study-discussion

[icy basin]

Ok

Now what os debate gonna be about

[proven hull]

I feel that too

Having right person around you really motivates you

Not only that one should always know their limits and boundaries

[icy basin]

Wait we need more ppl

[proven hull]

No its fine
Sometimes all we need is ourself

Completely not against socialisation

But ine should try to stay alone and bore for an hour or saw

[icy basin]

Ok whats the topic about

[proven hull]

It will help us to reflect

[proven hull]

Studies

And stress

[icy basin]

Ok

So for studying there 2 typoes of my main motivation a person can have one is rational and one is irratinal its badicly when u do smh to prove to others not for urself and rational is to become better person irrationallity can be used as a good weapon cuz its basically emotional thinking but if you let it control you and let how people see u be ur identity u might get problems with stress when it comes to proving urself

Hello?

[finite yacht]

I feel like there could be a lot of other motivations beyond those 2, like having a better understanding and apperception of the world around you and maybe learning skills that could help you in your career

[icy basin]

Yh this is rational

Cuz ur doing smh to become better person

Or for urself

Maybe enjoyment

[finite yacht]

But isn’t doing it to show off to others also doing it for yourself. I guess maybe what you mean is intrinsic vs extrinsic motivation

[icy basin]

No

Cuz then

Ur trying to shape ur identity on others views

Like its like having obsessive ideas and trying to proof obsessive ideas wrong

For example

Or tryung to show people that your better bcz u feel like they dont see u as best

Its basically smh related to ego mostly

And attention seeking thats why u see nerd thats are nice and help pfhers and ones that are mean and try to prove that best and are very defensive

Narriscm usually comes from this

[finite yacht]

Yeah that makes sense

Basically you’re trying to prove something about yourself to others instead of trying to prove theorems lol

[icy basin]

Like its when u dint admit ur mistake

Sometimes it can be good

Like it can work as a drive to make u insane

Talking from experience

And sometimes it can also be bad

Cuz holding to much responsibility for something is bad

Cuz it increase anxiety and obssessives

Like its a great way to reach high points dont get me wrong but

Dont make ur image ur first goal

But make it a sidequest

And u becoming better for urself is the goal

[finite yacht]

I think that being motivated to improve yourself is a lot more of reliable and allows you to be more consistent than doing things because of other people

[icy basin]

It is

But in enviroments like good schools and uni there a lot of competition

So people rely on this type of motivation to climb the ranks

Once ur there

U make a small mistake

U get more mad

Then when u climb for urself

[frosty gate]

Thabks for the tips, I could try sports , they do make me extremely exhausted sometimes but they work, ah well I definitely do not have ocd ig I do tend to have obsessive ideas but definitely not that extreme , maybe im just burned out, yet again thabks for ur advice on this

[icy basin]

Np

[frosty gate]

Ahh well, mosr of my friends too are stressed about exams and stuff so I feel like a leech when the discussions with them go about stress, maybe I should find seniors who can guide me better

Where can I find a study partner? I feel like it would be a lot more helpful tbh

[finite yacht]

Honestly I feel like it’s hard to find people that really motivate me and I can study with in my personal experience

Most people just aren’t willing to go so deep into a topic but just study to pass exams

[icy basin]

Me to

If u want i help

I am currently looking for ppl

[finite yacht]

I guess it depends on what year you’re in

I haven’t really got to stuff like Real Analysis yet

[icy basin]

I am grwde 8 but i study anything that other day i was studying defined integratiom

That other dya benford law

Like anything

[finite yacht]

That’s honestly pretty good tbh if you’re only in grade 8

[icy basin]

Thx

[finite yacht]

I don’t think I was that motivated when I was at that age

[icy basin]

I do robotics and coding to aswell as 3d design

Yh i understand

Its prob that i had better like

Consequences

[finite yacht]

Wait is defined integration the same as a definite integral

[icy basin]

Like

When u put numbers on integrals

Up and down

And then solve

For example 3 2 and then u have 2x next to it the answer would be xpower of 2 and then u subsit 3 and 2 and subtract both answers which is 5

My explanation is prob bad

[frosty gate]

Thats true, it is not that most of the ppl aren’t interested , but with the current system, the amount of exams , it gets hard to dig in deeper, because now the exams are around the corner and you’d likely be lagging a bit behind, it’s sad how things are

This is just the experience of a bunch of ppl ik

I’m sure there r a lot of ppl out there already digging in deeper, but im mostly talking about how things generally are where I am from

[proven hull]

Tbh same here
Even my friends are stress
We talk about it everyday amd then we all study at the end of the day
I guess that's a mindset few of friend helped me to develop

[icy basin]

Its cuz yall are taking the thing to seirously

It means u have great responsibility

And love to what ur doing

[proven hull]

The only stress we have disappointing our little self and are dream

[proven hull]

Mostly of dreams well atleast me and my friends
Some have society pressure

And also burnout

Like this week I've 7 classes

Including sunday

[proven hull]

But that doesn't work for a lot of exam such as those college entrance exams

[proven hull]

I agree a lot
And a lot of people dont have enough materials to study or even do extra curriculum activities

[proven hull]

Same

[brazen mist]

What's defined integration?

[storm tide]

Almost certainly a failed attempt to write "definite", given the subsequent explanation from 員わぼ.

[eternal sparrow]

I have a math test on Tuesday. I also have a really important exam on Friday. there is a possibility i can skip school on tuesday to avoid the test cause I don’t know anything at all and i would prepare for the exam which i care more ab. But that possibility isn’t guaranteed. And if i go on tuesday I will fail my class. But if I don’t prepare for the exam on Friday, I will lose a huge opportunity.
Does anyone have any suggestions 😭

There is just so much to study and I doubt i could do both

[bold lake]

Is there a discord server that can help with classical and quantum mechanics?

[storm tide]

There's a physics server linked from #old-network.

[snow prawn]

Hey everyone, I need some brutal honesty and advice regarding "mathematical ingenuity" or intuition.

I'm currently a 2nd-year math major and I feel like I'm hitting a massive wall. For every single subject, my study method has been to grind like crazy: I memorize all the extensive theorems, their proofs, and solve literally every single problem sheet provided by the professors (hundreds of exercises). I always go into exams feeling like I've done everything humanly possible.

But the exams always follow the same brutal pattern: they give us completely unseen, abstract problems. You're supposed to solve them by combining the theory with some specific "trick" or "mathematical ingenuity" that you have to come up with on the spot.

When we ask professors how to prepare for this, they usually just say that this ingenuity "can't be taught", that it just "clicks" eventually, or that it has to come to you naturally.

Well, it hasn't clicked for me. Despite giving 100%, I keep getting bad grades. My brain just searches its database of solved problems, and if it doesn't find an exact match, I freeze. Brute-forcing the study material just isn't working anymore, and I'm seriously considering dropping out because I'm running out of funds.

My questions for those who have survived this transition:

Is this "mathematical ingenuity/maturity" a real innate thing, or is my studying strategy (brute-forcing hundreds of repetitive exercises and memorizing) completely flawed?

How do you actually train yourself to see the "tricks" in unseen problems when you are studying alone? How do you transition from purely mechanical solving to actual abstract problem-solving?

Any advice is appreciated, because I feel like hard work alone isn't enough anymore.

[storm tide]

Ideally the ingenuity ought to have been trained throughout the course with exercises that are also completely unseen problems that need puzzling out.

[snow prawn]

So I should be ideally focusing on understanding the basic theory problems and then try to apply it to the rest?

[storm tide]

If the exercises you've done along the way have all just been applications of precooked methods already presented, whereas the exam requires independent thought, then there’s something wrong with the course.

[snow prawn]

Well all exams seem to be like this, the professors like to say 'We want to make you think a little bit more' then they make a problem with the same principle that use ''tricks'' that we havent even seen

[storm tide]

However if you did have such exercises, and you've been satisfied with just memorizing model solutions to the ones you failed to crack yourself, then you're using those ecercises wrong.

In case of the course not providing exercises of the same kind as exam problems, a strategy could be to train with old exam sets rather than the official homework. (Of course, knowing that to be the case before the exam can be difficult).

[snow prawn]

Alright I see, I apreciate the help tyvm

[tropic void]

in my case i found that anki flashcards were quite helpful for memorization

often when i found a new trick or insight or explanation of a misconception, i'd make a flashcard for it

my idea was that i might make mistakes or miss things at roughly the same rate as my peers, but ideally i'd only have to do that once

this helped me massively in doing undergrad math, perhaps it could work for you as well?

i also don't know how to force ingenuity or anything like that

but this strategy helped for me

often, i would figure out insights just from trying to simplify my flashcards

each area of math has its own bag of "tricks", sure, but it's a smaller bag than you'd realise

especially at exam level

it's just easy to vastly overestimate your capacity to remember tricks

[strong oar]

i KNEW you all used flashcards!!!

sorry for my excitement

[normal sleet]

Well i never

[bold lake]

Has anyone learned classical and quantum mechanics before? Dm me

[icy basin]

Understand bcz at the end u need to use this to solve problems so u cant just understand how numbers work u need to understand how they sre used more

Its the diff between an actual job and studying

And ur being prepared to solving problems so when u go to ur job yh

[proper rain]

Is Khan Academy good for reviewing?

[leaden laurel]

how confident do you feel at explaining / deriving those concepts to someone else?

[snow prawn]

Good question lol

Mostly I just stay it’s trivial and go on

[leaden laurel]

thats probably where these problems start, being able to explain something clearly is an important skill on its own, even more so for maths since it helps you to build up and use whatever you learnt in different ways

[snow prawn]

So overall I should first be able to understand the theory and concepts, and be able to explain them to a 12 yo pretty much and then move on to the theorems first and try to sketch for a while to figure something out, to get used to being stuck and not solving something in 10 minutes right? and then move on to the problems doing the same thing

[leaden laurel]

you might also find it helpful to go on sidequests by asking what if's even on simple things

eg volumes of revolution are normally done around the x or y axis, how can you extend that to find the volume of revolution around the line y = ax + c or y = xtan(theta) + c

[leaden laurel]

the main thing is to be able to reason and derive and convince yourself on how you could have reached that same result / theorem and go through all the steps of reaching it

[leaden laurel]

this can be a very dangerous mentality to have because it leads to weak foundations where you can only work with things that match exactly that, so its hard to offshoot from there without being confident and understanding what your doing

[snow prawn]

I see, I get if now. I appreciate the help

[leaden laurel]

you are really well though since youve been sticking to your major for nearly 2 years i think now even with all these difficulties present, which means you have really good commitment

alot of people in your situation facing adversity like that might have given up earlier so it shows you are strong willed which is very important and needed for maths

[snow prawn]

Lol I don’t like to hear that since it’s easy to just stay and keep doing this wrong even if I didn’t notice that I was doing then wrong.

But for example for real analysis, the last chance to pass the class I studied by memory 40 long proofs, didn’t understand 80% of them

just went with memorisation as the last choice

[storm tide]

In most situations it would be counterproductive to try to follow a strict phase distinction of "first concepts, then theorems". Very often, the only way to really understand the definitions and concepts is to see how they're used to support proofs, and spend some time thinking about how they fit together. If the definitions had been slightly different, would the proofs still work? Or could some proofs become easier with different definitions, but those definition would cause other proofs to go down in flames?
The more energy you invest in such analysis, the easier will it be both to remember the actual definitions and to use the concepts in new settings.

It can be useful to read though the text extensively at first, deliberately not trying to memorize any proof details, but just to get a feel for how things fit together. Then on the second and later pass, you can stop after each statement of a theorem and ask yourself "with the high-level overview I have now, can I reconstruct how this proof would go?" Having been past the proof once is not "cheating" for this purpose; on the contrary it will often enhance the learning benefit of trying to reconstruct it.

[snow prawn]

About the “what if”, is it worth it to ask these questions on the lectures? Or do I simply write them down for myself to try to answer them on my own later on?

[storm tide]

As a general rule, I'd say not in the lecture where the concepts are first presented. If you spend some time thinking about them afterwards and don't reach an answer that feels satisfying, then it can be good to bring them up afterwards at an appropriate occasion (after the next lecture, or at office hours, or with a TA, or in a study group, or online such as this server).
It will often result in more instructive answers to phrase the question not as "why isn't it such-and-such", but instead "would doing such-and-such also work?"

[leaden laurel]

"what ifs" and other offshoot projects are really useful for getting you to be more familiar on using those concepts your learning in a different way, eg you might want to extend reflection to be around a line in 2d --> around a line in 3d --> reflecting general space curves around a general plane

[snow prawn]

So I asume that the what ifs take majority of the studying time, they can be done anywhere right? What I mean is that I don’t need a paper out to write. Because I usually spend around 5h a day commuting to the university so it’s pretty tough

[leaden laurel]

on the 5 hours of commuting is like active commuting where you have to focus and go travel between many stops and if you dont pay attention you will miss your stop or is it like 1 long journey and you can just sit down?

