study-discussion

[coral sleet]

I hate to interrupt, but haven’t you’ve been asking questions like this for weeks now?

you’ve been giving advice and resources before

the best way to relearn math is to actually go and do math

instead of constantly asking about what the best way to learn it is

it doesn’t take very long to review all the material you’ve listed; you just need to actually get started

[tacit sapphire]

Why is study so hard

Feel my life is so uncertain 😢

[swift tartan]

why is it hard?

are you struggling on the content material or even getting started?

[tacit sapphire]

The more study the more stupid I felt myself

Insecure

[swift tartan]

i meannn tbh that’s the point

[tacit sapphire]

Unfortunately I am losing confidence as I used to

[swift tartan]

i hope you realize in a nice comforting way; a lot of people in math have some imposter syndrome but that also motivates them to push themselves further

[swift tartan]

why losing confidence?

[tacit sapphire]

Because, I used to plan to finish not only topology, intro analysis revision, abstract algebra and linear algebra during the summer

Now I felt I barely can do those all

And it made me so scared I might lack behind

[swift tartan]

that’s… a lot for anyone to do in the summer

you overloaded yourself

[tacit sapphire]

The product topology made thing harsh for me and again bad mental health

I started to question if I am clever enough

I used to be quite okay for being dumb but Becasue of the new study i started to care a little

[swift tartan]

lol this is funny bc we briefly talked about burnout and i’ve noticed the past couple of days afterwards of you conversing you are describing burnout yourself

[tacit sapphire]

But it’s not burnout

[swift tartan]

i think you might be in denial about being burnt out?

do you know what burn out is i guess i should ask

[tacit sapphire]

I am just unable to keep the progress and a bit insecure

Like you don’t do anything because of stress

Imposter syndrome probably

[swift tartan]

yeah this is what burn out is

imposter syndrome usually just means you feel inferior but that doesn’t affect the work ethic you have

burn out is characterized by having trouble being able to focus or maintaining upkeep and dedication to progress

like you are tired or stressed to keep continuing to do work

i honestly think, bc it’s summer, try to enjoy the rest of it

also even my professors only do one textbook at a time

no one and i mean no one can do 4 topics or materials without having some stress or lesser dedication

it’s better to just finish one textbook at a time that you can understand a lot better rather than half doing all of them

a personal analogy ofc, but everyone who i’ve seen who have done many different topics at once; i have yet to see them finish any one of them

if you feel a little stressed or tired even doing one textbook, i just take a short break before tackling that same textbook again

[tacit sapphire]

Maybe that’s the case

[open furnace]

is Cengeze book best for math jee??

[swift tartan]

#book-recommendations

[swift tartan]

it depends on what regard, burn out is when you have responsibilities or you want to do something but you are just tired and cant dedicate yourself to it

Its similar to the feeling senioritis where you are "tired of school"; but usually burnout is a lot worse bc the responsibilities can be a lot more demanding than what you can handle during that time

ive seen many people drop their semesters classes in total, because in part burn out

This is definitely true

Esp in the real world, burnout is hard when you are working a job and have bills

[tacit sapphire]

But if something is fun and couldn’t chase the progress I found it hard to classify it as burn out though

[swift tartan]

yeah def agree, dont think its a hot take, its a mix of stress of any kind

But yeah being used to it / having a sustainable practice or routine or even having tolerance does impact it, in this case studying

maybe the message you replied to was a little misunderstood, but I was moreso commenting on having burnout while in the workforce rather than a student is a lot worse

[karmic sparrow]

Hey guys

I need help with this equation

[scarlet arrow]

Wrong channel

Open a help channel ( #❓how-to-get-help ) or ask in one of the subject relevant channels ( #calculus )

[glacial raven]

This is a list of my desired master degree's courses, followed by a list of the pre-requisite mathematical knowledge I'll need in order to study the degree. I want help on which books to use to study the concepts needed

Multivariate Stats
Fundamental concepts of Stats
Statisticsl Software
Linear Models
Generalized Linear Models
Statistical Consulting
Concepts of Bayesian Data Analysis
Modern Data Analytics
Data Management
Advanced Econometrics
Survey Methodology
Structucal Equations
Fundamentals of Financial Mathematics
Statistical Tools for Quantitative Risk Management
Official Statistics
Sampling Theory
Advanced Applied Econometrics
Data Visualization in Data Science
Total Quality Management
Data Mining and Neural Networks
Support Vector Machines: Methods and Applications

[solid venture]

Math is a marathon not a sprint. You need to manage expectations. This level of load is unhealthy.

[shell glade]

i think this could make sense depending on what it means
if you followed math55's syllabus over the summer, you could totally do that. I can see getting both semesters done if you don't have any other time commitments, and you treat just that like a full-time job.

the problem is that the work required is typically a giant jump from what was previously being done
people don't go from "doing some math for homework" to "study, self-motivatedly, four semester math courses"

in my experience, i'm far more productive if I just do math in my free time on a pocket legal pad

because focusing on what you're going to do and how fast tends to distract from math

[eager halo]

Meanwhile me self-studying math in my free time

[shell glade]

and i find I don't need to do math for more than 5 minutes to get into a "let's focus on this for 4 hours state"
the point is consistency and trying not to spread myself too thin.

but then, since it felt easy to do that, i then say "oh, i should set aside four hours for math"

but then since I don't have 4 straight uninterrupted hours lined up, i find myself not doing math

the hard part, to me, isn't getting the stamina to work on one thing for 4-5 hours.
it's the first 5 minutes of doing a specific thing

psychologically, doing an exercise or filling in gaps in a proof with paper and pencil feels the same to me
as merely reading the proof and thinking about it in my head in the moment

actually writing makes your thoughts far more efficient and useful
it keeps them from wandering as much, since you have your memory laid out in front of you.
it's way more productive.

if I don't, the lack of visible productivity can feel demoralizing simply because i've wasted a bunch of time getting nothing done

but the other side of that is that even lemma sketches to flesh out later feel productive.
editing feels very satisfying. there's a confidence that's really nice.

i hope something in there is useful

[shell glade]

wait, your measure theory grade was bad?

well, if you're taking measure theory, but are looking to do "intro analysis" and "topology" over the summer, maybe you just had holes in your background

[tacit sapphire]

But measure theory i did with a lot of luck

[shell glade]

part of what makes that scary is that fixing the holes can be embarrassing

[tacit sapphire]

Indeed

The thing is, development of precise argumentation composition is never easy. I have been writing every single proof I saw I proved everything. But holes everywhere

And many things aren’t as easy as I thought too.

[shell glade]

i'm not saying that it's impossible to do that work over the summer, though it's probably unrealistic
why not just spend a week or two and see what pace you should be at?

[split jasper]

my measure theory grade was a 60

[tacit sapphire]

I guess i just worked too much

[tacit sapphire]

But I did it really with luck though, almost everything it comes to the exam was what I have prepared

[shell glade]

side note:
that proof for the matrices can be shortened by noting a field is a monoid, and inducting on products
you get the group structure that way too, since fields are groups

you also don't need commutative multiplication to get the commutative addition structure.
if you mean commutativity of multiplication, that's actually wrong:
take permutation matrices for example

[tacit sapphire]

You actually read it 🥰🫣

[tacit sapphire]

I was trying to show matrix are addition are commutative I guess

I wrote note to he thorough for many reasons, one is to remember for revision another is to create memorize path 🫠

[shell glade]

well, try just working through all the exercises

in whatever book you are going through

[tacit sapphire]

I do exercises too and usually I just rebrand them as propositions.. for abstract algebra the progress was quite slow

[shell glade]

you don't even need induction, actually, you just note that it's a group if it's a group pointwise since that's how the inverse is constructed

that works for infinite dimensions

[tacit sapphire]

You actually note one of the most important problems I have been facing I rely overly on heavy mechanism

[glacial raven]

Hey, any help please? :( My message got lost

[storm tide]

Unfortunately I think everybody despaired at seeing that laundry list of topics, and chose not to engage. That type of questions are very hard to answer, at least if you want to feel halfway confident your answer is even helpful.

[swift tartan]

literally me haha

[swift tartan]

If its something that you enjoy, just starting the task sometimes makes it run for much longer than intended. Like playing games, you say its only a short game, be it outside sports with friends or videogames, and it turns into an all day thing

[swift tartan]

unironically yeah

[swift tartan]

also this is a #book-recommendations question. but what tropo said still applies. If you plan on picking up one of those books in order, maybe just ask as you move along rather than having it all at once

I doubt just one person will have the answer to each one of those, another reason why

why do you choose to suffer

[split jasper]

so true

[shell wasp]

hi

so i havent done math in 5 years and i wanna learn math again i was wondering if i could show my notes to someone and could i get feedback on them if theyre good or bad

i wanna do this for algebra 1 algebra 2 trig geometry precalc trig calc 1. calc 2 calc 3... etc

so on and so forth

like im 100%

[scenic shuttle]

I'd suggest checking out khan academy or paul's notes at https://tutorial.math.lamar.edu/ since they have great notes here and helps u a lot with stuff

but feel free to share ur notes too

I'm willing to give u feedback

[tropic jetty]

just wanna leave this remark that as long as the notes are accurate in content, pedagogically speaking everyone has their own style

so good or bad depends on whether you understand your own notes

[tame vector]

does anyone have any ideas on how to

not screw up when

combining like terms

when solving polynomials

[agile hollow]

we define graph of f : X --> Y as G(f)={(x,f(x)) : x\in X}

can be find graph of of a relation that is not function?

like this

[storm tide]

That is a subset of R^2 that is not a function, yes.

