sapphire]

It’s often useful to completely reconstruct everything I personally feel, this way you can rephrase things in your own terms which is helpful

I never find language to be less powerful than any technique, a simple restatement of definitions allow you to see things in different angles. So I agree definitions are often good enough

Like outsider often says, redo the entire book for once..

[swift tartan]

reconstruction is fine as long as it has the same functionality and purposes, i see a lot of early ugs make a mistake in the proof tho (i tutor early ug classes until intro to proofs as a side hustle)

[shell wasp]

hello

so

could i tell u a little bit about my math journey

[tropic jetty]

!da2a

[wide crypt]

No need to ask “Can I ask…?” or “Does anyone know about…?”—it’s faster for everyone if you just ask your question! See https://dontasktoask.com/

[tropic jetty]

share ahead

[shell wasp]

so i graduated high school in like 2022

but like during high school i didn't rlly care so i got a d in algebra 1

a b- in like geometry

i dont know an a in algebra 2 i dont know what i got for precalc maybe a b

so basically i was coasting by and also i never took notes so i forgot everything

[tropic jetty]

is there more?

[main trail]

the question was that any open set is the union of countably many open intervals

[main trail]

RA1, UG

[small salmon]

If we take a counterexample, consider the open interval (0, 1) where the numbers are drawn from the reals. Consider the set of all intervals (a,b) which are open intervals drawn from this set, these are {(a,b) | a, b ∈ (0,1), a ≤ b}. The size of this set is uncountable, and the union of these sets is (0,1).

[main trail]

Oops

I meant disjoint open intercals

[small salmon]

Over ℝ? Or over a general topological space?

[main trail]

R

[shell wasp]

hi

[dire eagle]

you had a good start in #real-complex-analysis, did you not continue with it ?

you correctly spotted that for each point x, you should take the union of all intervals in your set containing that point, in a way building the biggest interval V_x (within your open set ofc) containing x

this is a good start, think about how to proceed

[main trail]

I did

But it took me the better part of yesterday

[viral osprey]

Do you need disjointness?

[dire eagle]

easier said than done tbh, teaching made me realize that even simple stuff can take a long time to do depending on your background

[viral osprey]

If not there's a pretty easy way to do it.

[main trail]

Yeah, got that too

[viral osprey]

With disjointness the maximality shit you're doing is the only way I've seen to do this.

[main trail]

My friend came up with an equivalence relation way

[viral osprey]

That's the same idea

[main trail]

The issue is taking a long time makes me feel I'm not cut out for maths

[dire eagle]

taking a long time is normal, as long as your presistant

im one of the people who also either solves something in a few minutes or spends a really long time to do so, but you just gotta push through it.

you dont need to reinvent the wheel really, as long as you keep practicing and improving yourself, you'll become really good at math

dont be harsh on yourself, if you like doing math then you'll be fine 🙂

[main trail]

Thank you

[dire eagle]

the only people not cut out for math are those who hate doing it (and i guess if you have some severe mental disability)

[brazen mist]

I don't

[swift tartan]

in what way?

practice

[sick raft]

more often than not, unless I've seen it a lot of times (teaching the material or solving a lot of problems involving said stuff, for instance) i usually don't remember. what i can sometimes do instead, though, is "feel my way around" due to experience/mental connections i've built up in the past and land on the results after pondering a bit

tl;dr: practice like already mentioned

[brisk widget]

Can someone explain me an simple French exercise

That tell me -30 is a bad answer

But I dont’h exercise why

[tropic jetty]

1/10^-5 = 10^-(-5)

[tacit sapphire]

Find math too abstract and hard how to make it more interesting and less abstract 😵‍💫😵‍💫😵‍💫

Do they earn massively?

What engineering disciple earns the most

I really want to be good at math though, despite it’s like an annoying gremlin that made me almost having no time to rest, can’t read stuff properly due to exhaustion.. I do find it a game however it’s just constantly so hard

[storm jasper]

Who

Who’s that

On a more serious note, are you studying abstract alg

No

Guess

idk

[tacit sapphire]

I am just a bit dumb but it’s fine math is fun🫠

[storm jasper]

Wait so wat do you wanna do

[limpid sinew]

Why is calculating sample quartiles in stats so confusing? 😥

It's so interesting but it's hard.

[silk thistle]

Yo

People

I need a help

I've test tmrw

I've to complete 9 exercises

Of trigonometry

Along with theory

What could be the best way to do so

[brazen mist]

Study for it

[silk thistle]

That's what I'm asking

How

[silk thistle]

You sins will be counted btw

[glacial raven]

Study for it

[silk thistle]

:/

Bro fr?

There could be a reason why I'm asking that

nvm

[coral sleet]

@silk thistle welcome to the mathcord!