[storm tide]

It will depend from topic to topic whether you can keep everything your need in your head. Sometimes one definitely can; I've gotten some splendid insights while bicycling to school/work.

[snow prawn]

nah it’s 1 journey on bus

[snow prawn]

I see

[leaden laurel]

if your on bus with only 1 journey then thats the perfect opportunity imo to try the "what if's" and any offshoot projects

[snow prawn]

sounds fair i’ll do that too

[leaden laurel]

the best way to do it is taking a notebook and pen with you and maybe use your phone periodically to look at notes if you need to look at it while doing it

[leaden laurel]

during that time you can also try to explain a concept you feel your already familar with but not all the way there to yourself until you feel confident that you can explain and teach it well

thinking about it and explaining it mentally to yourself

[gaunt ruin]

I'm scared of triple integrals surfaces and spherical and cylindrical coordinates

surface integrals I am also scared of them

[snow prawn]

Perfect, thanks a lot

[winged crow]

I got a question for all those doing problem sets/ assignments on their tablet. How do you do it? Do you split-screen? Copy-paste screenshots? Use a laptop/ PC beside to show the assignment and only write on it?

[rotund zodiac]

i do laptop/PC. if im in a pinch, i open the pdf on my phone and squint

[torn olive]

copy paste screenshot of problem statements

[marsh cargo]

Either I use a laptop to show the questions, or use goodnotes and copy paste screenshots

usually the second

but the first is pretty comfortable to do

[fleet moss]

Hello,
I need a favor. I need advice on how to study with adhd.
I have realised I need help with studying, albeit very late, although I was diagnosed early on. After being diagnosed, I have never once gone for counselling, which is why I am here.
I can study really well at night, I can focus really well and go very in-depth into the subject. Due to the fact that this is really close to my bedtime, I sometimes go past my bedtime and mess up my sleep schedule.
However, although I can focus amazingly during this random time, I cannot focus during the day at all. I have a really important exam coming up and the fact that I can't focus while studying during the day really puts me at a disadvantage. My theory of the subject is really good since I study in-depth at night, but I am not able to practice during the day.

So, I ask you, how do I study during the day?
Whenever I study during the day my mind is like "This is so boring, I can't focus. I'll close the book now and study later" , and by later I mean like max 1.5 hrs, but I just forget about it and study when I get a bout of energy at night.

[grave valley]

is it not possible for you to shift some stuff around so you have more time at night to study? in my experience its easier to try and shift your life around your brain than the other way around

but its easier said than done

[fleet moss]

It messes up my sleep schedule

it is already messed up, so I don't want to mess it up anymore

[grave valley]

that is fair

[fleet moss]

nice cat pfp

[grave valley]

ty :3

[fleet moss]

what's her/his name

is it hunter?

[grave valley]

in that case i'd recommend having a place where your brain is in study mode, like all u do is study there. like a particular area in the library or something. and dont go on ur phone or do anything that isnt studying there.

having a routine around this location is also helpful, like for example getting coffee every time before u go there. after a while ur brain associates coffee and the location with getting stuff done

this is a more generic study tip tho

my main tip for adhd is to work around ur brain and not try and make it fit ur schedule (which is hard)

[grave valley]

no idea lol

not my cat

[grave valley]

if you don't have obligations that make you keep a strict sleep schedule i would recommend seeing if you can bend it a bit to take advantage of ur nightly hyperfocus. like maybe take a nap when youre unproductive during the daytime and spend an extra hour studying at night or something

[grave valley]

another general tip is to take boring breaks like i literally stare at the wall 😭

[fleet moss]

I don't find that boring

I drift into another world

[floral musk]

lowk adderall if its available

otherwise switch books frequently

i slowly become illiterate when i spend too long reading a given book, but the progress resets when i switch books

idk if that holds for everyone, but its probably worth trying

[winged crow]

How do you not run out of space? I have tried the copy paste part, but had to always scroll back up to see the problem.

[torn olive]

You scroll back then

I mean presumably after working on a problem for a bit you just remember it as you work

[low viper]

Hello, people! I would like to ask for advice.

How do I exactly self study maths? I have a textbook, and I found a free course on YouTube which uses the textbook I have. Do I just listen to the course, write down notes, ask questions and do exercises, or is there anything else?

[winged crow]

Assuming that the problem is split into sub-problems a) ... d) with one big block of assumptions beforehand. Do you then also screenshot this big block seperately and paste it before the smaller sub-problems?

[torn olive]

I'd screenshot each sub problem

I mean again you will remember the assumptions as you work on the problem idk how you wouldn't

Also I feel this would have been more quickly resolved if you actually went and tried doing stuff rather than asking what others do.

Study techniques are quite personal, at the end of the day you must go try the thing

[torn olive]

Doing the exercises is the most important part

If you want to write your own notes go for it

[low viper]

Understood, thank you

[storm tide]

And not just doing exercises, but also actively think about what you can learn from them, other than merely "such-and-such is true".

[frank marsh]

i need some help

guys i have a friend who does pre-college mathematics and sometimes college level mathematics, I am just a level below him, im currently in 10th grade (he's in 10th too) but I study 11th and 12th grade syllabus, how do I reach his level?

[fleet hill]

I wouldn't worry about reaching someone else's level, just improving your own understanding. KhanAcademy is a good source!

[tired oxide]

hello everyone :) im not exactly sure how appropriate of a question this is, but i have mild to moderate chronic fatigue syndrome, and struggle to study (at school) full time as it is. i am currently self studying the entire algebra 2 course and planning on precalc in the near future, but i find it really difficult to stay consistent with my studying due to how much of my days get interrupted (by sleep) and how distorted my nights are. does anyone else suffer from this illness and/or have any recommendations on how to better approach my learning?

[frank marsh]

hey, thanks for telling me that :))

[frosty gate]

heyy guys, what are some of the things that help u feel well charged or refreshed during breaks (the problem im going thru is, im very productive in the morning but by evening im toooo exhausted to get things done, then i just mindlessly spend my time trying to feel relaxed, and hours pass by with nothing essentially productive being done) so looking forward to trying things u guys do

[crimson elm]

Watch a video on Edward Frenkel yapping during my break helps me get well charged when the break is over

[mental radish]

Hi everyone, what is the best way to prepare for ap calc bc?

[warped torrent]

hello,whats the best way to learn all of linear algebra in 4 days

before my exam

[storm tide]

Not possible.

[ashen totem]

you may accomplish 10% of your objective if you replace days by decades

in 4 days maybe you'll have time to understand what a basis is and know the rank theorem

if you go through the first chapters of a book really fast

[tacit pebble]

Idk, I just do more practice problems

Ooh or try to teach other people in your class

My teacher uses the Algebros

[mental radish]

what is algebros?

[tacit pebble]

It’s a website

They do AP bc, AP precalc, pre algebra, geometry and algebra

[icy basin]

Idk hpw

I was making up sh

[warped torrent]

im gonna try to do it

my short term memory is goated i can cram it in

[frosty gate]

Watxh one shot lectures

[compact current]

I just want to vent about algebra—damn, this is hard. They always make the course seem impossible and not very fun.

[leaden laurel]

it depends if you know what topics are going to come on your test

if its a blind test and all you know is all the content that youve gone through in class has a possibility of showing up in the test then its not going to be fun for you

but if you know whats coming up you have a better chance atleast

[pearl turret]

ggs

[pearl turret]

linear algebra?

[signal bay]

emdash!?

[edgy sierra]

probably abstract algebra

[left yacht]

It'd be quite funny if they were referring to middle school algebra

And I will headcanon as such

[rocky terrace]

Higher algebra

[crimson elm]

<@&268886789983436800>

[cobalt sun]

higher! algebra

[left yacht]

we need a channel for these clips theyre hilarious

[compact current]

abstract

[signal bay]

#discussion

[rose ferry]

Is there a site where i can test my level of education in math to see where or how good i am in math?

[astral lantern]

khan academy has course challenges i guess

[shell glade]

the problem is @crimson elm does algebraic number theory/arithmetic geometry.

shouldn’t he like higher algebra?

[left yacht]

he got hacked

idk

[weak geyser]

<@&268886789983436800>

[teal pulsar]

Next year I'm taking a gap year, and was thinking of doing some self study in math, and possibly add also chemistry and physics.

I have already chosen some books to study, I came to ask how many hours a week should I give to each, and also if you have any suggestions / improvements about the books, order, note taking, or anything else.

The books I chose:

1. A Gentle Introduction to the Art of Mathematics -- Joseph Fields
   1.5. Possibly after it I'll look at Book of Proofs by Richard Hammack
2. Linear Algebra -- Kenney Hoffman and Ray Kunze
3. Mathematical Analysis I & II -- Vladimir A. Zorich
   3.5. After Zorich possibly to look at Baby Rudin

[grave valley]

🐀 kunze

[teal pulsar]

Oops lol

[green terrace]

Afaik you don't strictly need rudin after zorich unless you want to do the exercises, ans zorich 1 and 2 + all the others in a year is a lot of work

[teal pulsar]

I think I definitely want to do at least Fields, H&K and Zorich 1
Do you have any suggestions for how many weekly hours should I give each?

[smoky canopy]

Would #advanced-analysis be a suitable channel for questions regarding complex analysis in several variables? Just need some validation I guess

[whole wing]

Yeah, it should be fine. If you post in #real-complex-analysis it'll just get drowned

[crimson elm]

@left yacht there u go

[cobalt sun]

unironically meta suggestion time?

[left yacht]

i dont think it would get approved

[cobalt sun]

i am serious

[left yacht]

ok ill request

[left yacht]

done

[cobalt sun]

ok we cannot discuss said proposal now

well i can

you can't

well i can't outside of #1386250529713422497

[left yacht]

i didnt like actually submit a google form

i snet it in #『meta-discussion』 to query people

@cobalt sun there is immediate backlash from a meta committee member. defend your honor.

[unborn venture]

What would you guys say are good resources to get started in coding as a complete beginner to which you later want to use for maths

[rocky terrace]

Maybe we can name it "highlights" or something

[signal bay]

What is ts cronism 💔

[edgy sierra]

j

[ornate sleet]

I need to study for a math test but I don't want to
Does anyone have tips??

[junior umbra]

<@&268886789983436800> here too

[storm tide]

<@&268886789983436800> Mrbeast

[signal bay]

rare troposhere modping

[left yacht]

"Rare"

[cobalt sun]

ok but this is off topic

[uneven jackal]

😭🥀

[slim temple]

yo

i waanna train fast calculations

like super fast

and i sit on a pretty slow speed now

[vestal shore]

like multiplication?

[slim temple]

how to do that

[slim temple]

multiplication addition division

all of them

[vestal shore]

wait

[vestal shore]

https://worldmentalcalculation.com/how-to-multiply-large-numbers-in-your-head-cross-multiplication/ prolly worth having a look

this is the fastest method i use

[slim temple]

thanks

[slim temple]

any vids you recommend

i am a visual

and sound learner

[vestal shore]

ill see

[vestal shore]

https://www.youtube.com/watch?v=LgJ5bNHBbD4

[slim temple]

https://tenor.com/view/heart-devil-may-cry-dante-dmc5-gif-8531990783288407119

[tropic field]

Hey tropo

[storm tide]

Hey

Been a while since I've seen you around.

[fleet hill]

hey clerk!

[tropic field]

Hi Eric

[fleet hill]

how are you?

[bold lake]

Has anyone learned Complex Analysis before? Dm me

[quick elk]

too bad there isn't a large server where you could discuss that publicly
such a shame

[tropic field]

<@&268886789983436800>

okay nvm

it's been resolved

[crimson elm]

It's the same scam

Never gets old

[mighty mortar]

mr beast and his consequences have done irreparable damage to the human race

[heady timber]

hes done it all

[left yacht]

do you guys think it's detrimental to typeset notes without any form of paper, just straight reading textbook -> typesetting? i think it worsens my retention but that might just be a skill issue

[worn dove]

I think if you are just copying the text book it is definitely worse and there's no real point to doing it

[fresh moss]

What are some good resources for like 3d vectors and like their proofs, thanks

[red rapids]

@uneven jackal Lets talk here

[uneven jackal]

Yeah, thanks!

[red rapids]

#book-recommendations message

I'm a mathematical physicist. Even if I'm currently not doing research in a uni atm it's by choice. I never gave the exam. I know tons of astrophysicists and ppl in several other fields who never even bothered with it. The market force just sells you the idea of JEE that hard. The public perception is also clouded by said market force, so the social pressure also does the same.

[uneven jackal]

Some of my friends were telling me to join one of the JEE batches because they teach much deeper than ncert, I was very unsure of what they meant by depth, i thought that they rigorously teach and prove the material in NCERT, and go into depths in this way.

[uneven jackal]

The online batches.

[red rapids]

They don't. Rigor has no meaning in the Indian system. You can explore the UG math curriculum in pan Indian states and you'll find a course on proofs only appear at the end of 2nd year at most and Analysis has essential theorems recommended to be used for problems without proof. If that's the standard of math in the country barring very few places, I doubt anything for competitive prep ever gets anything even close to rigor.