[karmic sparrow]

Hello

[tame vector]

does anyone have any ideas on how to
not screw up when
combining like terms
when solving polynomials

[sonic flower]

practice

[scarlet arrow]

You've asked this question before, what answer do you expect other than the one given?

There's no tricks to this

[tame vector]

because

the one im doing

isnt working

so i want to find a more efficient one

[scarlet arrow]

Show

Whatever you're doing

[tame vector]

im mostly stuck on

$ax^3+bx^2+5x-2$\
When f(x) is divided by x-1, the remainder is 6\
When f(x) is divided by 2x+1, the remainder is -6\
Find the Value of a, and b.

[mossy shadow]

Tan

[tame vector]

well obv

using the remainder theorem

you put f(x) into it

but then what

you already know that the remainer is gonna be 6

[rose peak]

What do you mean by put f(x) into it

You are supposed to equate them

$f(1)=f(-\frac{1}{2})$

[mossy shadow]

Real Lost Fruit

[rose peak]

Substitute those values in and then you will be all good

[tame vector]

??????

[tame vector]

i thought u find the equation for x-1 and 2x-1, and then solve em simultaneously

damn

i was wrong

[rose peak]

No

[tame vector]

nvm

it was not the answer

bruh how then

[rose peak]

What we were trying to do was to find the values of a and b, not the intersection between the two lines y=x-1 and y=2x-1

[rose peak]

I just explained it to you

Oh sorry wait

Ah ok so plug the two in

And then you can solve for a and b simultaneously like you said

My bad, brain had an error

[tame vector]

i did

but i got it wrong

:(

[rose peak]

Can I see your working

[tame vector]

sure

$P(1)=a(1/2)^3+b(1)2+5(1)-2\a+b+3=6\P(1/2)=a(1/2)^3+b(1/2)^2-5(1/2)-2\-6=1/8a+1/4b-5/2-2\Multiply by 8\-48=a+2b-20+2\a+2b=-26$

[mossy shadow]

Tan

[tame vector]

$a+b=3\a+2b=-26\b=-29$

[rose peak]

Why is there a one half in front of a when you evaluated P(1)

[mossy shadow]

Tan

[tame vector]

misclick

its 1 on my notebook

[rose peak]

When you multiplied by 8

[tame vector]

did i forget

to multiply the 2

[rose peak]

Ye

That’s why your answer didn’t match up

[tame vector]

okay

let me try agian

i got b as -33

how

[unreal mulch]

Don't help people here and don't ask for help here

[rose peak]

Take this to #prealg-and-algebra

[rose peak]

Sorry!

[tame vector]

should i just open a help channel

[rose peak]

Sure

That also works

[tame vector]

#help-8

[main trail]

do y'all's unis have credit limits?

[opal granite]

We're only allowed to bring 180/120 ECTS into the diploma, but there's nothing stopping me from doing more

[main trail]

Like in a semester

is there a max

[opal granite]

Oh I have no idea

I dont think so though

[main trail]

lucky

[opal granite]

Does your uni have?

That sounds odd

[main trail]

yes

25 credits

most courses are 4 credit

with lab 5

and some 1.5 and 3 credit too

[opal granite]

How many credits do you need for a bachelors degree

[viral osprey]

Per semester credit limits are common

For various reasons students famously like to overload themselves with more credits than they can handle. This wastes everybody's time and often wastes things like fin aid too.

Longer term limits can be a thing sometimes too.

[main trail]

150 i think

[opal granite]

Yeah, that makes sense

[main trail]

Yea , but even 0.5 more is hard

[opal granite]

Though in this case, assuming that the degree is supposed to be 6 semesters, limiting to exactly 150/6 credits is weird

Why cant you split them 24/26 for example

[viral osprey]

6 semesters seems kinda optimistic where I am from.

Hmmm

Idk how wai's situation works.

[main trail]

8

4 years

[opal granite]

Ohhh

[viral osprey]

Often in the US you can just request a waiver of some sort through somebody to go above the cap.

[main trail]

They've reduced it

[viral osprey]

So the cap exists but can be worked around if you get permission

[main trail]

Used to be 27

It's 25 now

[opal granite]

My mistake, bachelor's in EU are usually 6 sems and I extrapolated

[main trail]

Compulsory courses end after 3 here too

The 4tjh is to do research

[glacial raven]

Not really a study topic but how do you people try to maintain a healthy amount of work-time on PCs/mobile for college work/projects? Like staring at the projector screen for 4+ hrs daily in lectures then doing assignments on PCs/mobile really strains my eyes

[main trail]

how mamy credits is one course?

[swift tartan]

We have 3-4 credit classes and each credit is around 2 hours of work pretty solidly

so a 4 credit hour class is 8 hours of work

[main trail]

Mhm

For us a credit is normally an hour of classes a week

With most of my course being 4 credit

[split jasper]

what do you study

[glacial raven]

Pursuing Bachelor's in Engineering

CSE

[split jasper]

well i mean idk how you avoid staring at a screen for 10 hours a day, thats literally what CSE is training you to do

you can try to do as much as you can on paper

do all your thinking on paper

[main trail]

@green terrace , just curioous did I share my soc course and time table with you ( I'd like to if that's fine with you)

[green terrace]

Go ahead

[swift tartan]

hey Cat!

[green terrace]

hey nerd wsp

[main trail]

this is my time table

[swift tartan]

religiously in this channel frfr

[swift tartan]

seems like a tough sem

[green terrace]

Heavy but doable

[swift tartan]

operator theory is hype tho

i wish we offered it

[main trail]

and this is my SOC course description

[main trail]

ya, trying to do 23 credits every se

[swift tartan]

what?!

that’s insane but yeah glgl

[main trail]

want to finish requirements except for my paper early so that I can do fun courses in year 4

[main trail]

not really

most courses are 4 credit

[swift tartan]

oh valid, kinda what i did lol

i started taking grad courses in my 3rd year onwards

[main trail]

yea , going to take 2 grad courses next year atleast

measure

and FA

[swift tartan]

i guess bc your courses are 4 each then about 5-6 classes, still a lot (more than i can ever do) but yeah not bad

we have an 18 credit cap

[main trail]

we have a 25 credit cap

[main trail]

the course labled CCC is for 1.5 though

[swift tartan]

all of the math classes are also 3 credit hours but most other depts have 4 credits

idk why math is unique bc i sure am not only spending 6 hours per class

[swift tartan]

context

i’m also taking RA this fall too tho

[main trail]

oh, nice

that's probably the easiest course I have this sem atp

I'm going to hate probability

alg1 is hard

SOC will eb hard

[swift tartan]

oh im the complete opposite

[main trail]

and a 500 level course..

[swift tartan]

algebra was really easy for me

[main trail]

:ope

[main trail]

[swift tartan]

analysis is going to kick my behind

[green terrace]

we like algebra, it makes sense

[split jasper]

i think algebra is much easier than analysis, so it feels like instructors compensate by making the sheer content of algebra in a single course much more than an analysis course

[green terrace]

analysis is

[swift tartan]

ehh i disagree; maybe it’s bc we have more analysis ppl in our dept than algebra but our algebra hws are easier than analysis

also in quantity

[split jasper]

it of course depends on the course

[swift tartan]

idk, not to toot my own horn, but maybe i was just too good (joking obv)

[green terrace]

toot toot

[split jasper]

for example, aluffi prefaces by saying he intends for his book to be over 3 semesters but its usually in less than 2. my undergrad institution did it in 2/3 of a year and move on to finish atiyah macdonald for the rest of the year

i think that pace is just insane and i dropped midway through

[main trail]

henstien is so hard :(

[main trail]

and chat has died

[glacial raven]

[scenic shuttle]

is this engineering 😭

[main trail]

Pure maths

[scenic shuttle]

oh interesting

[main trail]

It's going to be hard but fun IMO

[swift tartan]

its only hard if you arent doing math every hour of the day

just do better

[shell wasp]

Hi

I got an D in algebra 1 an A in geometry an A in algebra 2 a B- in UW precalculus

I haven’t done math in like 3 years I was wondering if I could get an A in calc 1 at UW

[storm jasper]

Yeah

[shell wasp]

Wow rlly

[storm jasper]

Hm

[shell wasp]

Thx

[storm jasper]

Yeah you got it

[scenic shuttle]

uw stands for waterloo right?

yeah its possible to get an A in calc 1, just practice and you'll be fine

[split jasper]

it usually stands for washington

[scenic shuttle]

fair enough

[quaint viper]

<@&268886789983436800> another one

[swift tartan]

maybe im too canadian / east coast based

I live in the US but know UW (waterloo) more than I think about washington lol

[main trail]

bad question, but would. self studying RA and group theory at the same time be a bad idea

[wheat plume]

what's RA?

real analysis?