[silk thistle]

Thankyou higher you always welcoming people

[coral sleet]

well... if you haven't already studied for it, I suggest doing so now

there's not much else to say beyond "practice a lot"

[silk thistle]

sometimes stuff are very simple and humans complicate its alot

This applies to me i guess

[silk thistle]

Thankyou higher

But I'm confused about where should i study theory from

The books language is always kinda you know

not always but mine is fr

[coral sleet]

there're lots of good resources on the internet

Khan Academy and The Organic Chemistry Tutor have lots of videos on this material

[main trail]

just wanted to run past a few possible course lists by y'all as I have to enrol soon :D

1. Real analysis 1, Algebra 1, Probability, Differential geometry of curves and surfaces , micro/macro econ

2)Real analysis 1, Algebra 1, Probability, Differential geometry of curves and surfaces , operator theory
3)Real analysis 1, Algebra 1, Probability, Differential geometry of curves and surfaces , some sociology course

So my concern is 2 will be too heavy

but it also sounds very fun :D

don't know what to do

The course I'm most worried about is RA1, but

[whole wing]

Is this for a semester (so simultaneous) or a year?

[main trail]

a sem

[whole wing]

Hmm, feels weird doing diff geo without a bit of RA and LA first

[main trail]

I've done La

[whole wing]

That's good

Yeah idk this just feels like one course too many

For a sem

What's the syllabus for diff geo?

[glacial raven]

Is micro/macroecon less heavier than operator theory?

[main trail]

DG of curves and surfaces

[main trail]

I did most of this in 11th and 12th

now it's just with calculus

[glacial raven]

(1) seems nice then imo

[main trail]

yea, but OT is just idk exotic sounding

[glacial raven]

True dat

Is there any option to pick OT next sem?

[main trail]

maybe in sem 5 but time table clash problems

this time no clash

[whole wing]

Yes that's the name. I was asking for more details, esp the pace

[main trail]

Uh, we'll be following pressely

one minute

I had asked the prof

[brazen mist]

Are these lecture notes?

[main trail]

the contents of the book we will be using

there are 2 more chapters, but we mostly won't do those

[brazen mist]

which one is it again?

[main trail]

Pressley

We'll also use Do Carmo?( for reference)

idr how it's spelt

[brazen mist]

Do Carmo

[brazen mist]

I don't know this one

[agile hollow]

DG

[main trail]

Does the content seem good though

like is it missing anything

I don't have a copy

[brazen mist]

Table of contents looks good

[main trail]

I'm using Tapp personally

[brazen mist]

Ah okay

You have seen nothing

[main trail]

if I had to chose b/w this and an introductory operator theory course, which would you suggest

[brazen mist]

you know I'm an advocate of differential geometry, so pretty much biased

nothing against operator theory, that's great, too

[main trail]

one good reason to take this is that after this 2 more geo courses will be offered such that it doesn't clash with my time table

Introduction to manifolds and riemman geometry

[agile hollow]

manifolds mentioned

[whole wing]

Yeah diff geo is very important. If it was possible to do everything one sem later that might've been a good idea, but otherwise go for it!

[night osprey]

any tips on how to increase creativity and stop tunnel visioning

):

[storm jasper]

Well

It’s simple

[night osprey]

?

[storm jasper]

Gm

Okay

[storm jasper]

Well

What are you thinking about

When solving problems

[night osprey]

yes

[storm jasper]

??

So

[storm jasper]

So what

[night osprey]

for example

when solving problem, how u realize

those insane manipulations

no

or when a problem is simple

but ill start using some questionable techniques

how do u not tunnel vision

[storm jasper]

Well

Think about the foundations you know about

Stuff that relates to the problem your trying to solve

You just need to think of the things you’ve learned before hand

[storm jasper]

@night osprey

[night osprey]

what if u have a lot of possible thoughts

[storm tide]

Try all of them and see if one works.

[storm jasper]

Yeah

[cinder steppe]

so ive been trying to keep big lists of interesting examples (as everyone encourages) whenever im trying to make sense of kind of object like, currently, schemes…

but i recently had the realization that equally importantly, one should keep lists of interesting examples of maps of objects, which there unfortunatelt seems to be much less of a culture for

[night osprey]

😭

how abt under time constraint

[storm jasper]

Well

Just do it

Not under time constraint first

Prep

And then you’ll be more used to thinking

And just generally be creative, ask thought provoking questions to yourself

Well we know you don’t k ow it

I’m lazy

Still am

I’m lazy

Okay

Cool

This is false btw

Knief stop lurking

[wise cedar]

no

[storm jasper]

How

This sounds like you listen a lot to Andrew Tate

It’s false

Sounds rly weird

“Diffused thinking”

Just ask questions and think while using your fundamentals to your advantage

Ig

[main trail]

chat, I've finally decided which courses I'm atking next sem

[main trail]

option 2

[glacial raven]

Gl

[main trail]

Thanks!