What those guys mean is that they cover a lot more topics is all and that's by nature of the syllabus.

[uneven jackal]

Social pressure is soo true, friends trying to convince or force, parents looking at others excellent marks in examinations → parents telling to join the batch that they are studying from.

[red rapids]

Aye. Ignore the noise. Do what you like. Do it well. Take multiple opinions into account (by ppl who have nothing to do with JEE preferably). There are always ways to do things even if they're not as heavily marketed as JEE lol.

[uneven jackal]

Yes, I was a bit convinced about 2-3 years ago for giving jee advanced but I saw the insane amounts of competition, people losing their lives, losing the genuine interest or curiosity and so much more, and that was literally opposite to how I used to have the perspective on a curious driven kind of learning.

So later i thought about different examinations like NEST, IAT but then I was still extremely unsure about my future and still am, i wanted and want a job that can be enough for living comfortably and where I can still do self learning of mathematics and physics, some recommended being a data analyst can give enough time for hobbies like these but then I had and have no idea for what I will do for living and on top of that, I had long periods of gradual lose of curiousity and interest (due to some external factors) about the hobbies I am talking about and I had felt internally guilty because that kind of desire about learning about the universe and mathematics was kinda still there even with the loss of curiosity or interest, like as if it was internally hidden. And so because of that I am still very unsure of hobbies though I have a desire to continue to learn before i diy. And so can you tell me about how you dealt with that and are you still learning things related to mathematical physics while managing your job ?

Btw I wanted to ask, "Did you ever had periods of lose of curiosity or interest, like being unproductive for a while", if yes then how did it came back for you?

[uneven jackal]

Though, I have seen a lot of proofs in NCERT and even physics book asking for proof, though i am not sure how true those proofs are.

Btw do you remember the thales theorem proof ?

#discussion message

[red rapids]

And so can you tell me about how you dealt with that and are you still learning things related to mathematical physics while managing your job ?

My job currently is teaching for the most part and I'm blessed with a few students who are skilled and know stuff way beyond their age suggests. So that's good enough to keep me on my toes and prepared. Besides that I am writing books on a few things that range from senior high to grad level.

So I'm good when it comes to my field, but then again, research is a different game. That's something that has been slow going on my part as an independent atp. But I'll get back to it in a couple years when I start my PhD.

As far as hobbies and curiosity go, I stopped paying any attention to the noise around me while I was like 16. So I pretty much never lost any of that. And honestly, my biggest hobby which is to teach and curate teaching resources is now paying me as well lol.

Btw I wanted to ask, "Did you ever had periods of lose of curiosity or interest, like being unproductive for a while", if yes then how did it came back for you?

Around the end of grad school, I had intense burnout. Mostly because I had stupidly taken too much on to my plate beyond my research as well. I simply wasn't ready for that much. Not to mention living alone and on a budget so I had a lot of things to juggle simultaneously. That's primarily why I'm not doing a PhD rn. Needed some rest lol.

[red rapids]

NCERT isn't the worst, but it is also incredibly dry and devoid of life. And I wouldn't call the stuff in NCERT proofs really. They're like proof sketches for the most part. There were a few mistakes here and there too, but that was a decade ago so I hope they fixed it. Unlikely tho given I found the ISC board text to have 13 errors in the first 5 pages and their analytical geometry stuff had very very flawed proofs. It was so bad that I had to write type up impromptu notes for literally every construction and it's proofs. Thankfully my students were able to work through sketches and paid attention to the class where I fleshed them out.

[stoic brook]

how long does it take you guys to usually read a textbook? this semester we had linalg 2, but I didn't really like the approach the professor took, what with introducing determinants from the get go (the defn using permutations), schur compliment and stuff. i realize that these are probably important for solving some problems, but i don't like such a matrix heavy approach. i would have preferred if he had developed it for just operators and then moved on to how the permutations defn follows, like how i have seen it being done in axler (tho i haven't yet read it)...he went on to inner product spaces after that, spectral theorem and all that, but he just kept introducing new kinds of matrices without any motivation. it was all rigorously done ofc, but i found it dry and feel like i don't really understand linear algebra. so i intend to go through axler this summer, when i have a break of aboyt 2.5 months, from the ground up. i was actually reading axler during the previous semester, and went till half of ch3 (the one on linear maps), and it didn't take me very long about 4 days). usually do the exercises in my head, and i did go through most of the exercises that looked hard or interesting and not busy work. so do i realistically have a chance of covering solid ground in these 2.5 months?

oh and the most egregious of all, the definition of an adjoint didn't make any sense to me, like why that would be something we would want to study. feel like doing that without riez representation theorem is a fucking waste.

[red rapids]

To answer your last point, in finite dimensions, it is kind of a waste because it coincides with symmetric operators lol.

If you wish to a rather quick and very rigorous recap of Linear Algebra you can try Halmos's Finite Dimensional Vector Spaces. It also bridges to Functional Analysis quite well should you be doing that after.

Generally, 2.5 months is more than enough for a book like Axler if you've already seen most of the material tbf. Though, I'm not sure even he motivates things really well. Your prof might have been following Shilov's approach, which starts off with determinants. Perhaps have a look at the source. It's quite a nice book imho.

[stoic brook]

i did read some of halmos and i really liked his description of quotient spaces as a natural compliment, but I don't want to go through it cuz of the outdated notation. and axler really does motivate things, some of his examples are really good, and he even motivates the definition of the standard inner product on C, with the motivation being wanting to define a norm.

[uneven jackal]

NCERT's foreword and preface talks a lot.

[rocky terrace]

tbh I enjoyed reading them when I was in HS (like 5-6 years ago)

[iron wagon]

lmao, I spent like more than 5-6 months reading axler's LADR tho it was my first math book after calc 2 (I learned matrices, vectors, and scalars for the first time from there 😂)

[red rapids]

Typically a bad idea to pick up LADR if you've never seen matrices and vectors before.

[iron wagon]

yeah, I was so confused how one can think of linear maps (or functions, more generally) as vectors. It took me a while to get a feel for it. But I really loved and enjoyed the book, and made me major in math cuz I was so curious what would happen in infinite-dimensional vector spaces, and at that time I heard math majors learn that stuff in functional analysis. That was the main reason why I decided to major in math. I was just super curious lol 🤣

[halcyon fjord]

Any help would be great but I have a PAT coming up and idk how to do some of the things for it

[left yacht]

based alert and you're literally me and we're twins and other stuff

[tender gazelle]

@tribal spear you asked for help?

[tribal spear]

Ah yes, sorry I'm a at little loss here. Basically I was trying to see if anyone had any recommendations for resources that I could use to re-learn the fundamentals of fractions since its been so long since ive had to do that kind of math.

[ebon flume]

Youtube tbh or any social media rlly... i balled precalculus but because of the math vids appearing on my reels, i got a 96 somehow, i just designed my fyp to be educational >< if you don't like that, then consider making a new account just for educational stuff

[tender gazelle]

theres tutoring schools out there that can help, but mostly yt videos like that person said, books. if you have questions you can dm me. this is my alt but I will answer your questions when im online

[uneven jackal]

Did they feel explanatory and motivating to you ?

[tawdry flint]

I reccomend you to check out the website "Khan Academy" and the channel "Organic Chemistry Tutor" on youtube

[tawdry flint]

Reels are not a nice way to learn for reasons. One is that theyre shallow and the second you miss out on active learning which is crucial to learning problem solving skills.

[ebon flume]

Well tbf I do integrate active learning with it by answering questions alongside watching, it just worked for me and my grade was higher than my prev years :D the shallow part i think depends on the topics... im about to enter senior math so im not really that advanced into math since i havent tackled actual calculi

[rocky terrace]

Ya

[tawdry flint]

You can find depth in every idea. Imho 3 minutes isnt near enough for that.

[dapper glen]

Hello
Can anyone help me about pre calculus..???

[red rapids]

What help about it do you need?

[dapper glen]

Tell me the topics i cover before start calculus…

[red rapids]

Precalculus?

[elfin crypt]

How does someone use multiple books to comprehensively understand a topic? Do they go one book at a time or like what's the method?

[dusky glade]

How long does it take you guys to self study books from cover to cover (specifically higher math)?🤔

I did abbott’s analysis in 6 months, excluding some topics in the last chapter. Idk how some people read Riemannian geometry while in undergrad…

[iron wagon]

I read Axler's Linear Algebra Done Right as my first rigorous math book when I was in high school, and it took me about 5-6 months to read it cover to cover. Now I usually don't read a book cover to cover. But for baby rudin, it took me about 4 months to read chp 1-7 (also doing all the exercises). I think other books are kinda similar (such as Munkres or Folland - ofc not cover to cover)

[dusky glade]

Hmmm, so it does seem to take that much time

Thanks for the input

[iron wagon]

But for ladr, I was new to proof, so this is probably the reason why it took a bit longer

[dusky glade]

Yeah. I dropped ladr 2 times lol

Just realized i didnt have the background for it.

[iron wagon]

yeah, I also found it hard as a first linear algebra book.

I should 've read something like Friedberg's book (which I did after reading Axler's book)

[dusky glade]

If only linear algebra was taught to me like in hubbard and hubbard

Thats the good stuff

[rocky terrace]

I did Abbott's analysis in...

nvm

[dusky glade]

Nooo finish the sentence!!! 😭 😭

[rocky terrace]

Have a look at #1059828221887135774

[dusky glade]

[rocky terrace]

So basically 3 years 🥀

[iron wagon]

oh wait, I forgot to say that I read Tao’s Analysis I and II before reading baby rudin. That means if I didn’t read Tao’s book, it’d probably take more time for me to read baby rudin’s chp 1-7.

[rocky terrace]

But I was procrastinating like crazy and was going through 4 books at once

Procrastination is the big issue though

[iron wagon]

lmao, I started reading D&F Abstract Algebra book about 1.5 year ago, and I haven’t even finished the group theory part yet cuz I kept procrastinating and stopped reading for several months, and I’ve stopped again few weeks ago 🤣

[dusky glade]

Omg sameeee . Currently doing three books at once, havent event finished the first chapter of graph theory book since February. 😂

Surely this month (May) will be different … surely

[rocky terrace]

Go one or two books at a time

[rocky terrace]

🙏

[dapper glen]

Prerequisites

[red rapids]

Middle school algebra. Ability to count and do basic arithmetic operations on numbers. Basic Euclidean Geometry.

[left yacht]

intro group theory is so ugly to me

[left yacht]

twinning

i read ladr front to back, started in october and finished in february

but i also got really busy by december and ended up reading ch5 twice because i felt like my knoweldge of it was still bad after the first pass

im about to finish abbott (which i started in march-ish) btu its also significantly easier than rudin so /shrug

[frigid pivot]

Chat what topics do u think will be on gcse's im going to priortise revising them

I would check past papers

But they arent accurate

Plus they'll ask less of repeated topics

And if possible

Any tips and tricks for those topics (like the hand thing for sin cos tan)

[stable prawn]

wat do u guys think of trying to devise your own formal definitions for mathematical ideas? as in, dedicating substantial amounts of time to trying to derive the ideas from "scratch".

i have the impulse to do this for almost everything i come across (i might even call it a compulsion, i used to have pretty bad obsessive mental compulsions when i was younger and this certainly feels like an extension of the same "muscle") and i feel (probably irrationally) averse to internalizing concepts and definitions that don't feel like they're "mine".

i understand this is probably very silly and it does get immensely frustrating having to completely rebuild an idea due to a false assumption i made early on, but do any of u have advice ? how do u deal with this, if you've experienced it?

the first sentence was actually rather misleading. i don't actually think that's the question i care to hear the answer to. i know how i feel about that. i am more curious about how you all approach it, how you make it productive, when you choose to take breaks, and so on

i should also say - my grades don't often suffer because of this but my sleep schedule does.

i don't actually know if i think it interferes with my comprehension of things - it is just immensely frustrating sometimes. i struggle to put things down because i feel like the thoughts i am having will "get away" from me if i get up to take a break

[swift tartan]

when do you start trying to study relative to the assignment or exam/quiz?

thats some context that is important, if you are doing it the night or even a week before a quiz/exam, thats usually a red flag

[stable prawn]

it depends - ideally a week. this is usually long enough for me. but usually it ends up being 3-4 days beforehand

[swift tartan]

but your sleep schedule is still suffering?

It may be long enough to get it down, but you would likely learn much better with a proper routine (and this is coming from a recovered insomniac btw -- like literally prescribed sleeping meds in the past)

[stable prawn]

yes. this isnt a function of my wanting to keep my grades up. this is just a function of how obsessive i get, if that makes sense.