[main trail]

yes

[wheat plume]

Not much conflict between them, also common for undergrads ig

to be taking the courses at the same time

[main trail]

yeah, but I've done around a 1/4 th of what my first course in RA will cover

have just scratched the surface of group thoery

[wheat plume]

If you are in a rush and you need to complete a topic, then maybe focusing on one is a better idea

[tame vector]

why did Sri react with the Caret symbol

^100??

@swift tartan

[storm tide]

The reaction usually means "I agree with this post".

The 💯 reaction usually means "I agree 100% with this post".

[tame vector]

if he already agrees with the post

then why would he reply with 💯 again

he alr agrees with it

[storm tide]

To emphasize his agreement, I suppose.

[swift tartan]

Yes

I love inflating the reaction economy

[swift tartan]

If you do choose to go ahead with the RA + Group Theory. Def possible, it shouldnt be bad, and also, because we used baby hungerford, we started out with rings and fields first which made the class kinda easy early on instead of the amount of things we couldnt take for granted in group theory

but if its just a personal study, just focus on one thing and it would probs make the start of the semester a little easier so you can take that time to get adequate with the other

[main trail]

hmm, fair enough

[shrewd inlet]

can somebody summarize this im not gonna read the whole Quidditch rule

[main trail]

yeah, that's what I thought

They require different approaches too

[hoary kindle]

Not about maths but I don’t know that this channel is that specific, does anyone have any experience with self studying a language? I want to teach myself German (I know the absolute basics, like A1 level) and I don’t really know where to begin for self study.

Like I don’t know where to look for books and stuff because all the ones I’ve looked at so far have been entirely in German, presumably because they were designed for a classroom context, but not ideal for me right now

Aside from that how do people study? Flashcards with vocabulary and grammar rules? Listening to music, TV, reading etc is all obviously helpful too but aside from that, how’s best to approach it?

Talking to people is also obviously helpful (and not doing so is by far the reason why I’m still so shit at Spanish and French despite doing them in school) but thankfully my girlfriend and quite a few of our mutual friends are German so German speakers is actually the one thing I do have access to

[shrewd inlet]

wow! now i get it! thanks!

[amber field]

There's probably dedicated subreddits for learning languages with exhaustive lists of resources

For german, eg here

https://www.reddit.com/r/German/wiki/index/

[scarlet arrow]

(Sidenote, description says any discussion related to studying and studying methods is fine, not just math )

[swift tartan]

@long hedge my bad, i saw chatgpt and ignored the rest of your msg

[quaint viper]

i laughed

[solar valley]

hii does anyone have any links to good practice tests/study material for linear algebra or calc 2 (mostly linear tho)? i’m struggling to find some good ones myself 😦

sadly my classes r online so they don’t offer any😔

[crimson elm]

I'm studying German currently but not as active as I used to do when I was learning Japanese and Arabic but essentially I am still doing what I used to do but less frequently. I put my first priority to grammar and supplement it with vocabulary (use Anki decks). Read novels and stuff you are interested in like in my case I read about math and culture. Join discord language exchange servers and vc with people there

What I find out is that keeping track of these gets harder as you grow up because you have other things to do in life + extra responsibilities

[golden juniper]

Hello everyone

I eager to learn Math every time, but ending up with difficulties (trying from grade 8 itself) and score 58 of 100 in grade 10

Not mean I can't do... I do very slowly and with a lot of confusions.. but everyone other than me grasping as light. and me can't kindly help

This may be dumb, but I don't have any other hope other than this..

[gusty jay]

Hi, An English literature guy wants to self study math - contradictory I know. Any piece of advice?

[hoary kindle]

I’m more interested in the specifics though, where are you learning vocabulary and grammar from?

I feel like I have an ok understanding of the studying aspect, I’m just actually unsure of where to find any resources that work for self study, like all the books I’ve found have been entirely in German and I presume this is because it’s intended for a classroom setting with a German speaking teacher

[crimson elm]

I just consult websites. Try to get your hands on standardized German learning books for A2/B1 or whatever level you are comfortable with. I find some of the vocabulary useful and some are useless but I use these as a guide through the grammar aspect most of the time

Do mock exams (or maybe even attempt standardized tests)

[crimson elm]

What's your background?

[ripe sand]

it would highly depend on the quantity of work you'll put into it and the path you're willing to take
math is such a vast subject with very obscure branches
first try to delineate precisely what path you're heading on
is it more applied math stuff? more pure and theoretical? more programming oriented? puzzle, problem solving, and competition kind of math? try to find exactly where you'd like to go and you can build a path from there
if you're looking for some proof oriented work, your go to essentials imo right out of highschool are: formal logic and types of reasoning.
you need to know how to prove or disprove a statement, valid techniques, and the fallacies u might commit along the way. this type of stuff includes truth tables, inductive reasoning, the contrapositive of a statement etc
imo after that u can tackle everything else depending on the path you wanna take
calculus, linear algebra, number theory, all that

[gusty jay]

basic algebra, Calculus (Differentiation rules except for exponential functions and logs + except for integration by parts and partial fractions + I only know the mother Trigonometric Identity (sin²x+cos²x=1)), no geometry, A little knowledge about how Trigonometry works

[gusty jay]

Kinda about problem solving and a little bit of programming

[crimson elm]

What are your goals?

[gusty jay]

Oh yeah, and some of probobilites

[ripe sand]

self study is hard with no clear goals

set them up and don't let it be vague

make sure they're targetable and attainable

i want to be able to <...>
i want to read <...>

[gusty jay]

To improve my problem solving skills, to be able to calculate quickly when someone wants help with calculations, to be able to build projects that require complex math, and to turn it into a hobby and remove the fear of math

[crimson elm]

When you say projects, do you mean programming wise?

[gusty jay]

yeah

[crimson elm]

Alright

I suggest looking at linear algebra then

[ripe sand]

^^

[crimson elm]

It should be a good starter

[ripe sand]

discrete math can be fun too

[crimson elm]

Yeah discrete math is okay too. You get an exposure to some fields

[ripe sand]

as for calculating quickly that's a training thing more than anything

unless I'm misunderstanding

cus calculating quickly seems like arithmetics

[gusty jay]

I had fun with integration and imaginary numbers

[gusty jay]

I see these human calculators calculate 746 * 123 in seconds

[brazen mist]

,w 746 * 123

[mossy shadow]

Results provided by WolframAlpha

Click here to refine your query online
Upgrade to WolframAlpha Pro!

Requested by zanarcane

[ripe sand]

yeah is that what you're interested in?

quick arithmetics?

there's some techniques you can learn but other than that most of it is memory and practice

lots of practice

and some ppl are gifted

so they hone it exponentially

[gusty jay]

oh I got it

[brazen mist]

I'm not, so I let the computer do that for me

[ripe sand]

that's what most of us do

math is less abt calculating stuff and more about proving stuff and making sure they work

we don't do that a lot ngl especially after calculators

and computers

[gusty jay]

Back in elementary school I used to use long division easily, now I don't know how to do normal division lol

[ripe sand]

i haven't seen a number since i started uni

[brazen mist]

Yeah, it's a matter of practice

[ripe sand]

skills regress if not used that's normal
practice

there's lots of really fun stuff you can do in arithmetics it's not a barren field

number theory and modular arithmetics are really fun

bezout and shit

one of my fav courses in uni was modular arithmetics

[gusty jay]

That British content creator who manipulates in numbers and says "noine" I forgot his name

He does alot of stuff in arithmetics

[ripe sand]

yeaah

and then u can combine two fields to do fun stuff

modular arithmetics and linear algebra can be combined to create neat little encryptions

tada u peaked into Cybersecurity and cryptology

idk state a clear goal and work from there
if you're doing it for projects then discrete maths and linear algebra are your best bet

discrete math just means any math that's not continuous
so ud do graph theory, probability, arithmetics and all that jazz

[split jasper]

since when is probability discrete

[ripe sand]

some probability is discrete if done with graph theory iirc
i snuck into one of them discrete classes and found them doing almost entirely probability

chains of markov iirc

in my eyes probability is both

depends how u approach it

coin flips are discrete

i haven't done lots of graph theory so i didn't really study markov yet

[worldly rune]

every security definition in cryptography is defined in terms of a discrete probability space

[tropic field]

p(getting hacked) < 1e-9

it's a Bernoulli distribution

[idle hamlet]

im unsure if this would be the place to ask the following question, but does anyone know methods to improve non verbal reasoning?