@wheat ether

[wheat ether]

Uhhh

[misty mountain]

ok this is not really operator theory

[wheat ether]

This is just a linear algebra 2 course to me

but yeah you dont need real analysis for this

[main trail]

huh, I suppose we will focus a bit on operators in that case

[wheat ether]

and also you should take it

[main trail]

but mostly LA?

[main trail]

I am

[misty mountain]

so this is a terminology thing

operator theory, roughly, refers to studying this stuff in infinite dimensional spaces

so even though "operator" is used as a word, it's not really referred to as OT

[main trail]

like this course historically did cover infinite dim vector spaces

[crimson elm]

Linear algebra

[misty mountain]

but the thing is, without like several courses of analysis, it just can't do that beyond a few basic propositions

the techniques to do interesting things in infinite dimensions are just not there

[main trail]

Is it not possible to devlop them during the course?

[misty mountain]

not in one semester

[main trail]

I mean tbh, I will be taking FA in like 3 sems from now

[crimson elm]

You can self study ig

[misty mountain]

like, my university has one of the strongest operator theory departments around

[main trail]

I'm still doing single var toplogy

like toplogy of R

[misty mountain]

our operator theory course has the following prereqs: real analysis 2->measure theory->functional analysis, complex analysis, ring theory

https://uwflow.com/course/pmath810

[wheat ether]

u can certainly give some examples of infinite dimensional vector spaces but they have basically no interesting structural properties without imposing additional topological/analytic structure

[misty mountain]

not to burst your bubble btw

[main trail]

Measure is an elective in 3rd year here , and FA is usually only taken by PhD students though I can take it in year 3 or 4

[misty mountain]

this course is full of very interesting things that you should 100% take

and are useful in many contexts, both operator theory and beyond

but is really the finite dimensional prereq and not the subject proper

[main trail]

fair enough

[crimson elm]

Algebraic geometry when?

[main trail]

soon /srs

[misty mountain]

may I ask what country?

[main trail]

a prof who specialises in that just joined my uni

so maybe in my 4th year?

[wheat ether]

i think the distinction is important insofar as like

[main trail]

India

[crimson elm]

General topology is an elective here. I could graduate without pointset

[wheat ether]

"operator algebras" is a relatively specialized subject that most undergrads wont touch

whereas the course you listed is like

[crimson elm]

Linear algebra

[wheat ether]

very essential linear algebra that absolutely everyone serious about mathematics should know

[main trail]

I think a lot of this is covered in LA2 for me

I think the syllabus may just be old?idk

[misty mountain]

hilariously, my university only added a pointset course last year. like 5 different courses just each covered their own pointset prereqs at the start every single time, but couldn't assume you'd taken the other ones to skip it

[misty mountain]

it could also fall victim to the classic "university administrator misnaming a course"

[wheat ether]

my university is normal and has a topology class that most sophomores take

👍

[crimson elm]

There is algebraic geometry but it's taught iff a lot of people are interested

meaning it's a reading course because no way your average undegrad is doing it

[green terrace]

This is not operator theory, this seems more like proof based linear

[wheat ether]

we havent had any sane accessible AG courses while ive been here

which is kinda sad for people who dont know it

[main trail]

I've done proof based LA

[wheat ether]

actually lie one year the classical AG class was good

but another year it was unhinged

[main trail]

my first course was 25 % computations 75% abstract LA

[wheat ether]

we had a scheme theory class when i was a freshman but it was bad

[misty mountain]

fwiw if you want operator theory notes to self-study after you learn functional analysis, here are some freely available ones from a prof at my university https://www.math.uwaterloo.ca/~lwmarcou/notes/pmath810.pdf (his website also contains notes for the functional analysis prereq he is assuming)

[wheat ether]

and last semester they ran an AG class that was like a weird hybrid of classical and scheme/sheaf theoretic AG that i dont think turned out great

[main trail]

thanks!

[wheat ether]

(not that i took it but that was my impression from those who did)

[misty mountain]

i'm currently in the weirdest AG class of all time

[wheat ether]

But we had a cool minimal model program class last semester that i sat in on

that was fun

[main trail]

so this sem my options are LA2, OT, DG of curves and surfaces , maybe graphb theory, introduction to DEs, measure is offered, but don't ahve pre-reqs

I don't think I have the pre-reqs for graph theory either

[wheat ether]

What is the difference between LA2 and the class you just posted

[main trail]

there are a few more, but have no interest in any of them

[main trail]

lemme pull up the syllabus

[crimson elm]

OT seems very specialized for undergrad

[wheat ether]

well they posted a syllabus above and it was just a normal linear algebra class with an odd name

which is why im asking how it differs from LA2

[crimson elm]