[swift tartan]

Ohhhh yeah thats valid

Yeah honestly, similar boat, I just have to force myself into studying sometimes even if I dont feel it

But idk it became easier overtime, I now sleep by 11pm and have to try my best to stay awake, like rn 💀

Im studying for a final today morning

[stable prawn]

yeah fair enough

[swift tartan]

I personally like to study a little everyday for each course and then also being able to sit down after class and try to actually absorb and understand wtf happened in class that day bc sometimes im just writing down info in class, and then whatever break I have inbetween classes I take that time to type up my handwritten notes into latex and look into things I boxed/wrote questions about during class to look into on my own or even stuff I didnt consider while in class

[stable prawn]

i think i may also have to keep doing the same to some extent. hearing this from someone who empathizes makes me feel less confused and bad about doing this, so thank you

[stable prawn]

i see

yes im often very inconsistent because of how much of a time sink it is when i do actually sit down and learn. it's hard to find a routine

especially a daily one

but i might have to do it anyway

[uneven jackal]

You temporarily teach in a school right? And so, how did those few students reach functional analysis and different geometry levels ?
Is it because their curiosity sparked earlier and they self learned from books, youtube, internet, starting from lower levels to higher levels and gone through all the grind or they just loved to explore higher level topics or they did both (exploring those topics while doing the grind, like learning calculus I while trying to explore tensors).

What is an independent "atp" ? Btw you were in 10th grade 10 years ago, so you could be 15-16, 10 years ago so now I assume that you are 25-26 years old, so you are going to start your PhD later.

Yeah lol. Your hobby is to teach and so in your teen years did you used to explain concepts to yourself or to some imaginary person, like in my early teen years i remember that whenever I used to go for night walks under stars, i quite frequently and just randomly used to explain why a certain concept is amazing to a imaginary and internal person, and also used to explain the "why" properly to imaginary version of those people who used to mock my curiosity and interest because I was obsessed so I tried to express it to others and as a result, I used to get mocked from my classmates, though from late 2023, i completely stopped talking about my interests to anyone. Btw can you tell me, what sparked your interest in mathematical physics (or in any math or science related field), when did it begin and how you stated to learn stuff ?

Ooh, it's great that things got recovered. I barely remember somewhere, like a survey or something like that, where they described that PhD people are very depressed and they are getting more and more depressed.

[uneven jackal]

Geniunely cant believe, Analysis without proofs !? 😭

[random fractal]

Bro, ..., I think, Indian system is misunderstood.
There are good books that have decent rigor that even some high schoolers read and undergraduates read. Like "Challenges and Thrills of Pre-College Mathematics" by Krishnamurthi, or "Excursion in Mathematics."
Venkatachala's "Functional Equations"
"Topics in Number Theory" by S. Bhargava
"The Congruence Subgroup Problem: An Elementary Approach Aimed at Applications" by B. Sury
"Representation of Finite Groups" by C. Musili.

The Math programs at CMI and ISI are rigorous, and I think, deserves appreciation.

https://mathweb.tifr.res.in/Documents/Publications/Lectures/tifr40.pdf

I have intentionally started with elementary and easy book names like "Excursion in Mathematics" and built up my way to higher and higher levels. This is to show that at every level of the Indian system, there exists really good rigor-filled books to read, that have a lot of proofs.

It's just a matter of sight

[rocky terrace]

If you look at the best UG math programs in the country then yeah sure they're good, but I think they're talking about the average UG math programs

Or the bottom 90% even

[finite torrent]

hi

[red rapids]

Bro, ..., I think, Indian system is misunderstood.

Yes, by their own public for the most part. Mainly the ones who argue which board is the best without a second thought.

There are good books that have decent rigor that even some high schoolers read and undergraduates read. Like "Challenges and Thrills of Pre-College Mathematics" by Krishnamurthi, or "Excursion in Mathematics." Venkatachala's "Functional Equations" "Topics in Number Theory" by S. Bhargava "The Congruence Subgroup Problem: An Elementary Approach Aimed at Applications" by B. Sury "Representation of Finite Groups" by C. Musili.

These are great books indeed and there are many more. But let's ask the question of how large the country is, how many unis and colleges offer math programs and whether we see such books or any other good ones being used there.

The Math programs at CMI and ISI are rigorous, and I think, deserves appreciation.

Credit where credit is due. They are good. IISc is good too. IISERs are trying theur hand as well. Couple of private ones like SNU and Ashoka are pretty good too. Among grad schools TIFR, IMSc are amazing. So are 2-3 IITs. But let's look at the student proportions there and admission policies.

[red rapids]

You can see for yourself. It's not entirely without proofs but a few very crucial things are being omitted. I should add that among the courses listed as electives most would never be offered because profs aren't qualified to teach it or will be offered haphazardly. Also this bullshit was proposed last year as a revision.

[stoic viper]

Hey guys, how are you all?

[uneven jackal]

Thought, the explanations in latest NCERT feels kinda explanatory and motivating/meaning-driven, thought the questions in them felt very disconnected and as far as i have seen, no one really reads NCERT (so maybe only few people enjoys reading some parts of them).

Though, i have never seen someone deeply questioning the rigor in the mathematics textbooks (including other references that people use) and also the lectures they watch to learn math.

[red rapids]

NCERT like I said, isn't the worst when it comes to the natural sciences, but the modern context is missing still. But math, is a bit circumspect.

[stoic viper]

What kind of errors did you find? I am curious as I think I may have a look at NCERT books as references for HSSC-1 and 2 cuz I am giving my board exams in FBISE.

[red rapids]

The errors I found were in the ISC book. Mostly poorly thought out statements. Proofs involving straight lines that just straight up assume any line can be meaningfully expressed in the slope intercept form without specifying. No completion to the proofs even when specified. A lot of formulae which are easy to prove with the machinery developed are not proved in the text. It's weird because you can exclude it from being examinable but at the very least you can show how it works to help students understand as opposed to memorise. If I recall NCERT from a decade ago it very much was like this as well but to a lesser extent. Oh and the topic of mathematical logic is such an afterthought. If you're gonna include it, do it a little bit nicely ffs.

[stoic viper]

hmm, well that's a bit worrying.

[stoic viper]

But most textbooks here are like that anyways.

They really do often just spit out formulae at you, it's quite inconsistent as sometimes they prove them for you, most times don't, I wonder why.

[uneven jackal]

Yes, like physics. But what do you mean by "modern context" ?

like outdated sutff ?

stuff*

[stoic viper]

I remember that in my grade 9 book, they included a pattern for 'general geomteric proofs' but instead of giving an example, had us memorise the steps in order and then tested us on it. Like in MCQ's

[red rapids]

You temporarily teach in a school right? And so, how did those few students reach functional analysis and different geometry levels?
Is it because their curiosity sparked earlier and they self learned from books, youtube, internet, starting from lower levels to higher levels and gone through all the grind or they just loved to explore higher level topics or they did both (exploring those topics while doing the grind, like learning calculus I while trying to explore tensors).

Yep. Mostly self study and not letting knowing stuff getting to their head and building too much of an ego.

Btw can you tell me, what sparked your interest in mathematical physics (or in any math or science related field), when did it begin and how you stated to learn stuff ?

I simply wanted to study stuff that allows me to study far more than what I already know. Physics and mathematics by far have the most access to pretty much everything else. I was already quite interested in them, mainly physics after being unable to figure out whatever Hawking had written in his book "The Grand Design". I don't like not understanding things so I took that upon myself as a challenge. By the time I was in my second year of undergrad I'd done enough to mostly get it.

[uneven jackal]

text glithc ?

[stoic viper]

I c

[red rapids]

sYLLaBuS

[stoic viper]

truer words have not been said

[red rapids]

I got so frustrated in one year of full time teaching that I have taken it upon myself to write a book that goes above and beyond the syllabus but contains everything tailored for it as well. Honestly, it's a disservice to students who want to learn but don't know where to get the information in a manner that's accessible to them at their stage.

Let's hope that goes well lol.

[stoic viper]

I hope you succeed in your endeavor

Oh, I remember why I came here. Yeah so I was trying to make a timetable for myself specifically a holistic one (you know like those daily time tables that everyone makes). And I think I don't quite have the time to accomplish much of what I have set-forward for myself. Like I NEED to do Calc 1 till 4 by June the 30th next year, also need to do Linear Algebra (formally) and Geometric Algebra in the next 3 months so I can FINALLY embark on a project I have been wanting to do for soooo long. BUT alongside this, I also need to manage school( 2 to 3 hours a day after coming back) and extra-curriculur activities (45 mins a day) and I don't know how I am gonna do it.

I wanted to ask,out of these things, which would be the best one to slightly tune down so I have enough time to do the rest, like what's the best middle ground.

I know that matters on my priorities so:

Math: 8/10, School : 7/10, Extra-curriculurs: 6/10.

So yeah, if anyone wants to help feel free to do so.

[stoic viper]

Talking about your hobbies is a pretty good way to reflect on them I think especially if you talk to other people about it cuz you get a diverse set of opinions.

[stoic viper]

It's pretty cool that you have been doing something that you really like (teaching), so congrats.

[uneven jackal]

what do you mean by ego ?
Did you meant that they were reflecting and questioning the things they learnt and the resources that they learnt from, so that they don't assume to know a lot ?

I simply wanted to study stuff that allows me to study far more than what I already know. Physics and mathematics by far have the most access to pretty much everything else. I was already quite interested in them, mainly physics after being unable to figure out whatever Hawking had written in his book "The Grand Design". I don't like not understanding things so I took that upon myself as a challenge. By the time I was in my second year of undergrad I'd done enough to mostly get it.

So basically, you were interested into physics and mathematics, and you read a pop-science book -> did not understood few things from it -> took it as a challenge.

[red rapids]

What do you think people mean when they use the word ego?

[uneven jackal]

belief in oneself, like "i like math", "i like physics".

[stoic viper]

isn't that just confidence?

[red rapids]

I'd more so not only teach but do something to challenge the status quo of education today but let's see where life takes me.

[uneven jackal]

Oh.

I dont know.

[stoic viper]

It would be nice IF I do it, so well I might as well try

[stoic viper]

But not really sure if I can cuz of time constraints.

actually let me plaster my thoughts for one sec:

[uneven jackal]

I thought "reflecting on themselves and questioning stuff, so that they don't assume to know a lot" by not building ego.

[red rapids]

That's not belief. That's just understanding yourself.

[uneven jackal]

Is that what you truly meant ?

i dont know

[stoic viper]

2 hours for calc, 1 for L.A (for the next one month, replace with G.A after this period), 45 mins for extra-curriculurs, 2 for school, 1 for learning Python, and 1 hour for projects, that's about 7 hours and 45 mins so round about 7. I have from 3 till 10 PM on weekdays which is about 7 hours so I may be a bit short on some days by like 1 hour . On weekends I should have enough time, but I think I am genunely cooked. I wonder what burn-out feels like though I doubt I will have to go through that.

[uneven jackal]

yes, i firstly thought about "high confidence", like thinking that they know a lot while they really don't. But i don't truly understand ego.

[red rapids]

Honest advice. This time tabling stuff is just another way to procrastinate. Just go and do what you wish to in a flow. As you do it, you'll have a good idea about your pace and adjust on the fly for whatever target you have.

[uneven jackal]

High confidence may not be ego. I am not sure.

[red rapids]

https://en.wikipedia.org/wiki/Egotism?wprov=sfla1

[stoic viper]

Hmm, yeah ig I am just wasting time(no pun intended) doing this. Well I will let you know later how it goes ig, so C ya

[storm tide]

I don't think the word "ego" can be expected to reliably refer to "ego__tism__".

[red rapids]

I saw this with extreme certainty as someone who thought they work efficiently due to this only to waste most of my time doing this. I stopped this since Covid and I'm super productive lol.

[uneven jackal]

Oh, why do you think that ? can you elaborate, please ?

[red rapids]

In the context of what I said, it does.

[storm tide]

At least for me it primarily seems to refer to Freud's id-ego-superego model.

[red rapids]

I agree. That's another meaning.

[storm tide]

Oh, the conversation went deeper than what I scrolled back to. Apologies.

[acoustic salmon]

what do I do when i develop a slight sense of dislike towards the books that I'm using? im in analysis paralysis right now regarding real analysis books. some time ago i said "f it, let's choose one damn book and do something" and i did. i learnt everything except the last three chapters of Tao analysis 1. then I got bored with the way he does stuff( i don't remember the exact reason or feeling) so i switched to pugh. i was able to keep up with it's pace for the first chapter but it got tough so i quit again 😭. now I'm REALLY confused where to continue from. i've checked a LOT of textbooks and I can't choose one. pugh, tao, abbott, rudin, apostol etc..

[red rapids]

Lmao so you basically did most of the stuff before the meat of analysis begins eh.

It's hard to pick a book at times. What exactly are you looking for in it? Perhaps ask with your parameters in #book-recommendations

[iron wagon]

mmm I see. I also read Tao's Analysis I, and he spends quite a bit of time on set theory compared to other analysis books, which can be a bit boring for some people. However, things are very different in the last three chapters, where the book starts to cover calc I topics (continuity, differentiability, and the Riemann integral), which are much more interesting than the earlier sections (tho I personally found the chapter 8 on Infinite Sets to be the most interesting and surprising).