[torn olive]

can you elaborate what you mean by non-verbal reasoning?

[tacit sapphire]

@swift tartan you know what I think you’re right… after dealing with product topology I kinda got my confidence crashed

I probably will lightly revise on analysis and as much LA as possible..

I have been through a transition that I kinda wanted to understand one big theorem of topology to that I can routine produce basic proof of topology

Life isn’t a sprint indeed

At this point after decoding the product topology and index gymnastics, I kinda realized how unrealistic the goal really is and worse I even developed some resistance to topology as it got increasingly more abstract. Which has been genuinely very awful since I am drawn in this study voluntarily feeling I might love it, but the past couple days I have been avoiding topology.

Personal perspective I have for now at the moment is to study a ton of linear algebra since the study I haven’t got stuck conceptually except the proof for la places formula which I expect to be able to do it in a couple weeks since the main barrier is the permutation group..
Some light abstract algebra and some basic topology spread over days.

Maybe I should just in general, give up the mindset that I would be such a failure if delayed graduation by longer than 1 year (not easy though, I have never been competitive however I struggle with the mindset that I might fail myself, I don’t expect excellence, however the uni course work always made me feel I might fail if I didn’t do anything perfect)

Do you think it’s more realistic now? I mean previously my style was kinda solving any problems and prove every proposition.. now I only do this for linear algebra and analysis, for abstract algebra and topology I will just do some exercises on the book instead of forcing me to study again and again till I prove everything

[idle hamlet]

im really referring to the opposite of verbal thinking. so thoughts that come in the form of a visual sketchpad as opposed to words

[rocky terrace]

"Life isn't a Sprint"

-Neam starting Abbott, 2022, Colorized

[swift tartan]

what year of uni are you?

[swift tartan]

honestly, to each their own. I cant really say if something like that is unrealistic bc it just depends on what you can handle. doing like 4 diff studies at the same time is a lot, but ppl can still do it. most will probs feel burnout but its not impossible

thats really just for you to figure out what you think is important

and also math and perfectionism doesnt go hand-in-hand, you will never know everything there is to know

[tacit sapphire]

Let me still label it as second year so maybe I felt not awful though.. and I do have regret pill

I mean if we talk about total it should be the third year

[tacit sapphire]

I would think that but some parts are very difficult so even with good time management it’s quite impossible

[tacit sapphire]

Must have been a prophet…

[tacit sapphire]

To be honest it’s not really protectionism the whole other way around. I almost always think I am gonna fail if not working hard enough, I personally don’t have much expectation on grades though Econ was easy and it would be nice to have that grade but my main fuel is really fear of being a failure

I don’t really know why people can be optimistic all the time, I felt people are all good or better than me, and be anxious everyday if I am not advancing.. like uni is very stressful and coursework is often demanding, I kinda developed mindset of being excessively scared of myself failing that made me into workaholism.. perfectionism no, I don’t care it that much i mean perfect is good but without it it’ll still be fine but what I fear is failing 😢

[swift tartan]

given that you did transfer from econ into math, maybe you are feeling similar to how I did when I switched over to math and I felt like I had so much to catch up on compared to ppl who wanted to do this since hs or when they started college. For me its imposter syndrome, ive been told im pretty good at what i do, but at the same time i always feel like I have so much more to learn and do and frankly from what I understand, it will never get better

For even my professors who have also won awards and recognition at conferences and gotten distinguished titles at my uni, like if they have imposter syndrome too, idek if i can compare to how they may feel

its kinda just something you have to cope with and i personally look at it as a way like "oh there is so much more to learn and i can keep pushing myself to do better" and just bc you are cognizant of it doesnt mean that it will just go away

i know for some thats a lot to do and may sway them away, but i guess it just comes with the territory

I guess being tenacious is a merit of its own to a degree? idk if i am using that word right

but just stubbornly pushing forward

[swift tartan]

also lmfaooo you have so much time

if i could go back and just relax throughout my ug, i def would instead of stressing over falling behind and just constantly working at all times

i started my math major in my 2nd year, i also took calc courses my 1st year from Calc I onwards. And I finished the math degree in my first sem of my 3rd year and have been just taking grad courses and added another major on top of it

[mellow flicker]

Switching from CS to maths for my final year and I am currently struggling with writing proofs. The course catalog for maths majors at my uni does not seem to explicitly have a course about proofs and I am a tad lost on what to do

Lots of excellent book recommendations exists - are there any other resources that would be helpful?

[swift tartan]

math major in general is pretty short comparatively to other degrees (at my uni which is more extensive than others we have around 24ish credits so like 8ish math classes?)

[mellow flicker]

3 years here in Sweden

[swift tartan]

can i ask what made you drop the cs major in your final year?

[mellow flicker]

Very few interesting courses, most seem to focus on applying concepts rather than exploring the theory behind CS

[swift tartan]

yeah and i condensed that down to basically a year and half for me 💀

[mellow flicker]

damn

[swift tartan]

yeah tbf thats basically how cs is. If you had already taken algorithms + data structures, and ofc the discrete maths course that comes at the start for most cs programs, then i would just focus on trying to practice those proof techniques? You basically have all the ingredients and have applied some of them

The CS program just doesnt really care for super extensive proof writing

but it does matter for math, and also the diff proof techniques you learned from discrete like contrapositive, contradiction, direct, and induction; for cs usually youd only see induction, but for math you use all of them 10x-fold

[mellow flicker]

I am trying my best to prove each theorem in my discrete maths book and logic but I feel like I am missing a foundation

[mellow flicker]

Yep

[swift tartan]

also i was originally a cs major too but i switched out of it after 1st year, and just added it back this jan

[mellow flicker]

Which is what scares me as my thesis will be on maths

[mellow flicker]

big oof

I don't need to repeat a year which is nice

[swift tartan]

im certain you have already looked at or been recommended many different proof textbooks, but imo Book of Proofs by Richard Hammack (free and online by publisher/author), is a personal favourite

they instruct you on what you should technically be looking at when you are reading a math textbook

and also creating a kinda formulaic proof structure (which one might phase out of after getting comfortable)

Id say the formulaic proof structure might be a little more beneficial bc of your cs background, and it does a little introduction of diff ug math classes that one might take

also have you taken any math classes yet?

usually the point of ug math classes is to learn such skills, they dont expect you to be perfect from the start

[mellow flicker]

I have not heard nor read about this book, I'll definetely have a look now

[mellow flicker]

This is what I exactly need

[swift tartan]

yeah nws

[mellow flicker]

I need baby steps, small baby steps before being a big boy and writing freestyle

thanks for the recommendation siracha

Sri*

[tacit sapphire]

You did that too? Switching to math as an advanced student? Did you manage to retain as a second year or start as first year completely?

Though it’s kinda hard to really be unstressed.. like imposter syndrome is stubborn

[tacit sapphire]

Personally perspective, it’s actually quite effective and efficient to memorize definitions and then construct the proof oneself. Usually pretty easy and then see how much it matches the book

I don’t know.. like when I was at the measure course they often force you to make argumentation as concise as possible it’s torturous process for my then strength also my current strength but it’s quite effective in helping you learning the crucial parts of math proof

[mellow flicker]

I managed to retain my second year so I'll be starting as a third year

[mellow flicker]

One minute I am proudly proclaiming "This is easy! I am the smartest man alive!".. then realize my answer is wrong and I loudly proclaim "This is hard! I am the dumbest man alive!"

[mellow flicker]

yes

is this how I find out that you are my classmate? 🤔

SU?

nope

guess you are at UU?

rip

the Frescati campus is beautiful though

Albano is too brutalistic and modern agh

Lund?

🤔

Do you know someone called Solveig?

ah, she was a classmate of mine at high school

worth a shot, small world yknow

what's the exam?

is that not in the third year?

damn you grinding

I believe the course is read during the third year of maths at SU

the prerequisites are 60hp yup

Don't know, SU is kinda wacky with the names

Year 3, field of study in mathematics

At SU there is 3 major maths programs

One is mathematics, one is mathematics and statistical mathematics and lastly there is mathematics and computer science

then of course.. there are I think 3 more variants

It is really nice, professors are super social and helpful

Only bummer is the student life but if you manage to make a friend or two it's fun

I'll be reading this coming term now

I need it to graduate with a BSc in maths lol

I believe that the combinatorics course is recorded as well

If you have an SU account you can watch the lectures

same

The recorded lectures are not lectures per say but well edited videos, 5-18 min each

https://media.math.su.se/

yours is probably better than mine

I keep getting lost at the campus trying to find the right seminar room

ha.. I avoid those

they give me a false sense of understanding... and I go around acting like I actually understand it lol

They don't have CS, only computer engineer

My friends study there, it is more or less the same courses as we read at SU, suprisingly

nice

Funny enough, I work as a TA at the CS and System science department and two colleauges have studied at LTH*

Most of them praise the school, others... nein

Yup

EU?