If it's that then yeah

[main trail]

Tiis is the old syllabus though

different prof now

[misty mountain]

like I am taking it to make sure i had everything filled in from my knowledge of complex geometry and 3/4-assed attempt to read griffiths and harris, but the prof is the most esoteric man i have ever met (and I am in a math department), and spent the entire course on a combination between geometric topology, modular forms, and projective curves

[crimson elm]

It's just linear algebra you should be familiar with

[main trail]

i'll post that syllabus here when it comes

[wheat ether]

well there is no realistic way that they could do anything other than that without real analysis so

[crimson elm]

modular forms o.o

[wheat ether]

yeah i feel like algebraic geometers like to teach like this lol

its kind of a hard thing because like

classes either end up being wading through months of scheme theory foundations or a mishmash of geometric topics with an algebraic flavor

the former is tedious, the latter does not really teach you much in the way of actually doing AG

¯_(ツ)_/¯

[misty mountain]

yeah, just regretting taking it since it's been so stressful

[crimson elm]

My prof is open for different flavors of AG. He mainly does enumerative but if some student wanted a course where you contrast between DG for example he'd do it

[misty mountain]

mostly with just how he does it

[main trail]

I'm technically due to take LA2 next year

[wheat ether]

This seems like a slightly less sophisticated version of the other course you posted

[crimson elm]

This is linear algebra

[main trail]

this is LA2 , yes

[misty mountain]

my LA2 was just a combination of the 2 courses you posted

[main trail]

I mean I do Love Lin Alg

[crimson elm]

The other one you posted is also linear algebra

[crimson elm]

Based

[misty mountain]

the other one didn't have canonical forms i think

[main trail]

No harm in doing OT this year and LA2 next year I suppose?

[crimson elm]

Yes

I thought you were specializing like crazy

[wheat ether]

If you take the operator theory class you posted there is no reason for you to take that LA2 class

[main trail]

I anyway have to do LA2 to graduate

[wheat ether]

its just redundant

[main trail]

I have no choice

[wheat ether]

if you absolutely have to take LA2 then i would just take LA2 next semester

or whenever you have to if its gated

i guess you probably want to learn that stuff sooner rather than later. idk

[main trail]

I just hope the syllabus drastically changes then

tbh I did get permission to take LA2 this sem

[crimson elm]

Yeah you don't want to sit in a lie theory course and don't know jordan form

[wheat ether]

then just do that

[main trail]

but I also want to do DG , so can't do

[wheat ether]

classical differential geometry is kind of unnecessary anyway

[main trail]

It will be the pre req for manifolds next sem I beleive

[wheat ether]

its sort of useful for intuition building but its not really that important, certainly you should clear LA2 first

Can you get the prereq waived?

[main trail]

I doubt it

I don't want to take a risk

[wheat ether]

F

[crimson elm]

F

[wheat ether]

well you could ask

[main trail]

Eh, the DG course is extensive I'd saay

covers guass bonnett

[wheat ether]

I mean yeah it would be strange if it didnt

but like

its just not really that important

[crimson elm]

Whatever you take just don't forget analysis, algebra and topology

[main trail]

analysis and algbera are copulsory, I will take toplogy soon

maybe next sem

It's not offered this sem

[misty mountain]

if you have room only for the 2 courses, i'd probably go with the classical DG and the "operator theory", then make up the LA2 later. lots of overlap, but then you'll at least have a chill course in your schedule

[main trail]

thanks so much for all the help!

[misty mountain]

kinda sucks to have 2 courses on the same thing in your department

[main trail]

yea, allows me to do reseacrh next year

[crimson elm]

tfw we have 3 linear algebra courses and they all suck

[wheat ether]

we have 3 linear algebra courses and theyre mostly fine i think

[misty mountain]

yeah the union of wai's "operator theory" and LA2 was my advanced linear algebra 2

[main trail]

I wish we had 8 LA courses

[wheat ether]

Not sequential

[main trail]

LA my beloved

[main trail]

one every sem

[wheat ether]

linear algebra, honors linear algebra, proof based linear algebra

[crimson elm]

You take take more LA (representation theory)

[wheat ether]

and math majors just take the latter

[misty mountain]

here we have lin alg 1/2, both with advanced sections. all 4 are proof based, but the advanced sections are approximately intended for pure math majors

[wheat ether]

the first 2 are for like

engineers

[main trail]

I'm a pure math major 😭

Like I could take applied math electives

but nah

[misty mountain]

yeah your LA2 and operator theory are essentially the advanced LA2 section I took

[main trail]

Can I ping y'all if the syllabus changes?

[misty mountain]

go for it

[main trail]

thanks!