[acoustic salmon]

i liked the sequences and series chapters. and chapter 8 too. i just feel a little bit that he defines a lot of stuff just to get to the point

[acoustic salmon]

exactly and I feel like i have to go through all of those again 😭 to understand the significant part

[hushed latch]

the way I find textbooks I like is if they pictures (if they have color yay!) and if they have problems or questions you can try on your own, the key is engagement, like do you not like that Tao analysis? was it too rigid sounding and academic and did u wish he was more colorful and expressive with his language?

u deleted smth?

[acoustic salmon]

no?

[acoustic salmon]

i loved the integration(pun intended) of propositions and theorems into the exercises

made me prove so much stuff by myself that I never would have if I had just simply read

[acoustic salmon]

that does sound like something i would do 😂, i agree than engagement is the key. i worked through ch 1 to 8 of Tao in a single sitting

[red rapids]

Single sitting?

Really?

[acoustic salmon]

yesss, the first few (until rationals) were really easy. only from ch 5 I had to concentrate

[red rapids]

If that is what you're after, you can consider Cummings for a minimal read or Zorich for a lot of detail and variety of problems.

[acoustic salmon]

minimal as in less stuff to read?

[red rapids]

Friendlier and lesser yes. Not less for a typical first course in Analysis but for the entire thing. Tao has a continuation to Analysis 2 and so does Zorich. Cummings does not.

[acoustic salmon]

i do not think friendlier is what I need. Tao was easy, i would have liked something harder in fact.

[green terrace]

Rudin

[acoustic salmon]

😭 that just defined stuff and proved facts about it. i had no idea why I was doing things. (i did ch 1 and 2)

(my cat says hello to your cat)

(im sorry if I'm being a prick)

[red rapids]

Then you want to do Zorich. Considering you found Pugh a lot harder, which it kinda is given the nature of how it jumps across topics. If it's motivation you want, it's got all of it. Very comprehensive in coverage too.

[quick elk]

every time Killuminati recommends Zorich, a hungry child in Beverly Hills get fed
by their nanny
please support a good cause

[weary sable]

I am currently at the GCSE level and want to start studying A-Level to prepare for a university application. Are there any apps similar to Duolingo that teach AS or A-Level?

[red rapids]

Duolingo is famously useless for learning languages. Are you looking for famously useless resources for the same?

[weary sable]

I didn't mean the application itself rather its style of learning, or you meant that its style of learning is also useless but i specfically choose it because I learnt c extremely well on coddy.tech which has the duolingo style but that is anecdotal ofc, what is an ordered free course may you suggest then?

[red rapids]

It is precisely the style of learning due to which duolingo is terrible for what it markets itself as. In any case, I don't know much about these things (GCSE that is) but I've heard that Z Notes is good. Pretty sure it's mostly free too.

[weary sable]

Thanks

[barren remnant]

I've been procrastinating learning trigonometry for over a month now because there's an assignment I have to do in it that requires brain power and energy that makes me unsure if I want to expend that I don't wanna get burnt out but I wanna continue my math learning journey anyway

[red rapids]

I'm very confused. You have the undergrad math role and you're procrastinating on learning trig? Sus

[barren remnant]

There's a legitimate explanation, I could share it if you'd like.

Thanks a lot!

[red rapids]

Sure. I'm curious (and admittedly bored)

[barren remnant]

That makes me feel way better, I think I'll take my time

Sysiphus didn't climb the mountain in a month

[barren remnant]

I learned calculus before any of the basics

and I applied for post-grad role naively, thinking that what I was reading at the time (other than caluclus) was post-grad level but it was actually undergraduate, and got that role instead

[red rapids]

How does one learn Calc before learning trig?

[barren remnant]

I skipped the stuff that had trig in it

and as for the super basic stuff I understood it

[red rapids]

That's like, most of it?

[barren remnant]

Yeah, I only learned a tiny bit of calc, from the first few videos present in professor Leonard's youtube playlist on it

When did you learn calc?

Assuming you have

[red rapids]

Damn. I won't judge lol. I had very weird ideas about math myself early on. But what made you think that it was post grad lol

[red rapids]

Between 9th and 10th grade

[barren remnant]

I don't remember, I thought it was advanced stuff

[red rapids]

Tho it was not properly done

[barren remnant]

Oh wow, did you take it early?

[red rapids]

I only learned it the stupid way

[barren remnant]

Wdym

Did you just memorize?

[red rapids]

No. I was done with Precalc and also basic Discrete Math by 8th grade.

[barren remnant]

That's wonderous!

When I was in 8th grade, we were learning rudimentary algebra.

[red rapids]

Well. There's famously the old school way of doing math, which is rather imprecise and kinda useless for math itself but can help intuition and is ubiquitous among engineers and some physicists.

This is the kind of math they (rightly) tend to teach in schools.

[barren remnant]

I see, so was it more like how to apply methods but less teaching you what they do perhaps?

[red rapids]

Sadly most people do not have the instruction to suggest that this is not how math is really studied today and the reasons lie in a lot of rich history between the late 1800s to the mid 1900s.

[barren remnant]

I feel like the pedagogy of math evolves year by year at this point (21st century now).

[red rapids]

A bit of that but even the resources I used for my own self study were a bit more so not teaching me things precisely and I had no clue what precise meant until I took Calculus in uni.

And I thought I mastered that shit

[barren remnant]

I feel like math precision is best(est) taught with mathematical maturity, would you think so? I say this as someone with neither though in the sense that I'm still learning the basics, but I'd guess that learning something like analysis is when the properness begins?

[red rapids]

Not in practice. Not at the school level. Definitely not across disciplines either. Math itself tends to be rather flexible so long as you are precise and know to ask the right questions.

[barren remnant]

When I was in grade-school in a certain country, it felt like the curriculum was changing a bit each year. I could be incorrect though

[red rapids]

Depends on how you hammer it in imo. I don't think you need to be super precise or even care to write proofs but the language used should start getting precise at least around high school.

[red rapids]

Where is this and it's kinda strange that you would know that in grade school tbf

[barren remnant]

I'm curious about this and I'll ask you since you've seen more math than me, does math progressively become more logical throughout pre-uni to uni and strict in that sense by requiring more of say the process that gets you to the final answer for example solving algebraic equations?

[barren remnant]

I think I'm just hallucinating because how would I possibly know that without comparison to previous years.

[red rapids]

I tend to live in this boundary really as a physicist. I do care about the proofs as well but I care more so about the language I use and have caution when making heuristic arguments. Something that's uncommon in theoretical physics aside from ppl like me who do mathematical physics.

[barren remnant]

Interesting!

Mathematics and physics are fascinating to me, I wish to fully learn them someday

[red rapids]

Ideally should, but definitely does not unless you're in uni and pursuing math or are doing it by yourself in pre uni. Some places try tho. France and the USA famously tried this (mid-late 1900s) but in a very poorly thought out manner.

[barren remnant]

I've been trying to learn Cumming's proof book through his youtube playlist on it, and it has definitely taught me to think more precisely in how I write an answer to a question like "how many x."

[barren remnant]

Interesting, but I think the general population (through universal curriculum) should probably not be exposed to something that is only necessary to those -as you said- pursuing math.

[red rapids]

If you are indeed going through that book then I would suggest you to go through a book like Daniel Kim's Advanced Precalculus on the side rather than learning trig through some traditional text. Tho, something like Axler's Precalculus could be handy to have on the side.

[barren remnant]

I really appreciate the recommendations!

I'll definitely consider that, I've been learning precalc on Khan Academy

[red rapids]

Sure, I don't agree with teaching the general population all that logic, proofs and stuff. But that doesn't mean the language used in texts and teaching cannot be precise or be made aware that is not so when it isn't.

Good texts do that tho.

Teachers on the other hand are a hit or miss.

[barren remnant]

Though I've been procrastinating

[red rapids]

Yeah what I just suggested (Kim, not Axler) is nothing like what you'll find in Khan Academy lol. It's a proper math text. It does have its own flaws tho, but nothing that will matter too much. Especially if you use Axler alongside.

[barren remnant]

true

[barren remnant]

yep

[barren remnant]

from my p experience that's only in chem/bio

[barren remnant]

What if it's too hard?

I'll just check it out and see

Have you read LA done right?

[red rapids]

It's more on the abstract and proofy side. If it's hard but you're interested, all the more reason to do it. Besides you have a suggestion to help you "understand" beyond the abstraction ofc.

[red rapids]

Yes

[barren remnant]

Yep! And on top of that I'm a pretty decent math student.

[barren remnant]

Nice! I looked at some of the last pages to see what it looks like, and it looked like something I'd love to learn someday, like it's a deeper insight into mathematics (which it is)

It looked very detailed and simple because of the definitions and structure of the text.

[red rapids]

It's one of the most basic courses lol. You're supposed to learn some aspects of it in Precalc already.

[barren remnant]

Through matrices etc?

[red rapids]

And Euclidean Vectors and Linear Equations and Analytical Geometry.

[barren remnant]

Yes! It's a subject to pass if one wishes to study something deeper than that.

[barren remnant]

Fun things!

They're the basis of 3d games

[red rapids]

Yes and no. But sure.

[barren remnant]

Super interesting subjects

[red rapids]

Anyways. Nice chatting. Was an interesting case to hear about. Good luck.

[barren remnant]

Tysm!! Yea pleasure

Cya

You too

[violet solstice]

Hi everyone, I’d really appreciate some insight from those at the graduate level or beyond.

How do you approach studying serious mathematics in practice? By that I mean both the theoretical side (understanding proofs, building intuition) and the problem-solving side.

I’m especially curious about your workflow and routines:

How do you typically structure a study session?
How do you balance reading, proving, and solving problems?
Do you rely more on digital tools (LaTeX, tablets, note apps), or do you prefer a more traditional pen-and-paper approach?

Any concrete habits, strategies, or even small details from your daily practice would be very helpful.

Thanks in advance!

[red rapids]

My answer might prove a bit different from others since I'm originally from a physics background.

How do you approach studying serious mathematics in practice? By that I mean both the theoretical side (understanding proofs, building intuition) and the problem-solving side.

When I'm new to a subject, I usually read, make notes of the subject and solve in-text exercises if any. I usually add my own commentary to the notes for how I understand things and make sure to ask someone or look up if my understanding is flawed or if there are subtleties I may have missed.

I remember my analysis prof used to do this thing where he would make us defend our proofs to fill in gaps. I try to do something similar by myself by using online forums and mathematician folks ik.

How do you typically structure a study session? How do you balance reading, proving, and solving problems? Do you rely more on digital tools (LaTeX, tablets, note apps), or do you prefer a more traditional pen-and-paper approach?

I prefer a chalkboard when available. Today I have one at home too lol. Feels good to have something like that. I usually transcribe that onto TeX after as if I'm explaining the material to another reader. That personally helps me a lot.

I don't really obsess over structuring my time spent. I have found that to be a colossal waste of time. I just start doing the things I want to do and adjust on the fly depending on my pace.

[violet solstice]

Thank you for your response Killuminati. I would also like to ask about your approach to problem solving. When you are working through exercises, in measure theory for instance, and you find yourself stuck on a particular problem, how do you typically handle it? Do you tend to stay with it until it breaks, working through it with a kind of obsessive focus, or do you set it aside, continue with the remaining problems, and return to it later with fresher eyes? I am curious whether you have a deliberate method or whether it varies depending on the nature of the problem itself.

[dusky glade]

For me if i run out of options or ideas to test, i try to get some help. Sometimes there is a time limit to learn this stuff such as exams approaching, in which case i may look for help earlier

[red rapids]

I try a few things for a while and if I get stuck I try a couple more things obsessively for a while. It's at this point when I seek out a hint of some sorts. Whether what I've been doing is too roundabout or if I'm missing only one essential piece and stuff along those lines. In any case, once I find out, I take a break. Move on. Come back to it later. My fatal flaw is looking for that balance between elegance and explanatory power in my proofs. Though I've learned to do this AFTER I've solved the problem by whatever means necessary first.

A chalkboard really helps because you can just walk back and take a bird's eye view of what you're doing. Sometimes helps identify issues in how you're proceeding.

[random fractal]

There is no right way to study. So thinking much about structuring your study sessions does not seem fruitful (personally) to me.
There will ALWAYS be a better way to do what you probably did, just that it escaped your planning. Rather than obsessing over finding the best way (which likely does not exist), you should just study the way that is good enough, even if it has flaws.

[signal bay]

by zorns lemma the must be a best way, but best way is ill defined in this case

[random fractal]

"The Axiom of Choice is obviously true, well-ordering theorem obviously false, and who can tell about Zorn's Lemma?"

[storm jasper]

Nice

[junior umbra]

how do you know every chain has an upper bound

[green terrace]

axiom of choice equivalence to zorn?