UK?

maybe scotland?

Australian!

I thought they were apart of Schewez thingy

hmmm

Ukranian?

what continent?

Switzerland?

omg

my eye doctor Jurg is from Switzerland

yes

dont know

EYO

He works at S:t Eriksögonsjukhus which is the only speciality eye hospital in Sweden

ok maybe I should not dox my doctor

Yes

Solna

not on days when soccer matches are held...

[hollow plover]

soo.

can anyone give me tips on Verbal Reasoning, Non-Verbal Reasoning, Quantitative Reasoning, and Spatial Reasoning

for a cat4 test

[shell glade]

exercise regularly and eat healthily long in advance. learn mental math. there are books that will teach you add and multiply 5 digit numbers (and decimals) in your head, those trivialize some of the quantitative reasoning exams.

finally, read regularly and write down a word you dont know each time you come across it to learn it

[shell glade]

each of the above is good to do irrespective of any test you’ll take

[hollow plover]

Ty

[glacial raven]

hi excuse me, where is the discussion channel?

[mild hemlock]

i think they’re just trying not to dox themselves by giving the course codes

[mild hemlock]

wdym, you can’t see it?

[scenic shuttle]

u cant see the social channels when u have studying role

[mild hemlock]

i can’t read, my bad. thought you were responding to one post above you

[wicked trail]

very worried for next years major exam

i need to have very high efficiency and accuracy in maths

for 2 hours straight

[rocky terrace]

most literate math major be like:

[mild hemlock]

real

[main trail]

so my course uses halmos and hoffman ( glorified LA), how cooked am I

[rocky terrace]

You're gonna cook

[main trail]

🙏

[main trail]

no, I'm cooked

[glacial raven]

Gl

[rocky terrace]

If you think you are cooked, you will be cooked

[tacit sapphire]

My LA course seems to use a very computational heavy book from Cambridge

😭😭😭😭😭😭😭😭😭😭😭

I have been doing proofs, I almost never practice computation. I am almost half way proving laplace formula (after acquiring permutation group it’s probably doable). I will just dive into those intriguing trace based formula for fast computation

[scarlet arrow]

[stuck fern]

keep it on topic please

[agile hollow]

I had computational LA as well

It was supposed to be abstract but TA chosen to teach us computational things

A week on elimination method lol

Damn

We hardly did a few proofs

[tropic void]

"in this world, it's either cook or be cooked."

[tacit sapphire]

The thing is I haven’t been practice for numerical arithmetics in context of massive determinant computation (probably not gonna be very hard I have a bit confidence with la now).. I almost do everything symbolically

So I am a bit scared

And it’s often very effective to use traced based formula for Linear Algebra arithmetics like characteristic polynomial , it’s a master formula and you just derive though it’s significantly more complicated if it goes beyond 3*3 matrices. A bit scared with it

Probably will be fine? I’m not sure, since symbolic manipulation can be mirrored easily

[halcyon spear]

Unc couldn't take a joke

[halcyon spear]

Das wassup my man😎

[scarlet arrow]

:/ who let the robloxers on here

[stuck fern]

anyone have notebook recs

last time i asked i got a rec for a rhodia dotpad and i really liked that

[mental tinsel]

I have heard good things about Moleskine

[main trail]

We used a sligthly computational book, but being a coward I used axler

[mental tinsel]

computational as in?

[main trail]

like I had to compute stuff aswell as prove stuff

like find the basis of a vector space

( axler doesn't ask me to do such stuff)

[mental tinsel]

I see

so less emphasis on theory and proofs

[tacit sapphire]

I feel computation is usually harder

As arithmetics is very painful and messy

[main trail]

yeah

[tacit sapphire]

Some inattention will lead to unspotted mistakes

[main trail]

proofs are much easier in general

[mental tinsel]

depends on the goal of the class....it wouldn't make much sense in a Pure Math setting

[tacit sapphire]

However usually symbolic method has logical chains easier for tracing back

[mental tinsel]

I think the goal of these classes is to get you acquainted with basics of Proof writing, which you can later extrapolate to more advanced classes

[tacit sapphire]

I mean what kinda of proof in LA can exceed difficulty topologies and radon nikodym

I think it’s for foundational procedural skill though but essentially the same

Proof at basic level is more straightforward

[mental tinsel]

I am taking a different route however. I am learning Number Theory as my intro to math with some basics of Propositional and Predicate Logic down beforehand.

[tacit sapphire]

Number theory is very hard

It requires a huge amount of algebraic tool to do arithmetics

[mental tinsel]

I see. It reads very accessibly so far, although I haven't done much of it tbh.

[tacit sapphire]

Like use bare hand for extended Euclid algorithm is insane

[mental tinsel]

https://www.math.brown.edu/johsilve/frint.html

this is what I am using

[tacit sapphire]

You from brown?

[mental tinsel]

no lol

[tacit sapphire]

Almost triggered my jealousy

I am new to math so hopefully it’s not that computational

[mental tinsel]

I just happen to find out about the book by perusing Stack Exchange and related sites

lmao I don't have much experience with math (perhaps some seasoned folks here might be able to tell better) but writing proofs is very non-trivial at times. I find myself many times baffled at the inferential leaps in the proofs and try to re-create scenarios where I could have gotten the right instincts to make that logical leap.

with computational problems you can group certain problems requiring a certain algorithm/procedure and re-use the same computational patterns with wide variety of problems

so if you do a lot of them, you usually get a sense of how to do almost most of them

akin to how competitive programming or leetcoding is practiced by CS students

[tacit sapphire]

I just think in general computation is more exhausting and unnice

[devout sun]

i think the opposite ngl

i think at some point long computations like an integral or solving a de/pde just become attention to detail

[bleak tinsel]

Chat, how does one git gud at maths

[storm tide]

Practice. Lots of exercises. Use it constructively when you have to look up a solution -- that is, spend some serious time trying to distill it down toba strategy you could have found the solution with yourself.

[tacit sapphire]

Think a lot too, usually if you know where you have mistakes it would be very very easy

Proofs are the same, it’s just that you rely on prior established results to reach the first principle

[tacit sapphire]

Usually you want psychologists I believe

I do not know

Solve the exercises

In my opinion, it can be done very quickly

I don’t actually, provided I can’t even imagine how it’s not done.. sorry please ask someone else

[rocky terrace]

As many as possible, if you are stuck, you can use this server for help

[devout sun]

sometimes i get this feeling too, although its nice to get a hint or whatever after some point. sometimes when im typing up my question i realize a solution lol

[quick elk]

they're shifty

there's a few repeat offenders who do that for whatever reason

[crimson elm]

Probably relevant to what you said above

[rocky terrace]

You are embarrassed asking for help online, I am not even slightly embarrassed when asking for help IRL, we are not the same

https://tenor.com/view/gus-fring-jumpscare-gus-fring-jumpscare-scary-oby-gif-13022434999806691946

[quick elk]

I kinda understand
but nobody is being forced to help you, so I wouldn't be too concerned

[slow yew]

Online, people feel way more confident taking potshots at people for a perceived lack of effort of the asker's side as well.

Whereas in person the conversation goes
'Hi can you help me with x'
'What do you mean by x'
'I'm not even sure, sorry'
'Ok lets take a step back and work towards it'
or some such

People are generally actually pretty nice in this Discord imo but I see it a lot in other servers

[quick elk]

idk
I feel like irl you would only ask in a place that's offering help formally
and they have guidance on conduct and/or you're paying for it directly or indirectly
if you mean just asking a peer in class, that sounds too ideal

[slow yew]

Not to be 'nuh uh' but I think that's mostly rhetoric.

• This server is ostensibly a place offering help (albeit implicitly), since both there are channels per topic and a dedicated question triage section. So I'd argue that while one should use those areas, it may be the case that a new (or socially awkward) user doesn't know to use them or simply forgets.

• Experiences differ of course, but conversations in class are normally very respectful and work-oriented. I try to treat it like a workplace and I think most of my peers do too. There's of course exceptions: I remember one gentleman taking his shirt off mid lecture for seemingly no reason, and another class where three friends were all on their laptops Discord-messaging each other with audible giggles, so I'm not pretending unis don't have weird people out there. But it's the exception to the rule.

[quick elk]

... ok then
good for you, I guess

[crimson elm]

Yeah I mean as long as you ask questions that make sense and aren't silly, I don't see a reason why someone here wouldn't help you

Unless you purposefully ask people to check your majestic Collatz proof

[rocky terrace]

Or asking how to find the side length of a right angle triangle in #algebraic-geometry

[glacial raven]

did someone say COLLATZ?!