[misty mountain]

speaking for me ofc

[crimson elm]

LA1 is computational. LA2 is LA1 but proof based. LA3 is more involved but the truth is they barely cover anything meaningful for pure math students

[crimson elm]

Yes

[main trail]

I should ask for AG in my 7th or 8th sem

[misty mountain]

Delteto what country are you in? the course stream differences are interesting to me

[crimson elm]

Canada

[main trail]

Ah, nice

[crimson elm]

AG super nice

[misty mountain]

Oh nice, same

[main trail]

AG or some super high level course( well super high level for a 2nd year)

eh, atleast I'll have someone from mathcord taking the course with me( the OT course)

[crimson elm]

So far my highest course was an intro to semisimple lie algebra and representations

[misty mountain]

fwiw I don't think AG has to be this mythical beast of a high level course

[main trail]

I mean to ME it does

[misty mountain]

like it's a cool subject

[main trail]

right now

[misty mountain]

yeah totally fair

[crimson elm]

You don't need to do p adic hodge theory

[main trail]

Maybe I'll ask for fractal geometry idk

[misty mountain]

but once you have the algebraic prereqs, it's a pretty fun and natural thing to study

[main trail]

we've had some wild courses offered in the past

[crimson elm]

Classical AG where you do mostly varieties should be natural

[misty mountain]

(I say this as not an algebro, who only begrudgingly does algebraic geometry when the situation demands it)

[crimson elm]

I barely touch varieties

[main trail]

AT looks like something I may do too

If I can get it offered

[crimson elm]

If you can get both that would be cool but if not it's okay

[main trail]

Thanks a lot everyone!

[misty mountain]

if you end up being interested in DG and manifold theory, algebraic topology is a super important thing to study sooner than later fwiw

[main trail]

If I do i'll try to do it in sem 6

like in sem 5 I;ll do rienmann geo

My plan is to also do CA in sem 4

[misty mountain]

fun! hope you enjoy it as much as I did (I became a differential geometer)

[crimson elm]

Yeah Wai seems to be manifold pilled

[main trail]

I like exotic stuff

would it be a good idea to try to do HA too at some point

become analysis pilled

[crimson elm]

For me HA is super important

[misty mountain]

harmonic analysis? I'm not sure what the prereqs at your school are, but if you enjoy both real analysis (up to ~functional analysis) and fourier analysis, you'll probably like it

[main trail]

uh, okay, sounds scary

[crimson elm]

HA, representation theory, algebraic geometry and a lot of algebra

[main trail]

this is just for fun

probably will never do this

[misty mountain]

it's not a bad idea as an undergrad to just take essentially every course available to you in your schedule provided you think you will have fun

[main trail]

I have to do courses form other depst to graduate

😭

[misty mountain]

yeah, everyone does and that's not a bad thing

I mean within the confines of schedule

[main trail]

like I don't mind some courses ( I love sociology), but yea

[misty mountain]

like you don't need to specialize so fast, just see what math is out there and enjoy it

[main trail]

Sorry for yapping so much

[misty mountain]

dw about it

the purpose of conversations is to talk to other people

[crimson elm]

I might take model theory just because of how much illiterate I'm with the topic

[misty mountain]

like I took every available analysis and geometry course in my undergrad, and a decent number of algebra and combinatorics, and still had room to do a minor in CS and quite a few english literature courses

[main trail]

We have a very low credit limit

25/sem

most courses are 4 credit

[misty mountain]

fwiw the word "credit" at a given university is extremely nonstandard

yeah, so like max 6/semester?

[main trail]

basically, but I have to do 1.5 credit courses too( so have to fit that in too)

[crimson elm]

The max here is 5

[misty mountain]

so if you do approximately 3 math 2 non-math a semester, you will certainly get done most math courses at your department

[crimson elm]

You can take more but it's considered suicide unless you know what you are doing

[main trail]

yea, true

this sem alone I'm doing 5 math , will probably do 4 from next sem

[misty mountain]

and have room to take whatever nonmath you need and allocate your schedule to be easier as needed

or even 4 math/1 nonmath depending on how you're feeling/what works

I did ~3.5 math 1.5 nonmath a semester and got done as much as i did

this obviously depends a lot on scheduling and your department, but it's very possible

[main trail]

I could audit a ton of courses

yea, my dept is very flexible

we have like 100 students and 21 profs

[misty mountain]

or even honestly, you could just borrow books on a subject from the library and read them in free time if you don't wanna formally audit something

[crimson elm]

Unironically my favorite

[main trail]

will do that, yea

thanks a lot everyone!

[misty mountain]

nw, enjoy the math :)

[main trail]

last thing, this sounds so cool

[misty mountain]

i agree, big fan (very close to what i study)

out of curiosity, can I see the syllabus for that?