[mighty mortar]

I agree with this. I feel I “wasted” a lot of time/mental energy as a student stressing abt optimal studying

The truth is math is just hard; it’s not your studying method that’s the problem

In class do whatever keeps you paying attention. Out of class just make sure you’re doing practice problems

Outside of those 2 things it doesn’t matter too much what you do

[fleet hill]

I do think there's vicious cycles you can get stuck on that are counterproductive, like rushing through something without knowing the foundations well enough and then realizing years later you didn't understand anything that you thought you did

IMO if you have friends and people who are further along to talk to to compare study strategies, this is greatly mitigated

I agree there's not a perfect study strategy but there are certainly bad ones

[random fractal]

You can only decide good or bad according to a metric. It all boils down to study goals. A strategy that you deem "bad" may be bad just because you are using it to achieve the wrong goals. It is "mismatch" that's the problem, not the strategy itself.

[fleet hill]

Sure

[random fractal]

For e.g., if your goal is cross-pollination, like getting quick ideas, focusing more on breadth than depth, then your study strategy will differ compared to say, mastery over a subject.
So, you will naturally adopt different strategies that are "good enough" for the task. To claim a strategy is unproductive requires you to stick to one goal, and call it the metric for deciding the merits/demerits of a strategy.

[rocky terrace]

You waste time stressing about optimal studying

I waste time not studying

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

We are not the same

[rocky terrace]

There is also the other end of this, spending too much time on one thing and not learning the rest of the foundations

[iron ridge]

Hi, I need advice. I'm in 8th grade rn and i sadly got a b first sem and a- sec sem of alg 2. I was wondering if i should retake or not to help my gpa. And i would like to know if precalc is very hard?

[red rapids]

https://tenor.com/view/homelander-upset-sad-cry-boys-gif-6858682649598278649

[red rapids]

Difficulty is subjective really. If you like the subject and work on it regularly, I doubt it will be hard tho, at least for Precalc. Also, Idk where you are from but I've never heard of 8th grade GPAs being important anywhere. So, suit yourself.

[mossy shadow]

Removed the studying! role from you.

[tardy hemlock]

I study by listning to recorded lectures far above my paygrade whilst solving 2000 piece Jigsaw puzzles.

[real herald]

A person with perfect and optimal study setup (perfect lighting for eyes, perfect noise cancellation room, proper notebooks and all the other tools) with expensive hardcover books but no interest in mathematics would get nothing from it, while on the other hand, A person obsessed with mathematics would read Rudin on a cracked phone with small screen at 3 AM AND still deeply absorb it even with less availability of proper resources.

[tepid creek]

does anyone know who has the best course for University Math 2 (discrete math/structures)?

[frigid gate]

How do you guys deal with failure?
First time I truly don't understand something. How do you cope with that?

[red rapids]

I don't. I just continue failing at newer things.

[mental raptor]

how do i cope with studying the whole day everyday but still doing bad sometimes while others i know barely study and always do way better do I just have to accept that some are a lot smarter

[red rapids]

I don't. I only study for a few hours.

[mental raptor]

so ur solution is to give up at being "good" and just study a couple hours

[red rapids]

There's no being "good" to begin with. Sure, there are a few guidelines that suggest whether you're competent or not, but there's nothing overall that can suggest you're "good". It's not really giving up if the ideal itself is a fallacy.

Study because you like it and have the desire to learn more. Not because you want to be some facetious version of "good" that you may have built up for yourself.

[mental raptor]

I guess you are right, it's just some professors tell me you need to do better and grad schools are competitive and stuff and then when i look around me I see people putting in a lot less effort and doing better and It's difficult to cope with you know

[red rapids]

And have a life beyond that as well.

[mental raptor]

you are right I will try to convince myself that this is some kind of impossible thing I have in my head

[red rapids]

Ask them what's "better"

[mental raptor]

its just writing better performing better on exams studying more

[red rapids]

Written exams are arguably one of the most stupid ways to judge whether you're competent at a topic.

[mental raptor]

why

[red rapids]

All they tell you is that you can write an exam and solve those problems in that amount of time.

[mental raptor]

what other factors are there to competency in a topic

[red rapids]

You can't use that as a metric to judge whether someone is competent just by repeating it over different things. It's just logistically more feasible for unis. Doesn't mean it's a smart idea.

[red rapids]

Depends on the topic.

[mental raptor]

A pure math topic I guess

[red rapids]

If I'm doing analysis, how rigorous my proofs are for instance. More or less extends to other areas of math.

[mental raptor]

yeah measure theory is what im struggling with now haha

[red rapids]

Not only does it matter how rigorous the proofs are but how well does the proof convey the essence of the proposition itself.

And that's the part that helps understand things well

Formal proof aside, one should be able to build mental pictures to conjecture things and attempt to prove them.

The formal proof is only a guiding principle on making sure you're air tight.

[mental raptor]

I see.. that is a nice way of looking at it because I might be decent at those things, but I judge myself too harshly based on my performance at exams or my ability to do exercises quickly (which are kind of the same thing?)

Do you think that being able to solve difficult exercises in a topic quickly is a big part of competency in it?

[red rapids]

There's always a trade off. It's always two out of the three. Precise, Quick, Comprehensive. You can never be all three. Quick and Precise is ideal for doing formal math, but Precise and Comprehensive is ideal for understanding formal math. Comprehensive and Quick rarely meet the standards for rigor in formal math but that's helpful for teaching.

In my opinion, being precise and comprehensive is the most useful. Once you have gone through a comprehensive round of work which is precise, it is easy to whittle it down to the bare minimum to make things quicker.

It's a lot harder the other way around.

[mental raptor]

This is great to hear because I do feel that I am more on that side than the others.. I will just try to be better in this sense rather than be quicker or whatever

[red rapids]

That said, as you develop this over time you'll be able to make quicker reads more comprehensive. But that's a function of your mathematical maturity and experience.

[mental raptor]

Yeah

I don't have that much experience ive only been doing math for 2 years

[red rapids]

Might hinder you in exams a little bit for sure, but will get you through interviews and research better.

[mental raptor]

yeah

also like are math exercises generally difficult haha because i always seem to find (atleast a big part of them) difficult

im talking mostly about topology and measure theory

or are they not supposed to be really difficult

[red rapids]

Quite normal. There will definitely be some routine stuff but on average they'll be on the harder side for anyone new to them.

[red rapids]

This suggests you are quite new.

[mental raptor]

that's comforting to hear..

[mental raptor]

yeah and I have been rushing to take all the courses I can and stuff

i basically finished the standard undergraduate math degree at my uni

I guess I expect too much of myself too quickly

[red rapids]

Aye. Must pace yourself. And never compromise on the quality of your work with no regard for time taken. There's only so much you can do in a short while. Dumping too much onto yourself will hinder said quality. If the quality is hindered, there's no metric of performance that can justify taking on so much of a load.

[mental raptor]

You're right. Thank you for all this by the way it really helped me

[flint orchid]

I wanna pre-learn Calculus II before I start taking actual classes for it. Where should I start? Should I do a review of Calculus I first?

[mental raptor]

The concepts in Calculus I are important, however, from my experience calculus II is mainly integration techniques which isn't really strongly related to Calculus I

But its always good to have a strong foundation

[left yacht]

Learn calc 1 first

[left yacht]

How are you going to understand taylor series without knowing what a derivative is

Calc 2 absolutely requires calc 1

[left yacht]

Try khan academy they're good with calc 1-2, past that they're bad

[mental raptor]

well yeah i said its good to have a strong foundation but i interpreted calc 2 (or preparing for calc 2) as more of learning integration techniques

which does not really require calc 1

[green terrace]

Well, u-substitution and integration by parts are both methods that assume you know how to take derivatives, same with other methods of integration less commonly taught in calculus 2 such as leibnitz' trick or anything with taylor/maclaurin series, etc...

[red rapids]

It absolutely does.

To develop Riemann integrability, you don't really need knowledge about derivatives. So long as you know about continuous functions, you're fine. But your typical Calc courses do not rigorously define Riemann integrability and instead directly jump to the applying the fundamental theorem of calculus and integration techniques for which you definitely need to know how derivatives work.

[left yacht]

Calc 1 teaches ftoc

So if you do calc 2 first you won't know ftoc which is a yikes

Just do calc 1 then calc 2

[oblique prawn]

Greetings, I want to approach self studying some topics in my textbooks that were not covered in lecture material. I was wondering if anyone has done this, and if so, how have you taken notes? While reading, after reading, after completing the end of section problems, or not at all? Thank you.

[mental raptor]

honestly i forgot revising calc 1 means revising how to do differentiation i just thought that meant limits and continuity and stuff

my bad

[mental raptor]

agreed

[mental raptor]

yes

The way I learned this stuff in school and uni was a bit over the place so that's why i gave a bad answer.. sorry 😅

for example in A levels they don't teach you calc 1 in the standard way but u learn all the integration techniques and differentiation without knowing what is a limit

so in that sense I knew calc 2 before i knew calc 1

[red rapids]

When I was in uni, I used to revisit old courses on my own from beginning to end but be more comprehensive in my coverage. So I used to refer to material that allowed for this. What I would do is restructure and try to write notes in a manner as if I were teaching them, with detailed proofs and remarks to help intuition. I'd first do scratch work on my board and then typeset all of it. I'd maintain a separate document for problems but if I found the problem as a good addition to my notes on the topic I'd add them. For the problems I'd typically cherry pick things that seem interesting to me or stuff that I cannot think of how to approach at first glance. Long and tedious way to work, but very helpful tbf. I'd only do this courses I enjoyed tho.

[mental raptor]

also the person that asked implied that they already took calc 1 and said "revise"..

from my experience what people struggle with the most is integration techniques and time to get comfortable with those so that's what i meant

[oblique prawn]

Thank you for the suggestions. I am looking to balance how detailed I am with my notes, primarily noting key theorems but will also include some useful examples if I see them fitting. Regarding the problems, I will do problems that encapsulate each part of the section, and leave the more difficult problems as a way to test my knowledge.

[warm spire]

Yo everyone, im trying to get better result on math because i love MATH but im really bad at it ngl.. And im trying to get into a big ingeneer school in France, i wanted to know if anybody got any type of advice for me to get good please : D

[oblique prawn]

What exactly are you trying to improve?

[warm spire]

mostly Complex Numbers, Differential Equations first and second order, Laplace Transforms, Linear Algebra, and some mindset because even if i know the right formula to use i struggle to do the exercice right so

[oblique prawn]

Do you have past experience with those subjects, or are you approaching them fresh? Regarding the mindset, do you have example problems to see? Sometimes it can help seeing an example to understand how to approach certain problems.

[warm spire]

We saw all those topic at school but i didn't understood it well, and i know its reaalllyy important subject for my future school so im trying to learn them, i don't really have example right now ill try to look

[oblique prawn]

You're completely right about those subjects being important for engineering. Given complex numbers, I presume you're looking to study electrical engineering? Do you have textbooks on these subjects? If not, have you looked at Khan Academy or MIT OCW?

[warm spire]

Yeah electrical, I'm trying to work on HFT after school. I do not have textbooks about it and already looked at khan academy but i didn't like it, I don't know mit ocw I'll look at it rn

[oblique prawn]

Electrical is very math heavy, we are heavily focused on linear algebra, complex variables, and differential equations. I didn't see Calculus in your list so I presume you have a good understanding of those subjects. I am not familiar with HFT so I unfortunately can't give you advice related to that. Regarding Khan Academy, it gives a good introduction to the subjects, but not enough to sufficiently learn them. OCW offers many courses including the ones you listed, look for SC, scholar courses, those provide the most amount of material for self-learners. https://ocw.mit.edu/course-lists/scholar-courses/

[warm spire]

Oh ok thank I'll take a look tysm

[sick needle]

I find it most helpful to follow the derivations/justifications the textbook usually gives, and take notes in your own words breaking down each step to make sure you conceptually understand why they did everything. Then of course note any final forms of equations so that when doing problems you know what to use. If there is no generic formula, note down the general steps used to solve a problem so you can refer to it when practicing. I learn primarily from textbooks and I've found that sometimes it is hard to connect the derivations to what you actually use to solve problems, so make sure you do practice problems to ensure you know how to actually use what they walk through in addition to understanding the justification behind it works.

Sometimes you can skip taking notes on the derivation if all the problems follow a generic form, but it helps for more open-ended topics since it will get you comfortable the general background reasoning for cases where problems take a form you haven't seen before. It helps you not rely on just pluggin n chuggin.

[oblique prawn]

Thank you, my only concern is when the note taking process should occur. In my university, I will take notes during lecture and then read the textbook, then do the homework. My goal for self-study is to read the section, after this, take the main points, definitions, primary examples, and use the notes to solve the practice problems.

[sick needle]

I'd take small footnotes while initially reading through the section on anything you didn't immediately understand, then use those and all the key points to make proper notes to then use with the practice problems.