[stuck fern]

usually if you ask a question people will redirect you to the right channel if it's not in the scope or focus. if it's high school homework-style you can use the help channels as you described before

if it's some other math question you can try #math-discussion

[strong tree]

Hi! I’ve written a mathematical demonstration related to tilings and prime number within Pascal’s triangle, and I’d really like to get some feedback on it. Could you please tell me which channel would be the most appropriate place to share it? ( it's not short it requieres a good hour to read it )
Thanks a lot in advance!

[glacial raven]

Anyone wanna study mathematics together?

[brazen mist]

Depends on what kind of math

[glacial raven]

What do you study?

[coral sleet]

@strong tree welcome to the mathcord!

your best bet is probably in #math-discussion, I think?

but it may be overlooked due to its length

[strong tree]

yep that's the problem it's kinda long so no one really want to read it and focus more on helping quick question this is why i wanted to know if their was any more appropriate chanel but thx i'll try

[steel drum]

one by one

[dull aurora]

true

i like how

this is basically the only channel not on fire

because i don't think everyone has access to this one

[jade furnace]

Yep, we can talk about math and studying here.

I'm currently relearning Algebra 2. I know eventually, I have to learn how to divide polynomials by other polynomials again, so I hope coming back to that isn't too hard.

I know how to do it if there's no remainder, but not when there is a remainder. I forgot about that part.

[cunning imp]

Do you use long division or synthetic division? Its not too complicated, I can try walking you through it if youd like :)

[naive condor]

Real sigmas would use this to chat as it has no time limit

[jade furnace]

I don't remember, but maybe synthetic division?

[cunning imp]

Type shi

[naive condor]

A person who thinks all the time…

[cunning imp]

Synthetic is a shortcut that works really well when dividing by first order polynomials

You should prolly learn long division first

[jade furnace]

Okay, I'll learn long division (for polynomials) first.

[naive condor]

One ping and suddenly half the server is vocal about their political opinions

[maiden frigate]

Any recommendation to learn queuing theory? Although I have very phew time because my thesis is about that

Probably I said a wrong expression. Seems my English is not in its best shape now

[woven nimbus]

I was trying to find out where a beginner would go to try to understand proofs (the way I phrased this can seem broad) for the first time but I suppose reading some of the pins here will suffice but I would like some additional insight too. The channels are a little overwhelming and that is probably on my end because I tried to look into a few channels but there's definitely a lot of stuff I don't understand apart from the calculus course I enrolled in during the summer so I need to start somewhere

I don't want to feel like I only wanted to bother with this server because of an everyone ping so here is a legitimate concern (do ping me if you reply because I have a feeling this will be lost within the messages)

[green marsh]

hi guys im a high school senior and i want to take the SAT, what are some tips for somebody who is really bad at math?

[cunning imp]

im canadian so i never took the SAT, but ive taken other standardized tests so this is just general test advice.

do practice tests, all the ones that are available. figure out where your weak spots are; types of questions, concepts, etc. and tackle those. track how long it takes you, what questions you get stuck on etc.

do not go into the exam with a concept unclear. make sure you understand all that you need to know. if you need help, ask your teachers, ask in this discord, ask any friends/siblings/cousins in higher grades.

use online resources like khanacademy, organic chemistry tutor (on youtube), etc. to understand concepts

and for this last tip, idk if this is really relevant to the SAT, but one of the ways i improved a lot at math is dont just do homework. you have to UNDERSTAND whats going on, in order to apply those concepts

[green marsh]

i have a hard time remembering concepts, i do well in class and i ace all my tests but i struggle with foundational algebra

[cunning imp]

what i mean by that last point, ill use the place i started doing it; with logarithms for my test. instead of just doing homework questions, i went on desmos for a few hours and just practiced every possible situation. my teacher only had examples of log(f(x)) where f(x) was linear. but what if its quadratic? what would that graph look like? what about a function in the form b^f(x), where f(x) is quadratic? what does that look like? and guess what, on the test, there was a question where it WAS quadratic that wasnt in the homework. i knew how to do it, because i spent all that time fully understanding the concept of logarithms and exponential functions

[green marsh]

i have been doing that but i still struggle so much in math TwT thank you so much for the tips, im just not sure why I am so bad at math and if anyone feels the same way?

[cunning imp]

im really bad at math, thats why i decided to pursue a biology degree LOL

but ive got to a point where i can get through math 💀

^

you may not be able to get a good grasp on contest math that requires abstract thinking, but you can definitely get to a point where you can do SAT math problems with relative ease

thats what i mainly struggle with ^, contest math lol

[green marsh]

Oh i see okay so practice things that arent on homework

i see

i think so too but im really good at geometry and trigonometry

[cunning imp]

yeah from what ive seen, this is often the problem with ppl who think they are bad at math

i tutored younger students in math last year

and many of them lacked foundational skills, which carried over as they tried to learn new concepts

[green marsh]

im also really bad at problem solving too

[cunning imp]

problem solving can be challenging, but from my exp

if you do enough practice, it reaches a point of pattern recognition

[green marsh]

a pretty decent time actually, i get stuck on it for a while, but if im completely blanked on what an equation means ill look really fast

[cunning imp]

and slowly, you learn methods to approach problems

[green marsh]

so basically practice my heart out

[cunning imp]

this is real asf

blanking on a problem can be really time consuming but one of my biggest weaknesses was always that

i mess up a question and immediately check the asnwer key

because im too lazy to try to find where i went wrong

[green marsh]

how do i do targeted practice

sorry i know its a lot of questions

[lament goblet]

go to cb question bank and select areas youre bad at and solve those

[green marsh]

ooo

a long time ago

in 9th grade

do you suggest i read it

meaning i shouldnt?

ooo

heres my results from my first SAT

[split jasper]

ngl for the sat i assumed you just need to do a bunch of problems. thats how i aced the reading/writing section. i thought the consensus was the same with math. of course, you should gain understanding naturally by doing lots of problems. thats one way to gain mathematical intuition

i never prepared for the math section of the sat so i cannot give tailored advice

[split jasper]

i didnt get perfect

[rain patio]

Its just SAT

Although I dont know too much about it

[green marsh]

I never practiced for the reading and writing section and I got a good score

But the issue was math for me, I recently worked out some algebra kinks and I did really well, I find my problem is now in Advanced Math lol

That I’m assuming I’m gonna have to khan academy, that way it’s not too hard for me

[coral sleet]

@rain patio welcome to the mathcord c:

[storm jasper]

What was your score

[final sinew]

axkyn

[median talon]

Do you have any advice on planning to complete a problem book, similar to Engel’s Problem Solving Strategies? Also, how much time should I expect it to take?

[swift tartan]

If you are asking about general ug math texts, just read through the chapter and answer from a quarter to half the questions from the middle section to the end; that’s usually the best practice bc usually the first questions are like a sanity check when going through textbooks

generally a chapter and doing the questions ofc depends on the person but a course would probs dedicate a week or two to a single section/chapter but that ofc depends on the density of the section itself ofc

i’d estimate around a week to go through those select few problems you chose bc you don’t need to tackle all the problems just bc they are offered

[median talon]

yeah I was not thinking in "study for the test/course" but ,more into getting better at undergraduate mathematics as a topic. but yeah I think the main idea is to prioritize

[swift tartan]

if that’s the case, the more practice the merrier

[stone shadow]

Eh, similar advice tbh. Except this would be much easier to manage than a research project.

So have fun!

[median talon]

yeah, I was thinking on the "grind" of going trough all the problems of some "hard" books.

[swift tartan]

yeah for the harder textbooks, it’s fine even if the chapter takes somewhere between 2-3 weeks even it’s just a matter for how much you are willing to dedicate, but i would state that if it’s taking a solid 3 weeks of dedicated work you are likely doing something wrong and should try to reconsider the approach to the section/chapter

usually means that you understood the content wrong

that’s my rule of thumb that nothing more than 2 weeks of half effort work

half effort meaning doing it in my free time

[polar frost]

Sri sorry to ask again, I'd like to get into analysis but I haven't done much proofs work (only up to calc 3), how should i begin?

[median talon]

thanks , I guess the hardest part will be more the psychological or something similar, but thanks again for the advice.

[swift tartan]

definitely the psych factor does take a hit sometimes but it’s a matter of diligence and it’s also completely fine admitting defeat but also more important to learn from that experience

it’s alright to search up questions if you have zero clue

but doesn’t mean to get into the habit ofc

[median talon]

yeah , I would say the loneliness of working on stuff no one rather than me will care on that specific moment will be the hardest part, but will be an interesting process.

[swift tartan]

i think nothing is better than just going into the content but maybe pursuing lighter material might help rather than jumping into the river

usually some unis offer an intro to RA as one of their intro to proof classes

MIT ocw does this for one

My uni does too

[polar frost]

I'll check out ocw, hb textbooks?

beginner friendly ones, that are kinda intro to proof w/ real/compex analysis

[swift tartan]

I never really liked Abbott but that seems to be a favorite here, I liked Ross’s text , and Adams text for it both are available online for free

[median talon]

understanding analysis is a good one. for friendly real analysis

ahh lol, repeated answer

[polar frost]

I'll buy them tonight and get started on them when im able

[swift tartan]

Abbott just seemed too surface level imo

[median talon]

true, but good for intro to proofs.