[main trail]

ya

[misty mountain]

ok cool, it sounds like it will closely follow a book of the same name by Wells

very fun stuff

[green terrace]

COMPLEX MANIFOLD THEORY MENTIONED

👀

[main trail]

I just need to find 5 people to get i offered D

[green terrace]

awwwwww

[main trail]

So maybe I can get it later

[green terrace]

maybe!

[main trail]

though profs have taken classes for 4people!

[misty mountain]

if you have friends in your manifold theory or riemannian geometry classes you mentioned

you could shill this to them, people who enjoyed the riemannian geometry class will very likely enjoy this kind of stuff

[main trail]

oh, right

I will

[misty mountain]

(especially if they like complex analysis)

[main trail]

We;ll see if they like CA next year

[whole wing]

Yeah, FA is an essential prereq for actual operator theory

[deep inlet]

I'll be taking a class just like this next semester 🙂

[lusty tree]

The east coast here in delaware have been suffering with endless humidity but it finally breaks for a stunning 2 days early this coming week then it's back to 75-80 degree dew points

I am literally drenched in sweat and haven't even moved

[green terrace]

Virginia is no better so we completely empathise

[lusty tree]

Climate change is making delaware humidity like Florida in the summer for almost 2 months, which shouldn't happen

[green terrace]

Yeah it's terrible

It's like 90-100 here DAILY

Fucking awful

[limpid sinew]

Oohh I love Virginia

[rocky terrace]

How do I shill physics classes to math people? specifically QM 1 and QM 2

[misty mountain]

just say the class is really fun and they should take it idk

[main trail]

Hamiltonians

or smthng like that

[rocky terrace]

I'm cooked

[main trail]

uh question

in RA1, is it normal to not get proofs my myself

Like every perfect set is uncountable

[agile hollow]

Isn't it doable?

Ofc it is time talking, iirc there is proof in Abbott

[main trail]

there is

yea, it's very time consuming

I think I should study nested sets before I do this

[agile hollow]

you can, when i was studying analysis for first time i skipped like half of the book

and maybe thats why i never properly learnt analysis

[near timber]

your RA thing seems very PST heavy

interesting

[agile hollow]

PST?

[main trail]

PST?

Oh, point set topology?

[near timber]

Yes

[split jasper]

you can just skip this result until you have the big hammer of baire category theorem

then it's one shot

that was a joke, don't actually skip it

[agile hollow]

Ohh

[rose peak]

Analysis my favourite!

[agile hollow]

Not the case with me
I like topology and algebra recently

[main cliff]

I think I want to go into the realm of commutative algebra, algebraic geometry, and algebraic number theory....more so on the first one

[rose peak]

Math mood swings go hard

One day I hate discrete and the next I love it

:/

[agile hollow]

@rose peak i guess discussion random things in #book-recommendations isnt a good idea, that why i moved here.
A manifold is a space that locally looks like Euclidean space. For instance earth!
Earth isnt Euclidean space, but if you pick a neighborhood on the point where you are standing. You will find it flat (like Euclidean space) but globally (Earth) isnt Ftal (Euclidean)

i hope you understood this informal idea

i havent started abstract algebra otherwise it would be visible in my name

[agile hollow]

discrete math

[rose peak]

Worst part is when you like the subject more when you have no idea what is happening

[main cliff]

This is very true...I thought I know what algebra is then...I read Anderson and now I felt less certain let alone reading Berberian's linear algebra

[main trail]

ngl, every subejct is fun for like 4-5 months

then you want to do smthng else

[rose peak]

Not necessarily

Maybe for the first week after you understand something its fun

Like you can do so many proofs etc

But then after that

:/

[cunning totem]

[shell wasp]

hi

i havent done math in a good 4 years

i wanna take math 124: calculus 1 with analyitcal geometry

im wondering if khan academy is a good resource like is it enough to get prepared for this class

algebra 1 algebra 2 geometry trig precalc all from khan academy would that suffice

like heres an example of a question from a final

it doesnt seem too difficult

[main trail]

how essential is baire's theorm for RA

also do we basically study $F_{\sigma}$ sets in $\sigma-$ algebra

[mossy shadow]

wai

[storm tide]

Somewhat peripheral. Comes in handy from time to time, of course, (or it wouldn't be famous), but it's not like there's a whole edifice of important advanced concepts that rests on it.

[main trail]

And what about for DG?( I'm taking that course too this sem, so if required i'll study this

DG of curves and surfaces

[storm tide]

I would expect a DG textbook to call it out explicitly if it needs to apply it.

[shell wasp]

hi

troposphere

[main trail]

Do i need to know series to study functions in R

[storm tide]

You may be able to get through a reduced syllabus without them, but I wouldn't recommend it.

(For one thing, they're completely essential for complex functions, and that will be easier to grasp if you're already conversant with the real case).