[oblique prawn]

The point I am trying to make is how much is enough in terms of notes that I can look back and understand what I was doing as review. Following your advice and what the previous person said, I will mentally note everything on the page, and then on the second pass for notes return and develop ideas that either confused me or require a dedicated spot given the complexity, etc.

[sick needle]

Yeah that works, just putting like an asterisk next to the stuff you didn't fully get on the initial runthrough helps me.

[oblique prawn]

Seems like a simple problem, but at this point I may be overthinking about it.

[sick needle]

Yeah I mean you figure out what works best for you but I've learned my workflow works best as

Initial making small footnotes -> Proper summarized notes using the footnotes an outline -> Problems

[oblique prawn]

Thank you, how many problems on average would you say you do?

[sick needle]

I mean it depends on the topic but in general just until I feel comfortable getting the right answer without looking back at the notes at all

And make sure you do spread out problem #

so say they have practice problems #1-20 I'd do like 3 8 14 19 or smth like that initially

Just cause they typically cluster similar applications together

And then depending on how well you do on those go back and pick more etc.

[oblique prawn]

That's exactly what I was thinking of doing, and then doing the end of chapter problems as an "exam" to test my knowledge of the entire section.

[sick needle]

Yeah perfect and that use those 'exam' results as a gauge of what you need to go back and do more problems for

[oblique prawn]

Thank you so much for all this, I am just going into robotics, and want to go beyond what my courses at university offered for mathematics.

[sick needle]

Yeah of course man doing outside work is great

And the more you read the textbook the more you get used to the type of language it uses and the easier it gets

[red rapids]

Let's talk here @gaunt ruin

[gaunt ruin]

is the basics of linear algebra covered in highschool?

[red rapids]

If you're talking about the USA, I believe some aspects mainly around 2 by 2 matrices, Linear Equations and analytic geometry do get covered in Precalc. But I'm not American, so not really sure.

[gaunt ruin]

Germany

[red rapids]

Dunno much about the school system there. I'm sure some of the basic intuitive stuff about Euclidean vectors and plane and space geometry is taught tho. Because alongside Analysis the other first courses are Linear Algebra in uni math.

Again, a German person who's been through that would be able to confirm better, but you can just look it up.

[gaunt ruin]

i see

[radiant halo]

Not necessarily a "math" question but for anyone who has took the AP calc AB/BC exam what are your best suggestions and tips? Thanks!

[unborn venture]

Lookin for a study friend

currently learning introduction to matrices

[dusky glade]

Ain't no way, nobody is coming to my graph theory thread 😭💀https://discord.com/channels/268882317391429632/1499422558594797679

[signal bay]

!noads exists for a reason

[wide crypt]

Please do not advertise your help channel or thread in other parts of the server. There are many people who need help, so advertising can quickly turn into spam.

[dusky glade]

👍

[nova whale]

study g?

study guide?

[unborn venture]

Friend

[rocky kraken]

Hello

[junior linden]

Hi

I want to be rich with mathematics, Im in 2nd year of university pure mathematics

Could you give me a plan for that ?

[left yacht]

Rich with mathematics

[heavy needle]

Well, if you solve the Millennium problems

Shouldn't be too hard

[craggy bolt]

Severly lacking motivation to study for my final exam

Last exam I'll take in UG

[rocky terrace]

with that you can afford to live in New York for 2 months

[heavy needle]

maybe if you solve all of them

[rocky terrace]

1 year 🔥

[crimson elm]

Solve them all and you get 1 year sotrue

Very feasible

[icy basin]

Being in correct environment is what makes u realize the importance of ur life suffering makes u realize the importance of relaxing and being sick makes u enjoy being normal everything is bad is made to make whats good seem good If we dont have negative we dont have positive because everything will feel neutral and there will be no importance or enjoyment in our life so never try to run from suffering lr bring tired because it what will make u different its just a pain that will end even if its small of big it will make u tuffer and if its small its reward will be bigger nothing deserves to be sad for long but at the end the strong and the one who suffered will shine think of all of the proboems that happend in ur life and now you are here to proof everyone every situation wrong and show the world that u are not different but you are strong and you are the one who will make a change

[hazy vigil]

Blud is yappin

[icy basin]

Just an advice

[storm tide]

175 words of run-on sentence with not even a comma.

[icy basin]

I mean its not meant to be grammar homework

[storm tide]

Apparently it's not meant as a serious attempt to communicate.

[icy basin]

I mean u could focus on so much things other then punctuation

[storm tide]

I choose to focus on people who don't express themselves in unreadable walls of word salad.

[icy basin]

Ur choice

[lapis sluice]

i made some changes to hopefully make it a bit more readable. i don't necessarily endorse the contents

Being in correct environment is what makes u realize the importance of ur life. suffering makes u realize the importance of relaxing and being sick makes u enjoy being normal. everything is bad is made to make whats good seem good.
If we dont have negative, we dont have positive because everything will feel neutral, and there will be no importance or enjoyment in our life, so never try to run from suffering lr bring tired because it what will make u different. its just a pain that will end even if its small of big it will make u tuffer, and if its small its reward will be bigger. nothing deserves to be sad for long, but at the end the strong and the one who suffered will shine.
think of all of the proboems that happend in ur life. now you are here to proof everyone every situation wrong and show the world that u are not different, but you are strong and you are the one who will make a change.

[edgy sierra]

chatgpt can you please summarize this in 1 sentence tank you

[icy basin]

No point they just hating to hate

Average discord experience

Anyways thx

at least ur not like these ppl flaming who is tryna help

[junior linden]

😭

I'm not able

!

[heavy needle]

The punctuation is necessary, it helps people figure out what the fuck you're saying

Ah that reads with hostility. Unintended. Just emphatic

[red rapids]

I tried speed reading this and my mind slowed me down lol.

[red rapids]

...it will make u tuffer, and if its small its reward will be bigger.
Could've corrected the spelling of tougher*

[red rapids]

https://tenor.com/view/aww-cute-zootopia-zootopia-plus-officer-benjamin-gif-9810879141706630432

[stable onyx]

how do u guys read books,
my goal is building intuition and mathematical maturity, rn im in precalc and i feel like im doing too much
well to be fair this is a 900 page book including the non lesson stuff and i do most of the odd numbered exercises

[red rapids]

Just go and study. No sense in planning and setting goals only to come up short, contrary to what was mentioned as a response by another user. Adjust your workload on the fly depending on your pace. Ideally quick isn't as helpful as comprehensive, so take your time to understand every bit of what you're studying and do sufficient exercises.

As far as building maturity goes, see that you're able to check whether definitions make sense and can prove claims made about formulae, equations and methods that you learn in traditional Precalc. Most textbooks rarely go about providing proofs, so it's a good exercise for you to be able to write them while simultaneously solving the typical textbook exercises.

Be detail oriented and try to get feedback on your proofs and conceptual understanding from more experienced human beings and avoid using AI.

[calm trench]

in khan academy, if i do badly in an exercise, do i keep doing that exercise or move on to the rest of the lesson and come back to it later. I am fixated on getting every exercise 100% of the way before i move on to the next video

[edgy sierra]

do another version of the exercise

and spend a lot of time on your solution

[calm trench]

i don't see other versions of the exercise on the website, should I try to find excercises on the topic somewhere else? what do you mean spend a lot of time on your solution? like spend a lot of time before giving up?

[edgy sierra]

yes

ok what type of exercise is it

[calm trench]

im doing pre algebra, lesson 2 visualize ratios on khan academy

[edgy sierra]

ok so you can probably either create a similar exercise and solve it

or search for outside of khan academy

like online

then solve it

[nimble wave]

Hi!!
First of all, if this is the wrong channel to ask this, please just redirect me to the correct channel, if there is one :)

i read one article about fractional calculus and it looks very interesting and honestly even kind of fun to me
So i would like to ask whether anyone knows some good yt videos about the topic or articles about it since id love to learn more about it

[left yacht]

https://www.youtube.com/watch?v=SzNO8q0rlPc

[nimble wave]

Thanks!
Ill watch it rn

Yep i love this topic even more now

[heavy needle]

Lorentz be booostin

[rocky terrace]

aristocrat?

@devout sun

[devout sun]

https://tenor.com/view/ah-i-see-as-well-man-of-culture-gif-13853630

[last furnace]

hi do you guys have any idea how i can study for a math competition thats in about a week?

in the last one i got almost the same score as one of my good friends, off by half a point, and my teacher is expecting me to come this time aswell

problem is i geniuenly haven't studied for that last competition, nor have i worked anything outside of class for about two years. no homework, no math problems solved, nothing.

i cant say no to him and i don't want to disappoint, but idk if this year ill get a good score again

for reference im 17

and my brain is tiktok fried

i js need some advice bc i cant find any material that looks promising😭

are videos better for studying or will doing it by myself work better ?

if i order a book it will come in a few days and i wont have time to study

[scenic shuttle]

I had a math competition last semester and I didn't really study for it, still ended getting first place

your best is just know what topics are going to be and work faster

during my math competition, I had too many cheaters but still got first place lol

[last furnace]

man i wish i could cheat

but its gonna be really hard

theres like 3 ppl from schools all across the country

[scenic shuttle]

cheating won't make you win

[last furnace]

i got like 22/26 right last time and so did my friend and he studies consistently but theres no way i could do it again now

[scenic shuttle]

well that's still good

[last furnace]

i know im just saying what i wish i could do lol

i denied the olympiad and the teacher went bonkers

so i don't want to disappoint

[scenic shuttle]

it only works if you have friends with hosted people that doing the competition

[last furnace]

nope

[scenic shuttle]

we played on kahoot and whenever a question show up, there is always that one person answers fast

in 1 second

[last furnace]

aaa

ik i said i wish i could cheat but honestly i actually wanna do good by mself

[scenic shuttle]

btw there was a huge ass geometry question that I didn't really get but when I did random guess I got it right

[last furnace]

myself

[last furnace]

😭😭😭

[scenic shuttle]

my suggestion is don't cheat at all

[last furnace]

we also get a bonus question about some

[scenic shuttle]

yea

that was the question

[last furnace]

lmaoo

for us its like abt idk some old math philosopher or how u call it

and u had to prove whatever there

i dont remmeber

[scenic shuttle]

it's on paper?

[last furnace]

yes

[scenic shuttle]

icic

[last furnace]

im cooked

[scenic shuttle]

I joined math competition 3 times

2 in hs and 1 on uni

I only won the uni one

[last furnace]

i mean ngl i want to win this one aswell

[scenic shuttle]

goodluck

[last furnace]

its like

next to impossible

but

idk

the teacher also told my parents and they were also mad

cuz why i didn't go

so now im forced to go

[scenic shuttle]

🥀

[last furnace]

😵

[scenic shuttle]

my parents doesn't really force me but they call me stupid at everything

and they didn't actually believe that I could win

until I did it and they were surprised

[last furnace]

mine do both

[last furnace]

well im glad u won it and showed them

i wanna show mine too but

my math homework notebook is empty

like i have the one from 9th grade

still unfinished

[scenic shuttle]

sad

[last furnace]

and i don't work anything else at all either so

itll be hard

but ty for answering

atleast i feel better

🤒

[scenic shuttle]

like I said I didn't really study for it and still won

you are going to do it, I believe in you

[last furnace]

thank you 🥹

https://tenor.com/view/pet-lover-awww-puppy-love-gif-19978366

[placid cedar]

$\frac{\sin!\big((x^2 - 5x + 6)^5\big)}{(x-2)^2 + (x-3)^2 + 1} + \ln!\big((x^2 - 5x + 6)^2 + 1\big) - \ln(1) = 0$
Please solve this

[mossy shadow]

Weinnion

[tough tinsel]

What should I study for my AP Calc AB exam above all??

[edgy sierra]

the first term doesn't make a lot of sense

do you want to take the factorial of sine

oh i didn't notice it also happens to the second term

[placid cedar]

Yes

Use Gamma Function

[edgy sierra]

ok i had to read this again

this probably doesn't have a solution

ln(1) simplifies to 0

move the second term to the right

oh my bad it might

i forgot the gamma function can have negative arguments

[timber cedar]

Hello. I’m not sure if this is the correct channel for this type of question, if not please let me know. I’m looking for some advice. I am a Computer Science Major and also working on a minor in Mathematics. Here is a background of the courses I have taken so far:

Calculus I
Calculus II
Linear Algebra
Discrete
Probability & Statistics (taking this over the summer)

I would like to go to grad school to study mathematics and earn a Masters degree. That said I have been feeling uncertain about the courses which I should take to elevate my application. So here are a few questions I have:

1. Is it plausible for someone with a CS undergrad to pursue a masters in mathematics? That is to say, would grad schools look at my application?
2. If the answer to question 1 is “yes”, the next question becomes, what courses should I take during my undergrad to “elevate” my application and make me stand out. Some people have recommended real analysis, which would require me to take calculus 3 and intro to proofs as pre-requisites.
3. Am I looking at this the wrong way overall? What do you guys think?

Thank you for your time.