[swift tartan]

I am not particularly leading a reading group in RA but just tackling a couple of problems here and there of the Rudin text before my sem starts

[swift tartan]

yeah this is true

[rocky terrace]

Literally not

Rudin and Abbott have 85% similar content

[dim dirge]

oh gurl
no 😭

[swift tartan]

Perhaps I used the wrong word? But I still feel it doesn’t go as in depth with the content compared to Rudin and Pugh

I just pulled my copy up to verify and confirm what i felt

I looked through it during a reading group this spring early summer

Also cc @dim dirge

Maybe it could also be that I personally found that it was also a lot easier of a problem bank for me comparatively to that of rudin

Our uni uses Abbott for intro to real compared to real

My prof used Ross text and Adam’s text tho for my intro to real course

[runic crest]

Abbott barely covers anything

I agree with Sri

[swift tartan]

yeah that’s how i feel

I felt like it just touched the beginnings of each topic mentioned in Rudin but it didn’t explore too far beyond that

we have another prof in our dept who uses Abbott for intro to real so i’ll ask a friend and see what they took away

[storm jasper]

The proofs are just harder

[swift tartan]

Honestly this might be the reason why I feel such way perhaps

I do recall that I kinda zoomed through Abbott compared to Rudin

So who knows could def be a biased perspective

I liked Pugh though, excellent exposition imo and good questions

[green marsh]

1150

[storm jasper]

thats why i use easy stuff

abott

[storm jasper]

hm are you a freshmen

[swift tartan]

You get stronger through practice and honestly this may sound annoying but there isn’t really anyway around it honestly. You learn proof writing from ways that the thm is written and once you finish a problem verification is important but also shows possible fallacies in your own proof

@icy beacon ^

Just because you do Hammack over and over again it wouldn’t help past the foundations or basics

[icy beacon]

Yeah I think my approach is wrong and I’m not active enough while reading. I thought about doing hammack alongside Shilov’s linear algebra which I’m currently using but I despise “how to” books for some reason.

[storm jasper]

;-;

[green marsh]

no lol I’m a senior

I’m bad at math

[swift tartan]

You learn proof writing from ways that the thm is written and once you finish a problem verification is important but also shows possible fallacies in your own proof

This last part is esp true, and if you are in uni, your prof should def help if you copy down the proof or atleast the idea of how they prove things

The point of intro level classes is ofc to get introduced to maths, but at the same time, you kinda also subconsciously pick up diff proof methods and make it your own

For example, I learned induction differently in 3 diff intro lvl classes (proofs, lin alg, and intro to real analysis), but the prof who taught the last one made induction so uniquely easy

imo not really bc maybe ive gone too far that the problems themselves are a little too easy, but the methods they give lowk are more formulaic that it doesnt help too much in the long run

like hammack is a great text, but their proof method feels like im writing code

it helped out early on, but i like my style more now

This is also what i mean by its very formulaic, and each time when you input a then statement, you also add a thus at the end

Like nice idea tho

[crimson elm]

At some point it feels like writing an algorithm or a code. It gets very unfun

[swift tartan]

Yeah I like a bit of pizzaz in my proofs

[crimson elm]

You know what's really annoying? I have to take two courses that feel like this for my degree. Both of which come from the cs department

[swift tartan]

i cant wait until I use the most english words and have exquisitely picked out words from the dictionary

[swift tartan]

yeah dang

can i dm you something a prof this spring did?

[crimson elm]

the average math class is oike "yeah follows from induction" and these two classes feel like:
Proof:
......

....

...
Therefore ....
Therefore....
Therefore...

[swift tartan]

it was messy as hell

[crimson elm]

sure

This is literally just code

the way it's indexed too

horrible class lmao

[swift tartan]

oh god

[lapis sluice]

I like this tho tbh

[swift tartan]

skinwalker, get out of my head

[dim dirge]

yeah, same!

[dim dirge]

u know, it's like dividing your thoughts into paragraphs and such xd
just looks cleaner

ESPECIALLY, for simple and short proofs like that

[dim dirge]

tickles my brain somehow
maybe because i'm into algos and TCS

[crimson elm]

You say this till you realize you get docked marks for stupid things like "not following the procedure of the proof"

omg that class was a nightmare lmao

[dim dirge]

well that was the profs fault

it has nothing to do with this style being nice*

-# *for short proofs

[crimson elm]

It is nice and pleasant for the eye but it just feels too robotic if that makes sense

[dim dirge]

you just insulted Tao

big T if you will

[crimson elm]

Tao's proofs are not robotic afaik

The one's I've seen in analytic number theory

[dim dirge]

i meant his work in computer-assisted proofs

[crimson elm]

Oh

Yeah it's fine for robotic proofs in that case

[fiery iron]

what the hell

[unreal mulch]

I do this but with fibonacci tab unintentionally

[devout sun]

Me writing an analysis proof, running out of the words that are synonyms with "therefore" be like

[dim dirge]

$$ \text{{shit happens here}} \iff \text{{other shit}} $$

[mossy shadow]

emilia

[dim dirge]

i wanna try writing a complicated proof with absolutely NO words of explanation, just quantifiers and other logical symbols

preferably so that a prof I dislike would have to read that

[devout sun]

I swear I'm literally just spamming "therefore, so, thus, it follows that..."

"since [...], we have"

Yes hence is a good one

I should make a list

[glacial raven]

C l e a r l y

[devout sun]

trivially

[rocky terrace]

Whence

[devout sun]

ngl it annoys me when ppl say from whence

like it sounds nice, but youre just saying "from from where"

[quick elk]

from whence did you get this annoyance?🤡

[swift tartan]

https://www.merriam-webster.com/dictionary/whence

iirc it’s just a shortened “where hence forth” that’s more so what i get from it

it’s like a timeline / describing the origin of something

[bleak tinsel]

I need some guidance, and I thought that this might be the place to get it since I’m mostly isolated. Here is some context: this year I’m going to move from 10th grade to 11th grade. I did Calculus BC last year and will likely do Calculus 3 next year (US maths is not very advanced tbh). During the last couple years, I have gotten more interested in maths and have started watching and solving math videos (Mind your decisions, black pen blue pen, etc). Also, I attempted to do AMC 10 and got only 49.5 (damn). I want to do more math questions and get better at it, but I am not certain exactly where to start. I’m at the point where I’m too dumb to do competition math but also want to git gud. So, if anyone has any suggestions, it would be much appreciated. (Ironic how my last question was to just "git gud" I guess I backtracked hard)

[swift tartan]

Honestly, contrary to popular belief, competition math is just competition math its meant to just have fun

Sure you can do it, if you win that looks cool, but it relatively "improves your critical thinking skills" but I wouldnt say it makes you "better at math"

Since it sounds you are in hs, dont worry about whats going to happen in college or future. Just focus on what you have now and whats available to you and just try to be diligent and good at it

[swift tartan]

also mind you, competition math are generally topics from most common areas of math but comparatively easier than a ug or esp a grad course. Its usually a little more challenging bc most dont do proof writing in hs, but also familiarity of content material

[swift tartan]

yeah looking back at competition math like AMC made me realize (maybe just due to mathematical maturity) but its not that bad

But thats also why there is specifically collegiate math comps too tho

Its def a lot harder even for grad students

For one competition some may know from the US, called the Putnam Exam

But also recognize, if you took the classes that the Putnam Exam usually includes, youd have a pretty good chance to atleast get 2+ questions but also being able to have enough brain to understand is another thing lol

Thats why most seniors do well on the Putnam

[split jasper]

this is not true

[swift tartan]

Can we discuss this in #math-discussion , id like to know more tho

[swift tartan]

we did not end up discussing

[rain patio]

LOL

Both are pre mid ngl

[limpid hamlet]

Actually I think it does compared to what most people do in school.

The basic thing of having ever tried problems where you weren't given the algorithm to solve them in advance is pretty useful

Having ever figured out how to solve a problem without already knowing in advance is rather unlike most early exposure to mathematics.

I have noticed that if you give something that is not instantly recognizable as one of the preknown forms of problem to even a good student in a stem field, they will often just... sit there... not seeming to do anything or think of anything... or give up immediately. Seemingly this is because they do not have the skill of how to work on a problem they don't know how to solve, or stuff like "play with it" or "try some small examples".

[swift tartan]

i’m at odds, some points i agree with and definitely changed my perspective but not completely. I think you are right that competition math does make them more adaptable at facing new challenges and overcoming them, which usually involves some sort of algorithmic approach. But, I can say this about almost anything else because people like to do what they are willing to put interest in. I have to say specifically for hs and lower level competitions it doesn’t provide anything beyond than just being able to memorize and use such calculations.