[green terrace]

It's good to know

[main trail]

Oh

Because we cover it after functions of I remember right

At uni

But I'm self studying

[storm tide]

Just because there's a section heading saying "functions" doesn't mean that nothing else you learn will be about functions.

[main trail]

@crimson elm found a free AG book which only requires a course in AA and LA

Maybe i can get if offered earlier

[green terrace]

Is it Cox Little and O'Shea?

If so, we love that book

[main trail]

Lemme check

[green terrace]

but that book isn't free unless your uni has springer access or something

[main trail]

It's an open access book

[green terrace]

ahh

[main trail]

Beginning in Algebraic Geometry | SpringerLink https://share.google/zhc2Z2bU5YgHmgTLV

[main trail]

Mind providing the entire name ?

Like book title

Question, how bad an idea would it be to stay back an extra semester on purpose

Like there are a lot of courses I want to dp

[unkempt quarry]

Ideals Varieties and Algorithms

[main trail]

Thanks

[crimson elm]

That's cool

[iron barn]

Hey guys, do you have any tips for like calculus. I want to focus on understanding like an introduction to it. Like from scratch

[heavy rock]

Khan academy

[eternal wadi]

Hi guys! I would like to ask those of you who did a phd in mathematics what it's like. What level of understanding mathematics and idependence is expected from you? Was there something that surprised you when you started? What advice would you give for someone who thinks about doing phd in math.

[green terrace]

Sorry, I'd fallen asleep by then, but yes the title chmonkey gave is correct

[main lodge]

Words cannot describe how frustrated I am with study finance

It is always a miracle when i get the same answer as the answer that is in the solutions because they always assume the wildest most unhinged things

This is not cope, this field is just as chaotic as it is to do stock trading at NYSE i bet. Even GPT is trying to gaslight me into believing the problem text is completely reasonable and im the mad man here

The number of prompts ive wasted on trying to make it realize and clear up its contradictions is reaching triple digits. And every time I try to do this it always internally thinks "the user is confused", "the user is mixing up.." etc. goddamn man it has me fuming

But still it's 10 times better than the lecture notes and teaching materials

[main lodge]

Genuinely feels like learning a programming language and the only teaching material is spaghetti code with syntax errors in it

[lusty tree]

how do i study serge lang's basic math because this book is esoteric as fuck

[knotty linden]

I'm about to start the third year of my PhD, the level of understanding of mathematics required isn't that high, and my advisor is rather hands on.

We have weekly meetings and he expects me to try to make some amount of progress each meeting, even if that progress is "I tried this method and it didn't work"

As far as advice goes, I dunno. Learn how to program a computer

[knotty linden]

I have full funding from being a TA

[torn olive]

on paper most TAships are 20 hours a week

at least at my university, it's more like 13-16 hours a week

unless you get stuck with some hellish courses or hellish grading which gets to be over 20 hours a week

and from everyone I've talked to at other universities, this seems to be the norm

on paper 20 hours, usually less, sometimes more if you aren't lucky

[limpid sinew]

I've been reading through a stats and probability textbook and working through some of the problems just for fun. I was doing a little every day but I haven't read any of it since Saturday. I want to get back into it but now its harder to keep motivated. I just want to read novels and relax. Has this happened to anyone else? 😥😢

[tropic jetty]

yes. when that happens i jump fields

[raw axle]

Quick question, I self study math and I wonder how you guys take notes. I’ve tried a couple methods (Cornell notes, quick bullet points of important things, and sometimes just copying down half of what I see) and I’m not sure which is the best in terms of actually helping me learn/understand what I’m reading. Do you guys copy down theorems and their full proofs as well?

[tropic jetty]

i don't just copy, i'll try to reason every step out myself

[raw axle]

I see 🤔

So jot down difficult stuff, and reason through proofs yourself

Thanks I appreciate the help 👍

[split jasper]

mfer pulled out the cornell notes trauma intensifies

[eternal wadi]

I dont take notes at all. I think everyone has different learning style, but taking notes was never helpfull for me. Maybe becouse I have dyslexia and I don't work well with teksts. What I do I just try to understand every step of the proof, but I don't try to remember it. I don't see a reason to do so. But I use flash-card app to remember theorems and definitions. I just write question and then put a photo from a book as an answer. Then from time to time I just go through this flashcards in app as a gamę.

[eternal wadi]

Thank you for an answer. Have you started preparing for phd before you strated? Is programming really that important?