[hoary kindle]

If you want to do a maths degree, you 100% need real analysis, a proper linear algebra course and a course in abstract algebra at the very least

I would also reccomend you taking those to see if you even want to do a maths degree, because as it stands youve not really gotten into what a lot of maths is

[red rapids]

1. Is it plausible for someone with a CS undergrad to pursue a masters in mathematics?
   Plausible, yes.

That is to say, would grad schools look at my application?
That would depend on the grad school but based on your present coursework alone the evidence suggests that you've not yet been through the proper undergrad math training which beyond the syllabus is more so about the ability to write rigorous proofs. This will make things a challenge unless you look for an applied math track. But of course, some grad school applications are purely based on entrance examinations. If you're in such parts of the world you'll be in luck.

2. If the answer to question 1 is “yes”, the next question becomes, what courses should I take during my undergrad to “elevate” my application and make me stand out. Some people have recommended real analysis, which would require me to take calculus 3 and intro to proofs as pre-requisites.
   Real Analysis is a must. That is typically the course where people get properly initiated into rigorous mathematical proof writing. A proofs course is more so about the know-how of it. As far as other courses go (Abstract Algebra is a must), it's best to look at the expectations the grad programmes you're targeting have from their applicants. A better idea may come about by looking at the same department's undergrad programmes. Since this varies from place to place, one needs to be careful about how many credits and what not you have. You can also do courses that you prefer over others if you have a choice in this regard.

3. Am I looking at this the wrong way overall? What do you guys think?
   Nothing wrong about it. Where there's a will, there's a way. Might be hard tho. It may be more feasible to switch to a math major with a cs minor if a math grad school is your next goal. But you should evaluate this once you get a taste for what it's like. Best way to do it is sit in a few real analysis lectures randomly.

[hoary kindle]

Yeah where you are is a big thing. In the US or elsewhere this might (might being operative) be reasonable, but in a lot of europe this would be equivalent to about a semesters worth of university maths, and I think youd really struggle to get into a european programme without taking a lot more courses

[timber cedar]

thank you guys i will definitely take this advice 🙂

[sterile rapids]

yo, how hard is a level further mathematics?

[tranquil nimbus]

it's considered the hardest A Level subject (second hardest by those who think chemistry is the hardest). i dunno much other than that. I'll start my further maths course in July

it also has one of the highest pass rates of any a level subject

because most people who take it know what they're getting themselves into

if I'm gonna be completely honest, i don't think it's as crazy as people make it out to be. even before you get to pick your o level subjects, your seniors and teachers will put an idea into your head that a level f maths is this boogeyman that you've always gotta be scared of. but so many people take it every year and get A*s. if you enjoy maths and are decently good at it, you should just take it. if you don't like it, you can always drop it later. then again i haven't even started my own course yet so take everything i say with a grain of salt

[limber oriole]

would anybody happen to know/have some problems i could practice on for my upcomeing finals? (I'm in 9th grade geometery)

[pulsar saddle]

Hard is subjective. You would be better off looking at the grade statistics, syllabus, and past year questions for you to develop your own understanding of the difficulty of the subject

[pulsar saddle]

what topics were you taught?

[limber oriole]

we just finished a proportions unit

ill try to some find past units though

[whole wing]

Mods so fast you don't even have time to ping them

[hollow fable]

How do I remember and never forget what I study?

[scenic shuttle]

by reviewing your materials

or notes

[placid cedar]

X-3=2
X-3-5=2-5 [-5 Both Sides, Balancing]
X-8=-3
(X-8)^2=(-3)^2 [Square Both Sides]
X^2-2X.8+8^2=9
X^2-16X+64=9
X^2-16X+64-9=0
X^2-16X+55=0
X^2-11X-5X+55=0
X(X-11)-5(X-11)=0
(X-5)(X-11)=0
X=5, X=11 since we have to satisfy the condition.
Add - both sides at both answers

SOLVED THE HARDEST ALGEBRA

[whole wing]

Please stop spamming (and in multiple channels to boot)

[tranquil nimbus]

when you square both sides, you add extra solutions to the problem since you lose some information about the signs on both sides prior to squaring

so you're also solving -x+8=-3 now

because x² is basically |x|²

that's why you can get some weird answers when solving problems with a modulus on both sides of an equal sign

[marble relic]

hi, how do u make those bot commands

over here

like this rotated the pic

nd this

(yea i use dc on light mode, cry abt it)

[normal sleet]

rcw and rccw probably
But idk if you have the permissions for that

[marble relic]

hmmmmmmmmmmm

[marble relic]

rccw

[marble relic]

,rccw

krezi

[normal sleet]

rcw is rotate clock wise btw

In case you didnt get that

[marble relic]

ah nvm i found cmds in #helpers-info

ty tho

[upbeat wraith]

numerical analysis seems very interesting to me where should i start

any tips

[left yacht]

<@&268886789983436800> @storm tide mr beast

[storm tide]

Please don't do that.

[left yacht]

oka

[red rapids]

FNC Book

[quick elk]

how is Solomon's Numerical Algorithms?
he has the 1st edition available free, and a 2nd in the works that isn't openly distributed (yet)
and recent lectures on youtube

[jagged cedar]

guys how can i study for the ap precal test on tues

[quick elk]

start now

[jagged cedar]

bru

like what i do

[quick elk]

the real answer was start months ago
idk, take a practice exam, identify your weak points, follow a study guide to focus on these

[jagged cedar]

i mean i alr took a practice test in school last week

got exactly a 5. one less point and i wouldve gotten a 4

[red rapids]

Haven't come across it really so dunno

[red rapids]

#book-recommendations message better to discuss it here @quick crane

[quick crane]

my bad

[red rapids]

Since you're in high school still for one thing you shouldn't get obsessed with theory for the sake of theory. Learning how experiments work and how the data is studied is just as important.

And I'd suggest you to start doing mathematics rigorously. You don't need to train yourself in being able to write air tight proofs but at the very least you need to be able to read rigorous mathematical arguments and be precise in your use of terminology so that you know the subtle details where your intuition may not entirely hold up. I see that you're already attempting to study differential geometry and have seen some analysis before so that's good. Make very elaborate notes on the basis of your own understanding and make sure they hold up.

A nice exercise you can do occasionally for yourself is see to what extent you're able to rebuild the physics you've learned using what you already know. Intuit, formulate, derive and prove whatever ideas you get in your head in the process. And as you go forward, think about stuff you haven't learned about properly yet and try to guess how they might work based on some surface level understanding if you have any.

[midnight beacon]

Hi!

I need advice or tutoring on how to study math reasoning effectively. I've been given the opportunity to apply for a scholarship and I'm afraid of losing it.

Could someone help me or give me some advice? It's basic high school reasoning, but I don't know where to start practicing.

[quick crane]

Thanks! I've taken a few physics courses, such as AS-Level Physics and Physics C-Level. I've found labs terribly boring, very hard to learn from. The math portion has always been easier for me

[quick elk]

it's not 100 clear to me what you're asking, but it sounds like you want something like Book of Proof
if you look at it and that's not what you mean, try to explain clearer

[midnight beacon]

Sorry, my English isn't good, please wait a minute.

[red rapids]

They might be boring, but the complete package generally requires us to be able to suggest how to test theories too. That is quite a difficult thing to do unless you're well acquantied with the essentials of experimental physics. It's less to do with the technical know-how of troubleshooting experiments in a lab but more so about how the experiments work. To this end, even simulations are fine, but the lab exposure is best. And this becomes even more important on the quantum side of things where there is a pretty big gulf between theory and experiment.

[midnight beacon]

I’m preparing for a scholarship exam and I’m a bit lost with the "math reasoning" section. My background in this area isn't the strongest, and I’m afraid of failing. Could someone help me figure out a study plan or suggest some practice materials for high school level reasoning? I’d really appreciate any guidance on how to get started.

[red rapids]

You should specify what this section entails. It's a very broad term, even when limited to high schools. Not only that, high schools are different across the planet.

[midnight beacon]

To be more specific: I'm preparing for a scholarship exam focused on 9th-grade level skills.

The 'Math Reasoning' section covers:

Arithmetic: Averages, percentages, and ratios.

Logic: Syllogisms, Venn diagrams, and sequence patterns.

Basic Algebra: Variable substitution and simple equations.

Problem Solving: Rate/Time problems, combinatorics, and data interpretation (graphs/tables).

Since I feel my school background is a bit weak in these areas, I'm looking for resources that explain the logic behind these problems rather than just the formulas. Any suggestions for platforms or study plans for these specific topics?"

[red rapids]

For basic algebra check our Hall and Knight's Algebra for Beginners. The others I'm not really sure what to suggest. They're a bit all over the place. Perhaps you can use Khan Academy?

[midnight beacon]

"Thanks for the tips! I actually hadn’t heard of Khan Academy before, so I’ll definitely check it out to brush up on the basics. I'll also take a look at Hall & Knight for algebra.

To be honest, my biggest issue isn't really the theory or the formulas, but the reasoning part. My school system was pretty bad and they basically just taught us to memorize stuff without actually understanding it. So, I struggle a lot with the transition from reading a problem to actually knowing how to set it up.

I’ll use those resources to refresh my memory, but if you have any advice on how to develop that 'logic' mindset from scratch, I’d really appreciate it!"

[livid knot]

Hi I want to pursue a degree in either maths or physics in the future subsequently after I study those subjects deeper and conceptually while building a "mathematical mind" but i've only just finished the GCSE additional mathematics syllabus. I did went quite deeper for differential calculus, like just going through all of 3b1b's essence of calc playlist, but Idk if this is even where I should start for this roadmap, there are lots of fields in maths I dont even know their existence of and Idk which to start on and how to build them up with effective understanding. I'm starting my a levels (a pre to early uni course) next year and I'm planning to prestudy their maths and further maths syllabi, finishing it before I even take my first lessons on them at school, as Idt time is sufficient if I actually want to excel. I also want to take competitions on maths, small to big, Idk which is good enough for someone like me with a knowledge merely like a mote of dust in a large room full of universal theories. Which should i try participate in after I finish which parts of maths in detail? For their preparations is a separate inquiry but just the whole idea of a journey to enlightenment is what I'm emphasising here for advice. Pls help.

Specifically, a roadmap including the order of the branches and fields I should go along, the tips to actually develop this mathematical mind and resource suggestions by someone who are already walking along that path successfully?

[livid knot]

How do I learn the content through it? I assume it's impossible to just read through all the content from scratch and be able to understand all of them from the book itself only

Is it beginner friendly? I just finished grade 10 mathematics so

Omg I never realised 'numbers' itself can be this large 😭 with the sets too

cus they're the most trivial topics in my curriculum right now

From the book too?

Wait I'll just skim through it a bit

I mean the Napkin book seems too concise but I was able to understand 13.2 and 13.3 from Hammack's book

he explained deeper

[red rapids]

You might wanna try looking at Cummings's book titled Proofs after having stuck it out with Hall and Knight. The entire thing might be too much for a 9th grader who's just starting out, but I think the first 5 chapters may be very accessible and will help you with this goal. In any case, it's a nice book to have and you can check out the rest of it once you're more comfortable with math in general.

Anything I can offer as advice, you'd be better off learning from the book directly. It conveys these things rather well. It's also worth playing around with mathematics puzzles appropriate for your age and writing down elaborately detailed solutions when you figure them out. You'll start being able to whittle out the core steps of your reasoning to solve them eventually.

Martin Gardner has some great books in this regard.

[livid knot]

thx

[bold path]

Hi, I wanna master the GCSE maths and Addityonal maths course.

I was wondering if anyone could help?, I have a cpg book for revsion and pratice fpor the normal one.

but like videos and practice questions could come in handy.

[bold path]

im tryna get like hella good for my age, not insa e but reliable knowledge

[shadow sinew]

have i cooked or am i cooked?

[whole wing]

Wrong channel (and server), but seems correct except for the units in a)

[shadow sinew]

what is it supposed to be

[whole wing]

Ohms

[shadow sinew]

Omega?

[rocky terrace]

That's the symbol used to denote Ohms, yes

[whole wing]

Yes, that's the symbol for Ohms

[shadow sinew]

ok thanks

also i cant send any work that isnt math here?

since this is sudy, not math study

[rocky terrace]

You can check the physics server in #network

[whole wing]

#study-discussion is for discussing studying strategies etc, as indicated in the channel description

[shadow sinew]

im alreay in it its just dead

[shadow sinew]

ohh ok, My apolgies then

[rocky terrace]

It's not dead

[rocky terrace]

it just might take some time for people to respond depending on the time of day

[rocky terrace]

10m ago

[shadow sinew]

ok u got me there but i made anoth one 2 days ago and still 0 responds

[whole wing]

can somone tell me the basics and give me questions to solve(please @ me)
Of course most people can't be bothered to teach you a subject...

[shadow sinew]

well i just finished learning it

[shadow sinew]

u are a great detective BTW

[edgy sierra]

how do i study while sleeping

[shadow sinew]

u dont

u dont sleep at all

sleeping is over rated