I guess to put this into context, for example being a programmer I can learn as many languages as I can and I can also output the right code for the program at need. However, if i wanted to be a “good computer scientist” and not just go into industry or apply myself, aka academia, then it doesn’t really serve me much help just because i know a little of everything rather than the theory. Ofc this last statement is purely subjective with a clear goal of academia in mind.

It’s a useful skill set for any point in life, but I think as a hs; i’d honestly just recommend trying to enjoy it and do stuff that’s fun for them instead of worrying if it makes them better at something

[swift tartan]

I hope this last part summarizes better what i was trying to say

Also we can actually move this to #math-discussion for the future of the convo and just tag me

[deep pulsar]

how do i drop the study role

[safe harbor]

In #bots ,iamnot studying

[deep pulsar]

ty ty

[limpid hamlet]

hs and below competitions definitely have problems that aren't just rote computation

[runic crest]

[grizzled bluff]

yo

Hey

[tropic void]

[main lodge]

It's done. Last exam over

One of the most brutal semesters ive ever had and school already starts next monday

[normal sleet]

Oof
Its over at least
Good luck for next sem

[agile hollow]

[tropic void]

hiiiii

[agile hollow]

hi Pseudo

how are you

[tropic void]

happy :D

figured out even more cat theory

and I also understand homology now

[agile hollow]

yey :D
omg really?

[tropic void]

mhm!

[agile hollow]

wow

this is impressive

iirc previous time you were studying some like inf - inf categories

[tropic void]

mhm

[agile hollow]

or omega categories something

[tropic void]

mhm, that’s what they’re called

then I had an arc doing some more elementary cat theory

[agile hollow]

that is so cool

for real?

[tropic void]

mhm!

im really looking forward to sharing my findings

[agile hollow]

sure sure

i would store that information for my future use--when i will officially learn cat theory

[tropic void]

I am working on making it easier to learn!

[agile hollow]

Best of luck Pseudo

i would try to keep checking your arc, and i hope i will learn something new as well

[tropic void]

The main thing I’d like to share is a different notation

Which makes a lotta results visually transparent

[agile hollow]

yey !!

:-D

[rocky terrace]

TRANSparent?

[tropic void]

[rocky terrace]

damn liberals bringing trans stuff into my cat theory

(/s)

[green terrace]

we've got transparent, where's my cischild results

[wanton dome]

(probably) weird question: does anybody know of any platform/website/app/whatever that gives you random problems based on difficulty on determined math topics that also has solutions + explanations?
Ideally i'd be able to just open the thing and get a random problem to solve daily. Primarily word problems

[swift tartan]

At what level?

undergrad, grad, or hs?

[halcyon wave]

Do you have a lot of samples?

[cloud gale]

No that much

Well, in catalan (my language) i have about 8 of them

[halcyon wave]

I would argue that the best way to prepare to this kind of test is just by doing a lot of them

8 is good

When I am studying for my exams i'll do about this amount of previous exams

in the best case

[cloud gale]

I struggle w this exams because i know the math to solve it, not WHERE to apply it

And its very frustrating tbh

[halcyon wave]

If you know the math, studying more the math itself won't be very useful for you

if the issue is to apply what you know

the best way is to try to apply, understand what is asked

if you make an error

why did you make this error

[swift tartan]

By solving the math, do you mean just the arithmetic, and not knowing when to use which arithmetic operation to solve a problem?

[cloud gale]

The only field where i'd like to learn the math is geometry, I'm weaker on that spot

[halcyon wave]

we can do some exercice together

from the sample you gave

[wanton dome]

i'm not sure. I'm studying math to get better at 3d graphics programming, and since i'm dumb it's going to take me a lot more effort to understand and remember

[wanton dome]

referring to this, sorry

[cloud gale]

Won't it be hard because of the language

[cloud gale]

If I sometimes struggle with my own language, I can't imagine with English 😅

[cloud gale]

Np

[cloud gale]

Wdym? Sorry if i do not understand

[halcyon wave]

no worries you can always translate, or you can just try to do it

and if you're lost you ping me and I'll try to help

[cloud gale]

Ok

Are you from the US?

Cause idk if our time zones coincide in an appropriate time

My parents won't let me if it is too late

😔

[swift tartan]

Yeah no worries, I guess the better question is: What do you mean by you are able to know the math for the problem but not know when to solve it?

[swift tartan]

its based off of this message

[storm tide]

It sounds like you have up to three distinct problems here:

1. What you can't change: That admission to a serious institution of learning you want to enter is based on a math contest -- your example test explicitly identifies itself as a contest, and at some of the questions are clearly contest-style, e.g. number 18 and especially 22.
2. Language: Without a good command of mathematical English you may end up wondering whether a word in a question that you don't recognize is a precise mathematical term or just a "flavor" word from the motivating story. There's probably no other way to improve on that than to get as many previous tests as you can and go meticulously over them and make sure you know every word, mathematical or not. Then hope that this sampling has covered all the mathematical terminology you'll need.
3. You write "I know the math to solve it, not WHERE to apply it." That sounds like you might be saying you can only answer the question once it has been reduced to a symbolic form that tells you which procedure to apply. But if so, that means you have not really learned those procedures yet. It's not enough to be able to perform it; learning it also means you must intuitively understand what the procedure achieves, well enough to be able to recognize when that procedure is what you need. To remedy that, I think the best you can do is to be critical when you read solutions to this kind of problem: Don't feel satisfied just because you can follow the calculations in the solution; you must also for each such solution spend time understanding why those calculations gave the answer the question wanted.

[swift tartan]

^^^^

Yeah that third part was what I was trying to understand more of but thats really the main issue

Like for math, being able to be told "do xyz on this problem" is easy to do, but being able to recognize when to do it on your own is what actually shows proficiency

A lot of ppl I tutor struggle with this and they usually quickly pick up the content/material because once they understand that sort of "situational awareness" but to a math problem they usually are good to go and are chilling for the rest of the year

Practicing is really the key as youve been told before

[cloud gale]

I get what you said there on point 3. Which I believe is the closest way of describing my problem. This comes from my educational system. Specifically, from my school itself. We usually see exercises on exams where the operation needed is given explicitly unless it is an "extra exercise". Those are somewhat difficult only because they make you mix the concepts or make you deduce which concepts to use.

Obviously, none of this helps when you're doing an exam like this, and it's a pity my school (and lots more in Spain) teaches like this.

Per your recommendations, I'll try completing the exams, and giving you feedback if I struggle somewhere (if you'd like to help me further).

I don't know if this might be a good idea, but do you guys think that I could try using ChatGPT to ask how to resolve questions after finishing and reviewing the test?

And @halcyon wave, can I send you a DM in case we review exercises?

[storm tide]

ChatGPT for math help should be approached extremely carefully. Sometimes it produces good and useful explanations. At other times it can make horribly wrong claims -- and it is very, very good at making its horribly wrong claims sound authoritative and convincing. So if you use it at all, you MUST be on the lookout for mistakes, and not trust anything it says unless you've really convinced yourself that you believe it because you can see for itself that it must be true, rather than because a bot on the internet says so.

[cloud gale]

Thanks for the help! Really appreciate your work 🫡 😊

[halcyon wave]

yes

[swift tartan]

I am personally in the old school boat that I dont at all recommend chatgpt. I have seen it be used and also provide atrociously bad results (even the new one is still bad). Its just not great at critical thinking

So if you use it at all, you MUST be on the lookout for mistakes, and not trust anything it says unless you've really convinced yourself that you believe it because you can see for itself that it must be true, rather than because a bot on the internet says so.
At this point, imo, you might as well just do it yourself and learning via the textbook lol. Also google and stack exchange are good friends

But it is definitely the future, I just dont think its all there yet

[fleet hill]

I think GPT is great for many things but for most math you learn in school there's so many high-quality free resources out there already that I don't see what the point of using it is

[storm jasper]

I meannnn earlier real analysis proofs are easy to understand : D

[atomic prism]

so out of curiosity what is the best and quickest way to learn like college algebra

[storm jasper]

Like linear alg

[atomic prism]

(i've never properly studied so i have no clue)

[storm jasper]

what is college algebra

[atomic prism]

just algebra as a whole tbh

i don't know how to describe it 😭😭

[storm jasper]

Um

Abstract alg then?

Troposphere can carry big

But

I think ur talking about linear alg and stuff

Maybe abstract alg

[storm tide]

I think someone once explained to me that "college algebra" is a euphemism for "high-school algebra, but taught at a college as a remedial course".

[storm jasper]

So like algebra 1

[storm tide]

I don't know about "<topic> <number>" divisions.

[atomic prism]

uhh it's like linear algebra

[atomic prism]

remedial is a whole other class

apologies for being confusing i'm so tired

[storm jasper]

Does linear alg have at least some form of Galois theory

I know it’s in abstract alg but still

[atomic prism]

i looked it up and it said yes

[storm jasper]

Ring theory?

[atomic prism]

i've got no clue