[torn olive]

it really depends on the field

my 2 cents is that if you want to do anything algebraic and or combinatorial you really really should learn how to program

if you want to ever go into industry (software, cryptography, machine learning, finance, etc etc) you have to learn how to program

and I'm going to be real, if you can do math you can do basic programming it really is not that hard

math is much harder lol

[green terrace]

Programming is also quite fun (IMO; obviously biased as a CS major but still)

[torn olive]

I'm mostly saying this based on my experience (since I like algebraic and combinatorial things)

but even like learning basics allows you to make a website and like

every academic should have a website IMO

[torn olive]

I mean learn numerical analysis if that's applicable to you but I mean you should be able to use a programming language or two

the biggest use case for me is being able to compute examples of things, and a large number of examples at that

but like also part of this is knowing your basic data structures and algorithms

knowing what lists, dictionaries, hashsets / hashmaps, trees, and other data structures and knowing how they're used and how they can speed up or slow things down

but also like, idk there's alot of very clever stuff in data structures and algorithms I think most people interested in math would find those things interesting in their own right

[tropic jetty]

i would add stacks and queues to that list

[torn olive]

yea there's alot in the "other data structures" lol

min/maxheaps are also good to know

adjacency list vs incidence matrices for graphs

I kid you not there's probably dozens of english DSA resources and textbooks online

if you do some research, you can find stuff

for algorithms, I really like this textbook: http://algorithms.wtf/

that textbook assumes you know basic data structures but guess what

that webpage lists 4 resources

but personally I didn't use any of them for data structures (I took a course at my UG) but I'm sure if you take a little time you can find more online

but I really like that algos textbook

[tropic jetty]

i actually enjoy studying maze generation and pathfinding algorithms ngl

implementing and animating them is a whole other story though

[tawny estuary]

@young cobalt ioqm marks?

[young cobalt]

was it out of 102?

[tawny estuary]

its out of 100 right?

idk tho

i just found out about it

ts my first time'

[young cobalt]

yeah

[tawny estuary]

no??

[young cobalt]

IOQM is out of 100

[tawny estuary]

how much thn

[young cobalt]

RMO is out of 102

[young cobalt]

75

[tawny estuary]

ohh'

damn

isnt that a great score

[young cobalt]

6 qs, 17 marks each

[tawny estuary]

my friend got 12 in ioqm last yr

[young cobalt]

yeah it is

[tawny estuary]

he said avg marks is 6-8

[young cobalt]

i dont remember how much i got in ioqm what i said might be wrong by like 5-10 marks

[young cobalt]

yes

then again

[tawny estuary]

Can you solve ts btw

The pw guy left in the middle

[knotty linden]

I had proof based mathematics starting my freshman year of college, so in a sense I was prepared for it. As far as a career in academia, I don't think programming is that important, but it gives you nice options

[steady cliff]

have y'all heard of this 'three-sided flashcards' thing

[reef ocean]

no I haven't, what is it about

you mean literally a flashcard with three parts or the AI app that seems to be the first result when searching?

[pseudo cedar]

I personally write chaotically whatever i feel is important on paper and then move the most important stuff into note taking app (obsidian in my case).
i feel like anything more than that is too much since you can always check the book anyway

[tacit sapphire]

How to refine one’s logic? In adjacent to massive amounts of exercises? Like people will have tired moments, is it possible to use that moment to think something to sharpen logic?

[plucky dagger]

What do you guys think is the most effective way to study as much math as possible in a certain time frame?

Because sometimes you can get stuck and have really slow progression or even none.

I'm really interested in hearing your opinions, because I find learning to learn is super important to do any kind of progress in any subject

[split jasper]

dont be afraid to look things up

but dont become reliant on looking things up either

[limpid sinew]

What is the best way to determine how many practice problems to complete? Should I try a few and if I feel good about the concept, then that should be good?

What does everyone do?

[candid berry]

Do a few, see if it seems too trivial. If it is, then stop. Otherwise, you need more practice.

[candid berry]

Never skip them—leave them and come back later. Also, you can consider asking help either here or irl.

[scenic shuttle]

type em dash on google and copy it

only works on pc, right?

oh linux user

honestly I wouldn't use em dash that much unless I'm writing assignments

[scarlet arrow]

On phone you can hold click the - icon

[scenic shuttle]

sometimes I hate it cuz most of professors say it's ai generated btw

[scarlet arrow]

—

[scenic shuttle]

—

thanks ex

[scarlet arrow]

Just use gboard atp

[scenic shuttle]

btw have u done stats

[scarlet arrow]

Nope

Just basic stuff

[scenic shuttle]

fair enough

[scarlet arrow]

Y?

[scenic shuttle]

I just barely started learning about it and I think it's too hard

[scarlet arrow]

Ah, sad

[steady cliff]

https://three-sided.com/search.html

[shell wasp]

hi

are there any resources for me to re learn math

i graduated highschool in 2022 and havent done any high school math since

in other words i havent done any algebra 1, algebra 2, trig, geometry, precalc, or calc at all

from june 2022 to now 7/24/2025

how can i relearn math?

[cursive oracle]

Khan academy I suppose might help