Help me craft a self study program for maths

[limber roost]

Say you have one or two years and you want to study pure maths to the point of understanding it pretty well while acquiring skills in Logic and philosophy, how would you go about it? What courses or textbooks are essential? I assume you start with Calculus but then what? Assuming you're not a genius and have average math skills and learning speed.

[gentle dock]

I am kind of in the same boat myself at the moment. Personally I started with Calc as you did, but I also study linear algebra and classical analysis at the same time, distributing them evenly throughout the day/week. For example first I do calc for like 1.5 hours, then I take a break, then going on with linear algebra, say 45 minutes, as I am quite comfortable with linear algebra, so I don't really need too much time on it, and then another break followed by classical analysis. It all depends on how confident I feel in each of the topics however. One day might be all one subject etc. At least this is what works for me, it might not work for you, so keep in mind, study in the way you find most efficient! Good luck!

Also, I have read a book about proofs and logic on beforehand, and that really helped, so if you can get your hands on a proof book, I think that will help you signficiantly, especially if you consider classical analysis as well. Book is filled with nothing but proofs haha

[restive trail]

well whats your starting point

[limber roost]

i don´t see why calculus is usefull at all.

possibly the most boring topic in math. projective geometry is most interessting and since you wanne think about mathematica puris. so this is complex geometry.

so why studying everything else as a sort of rigorous fundament or somethink and then giving up halfways without studying what is the thing that´s of interesst.

???

[limber roost]

Can you please reformulate this question?

[limber roost]

What book was this

[limber roost]

haja, today i somehow managed to get a twist in the focal point of a parabola, and via the tanh i could manipulate the cardoid.

@limber roost

progress is slow but little after little

i don´t know what the official goal is, so yeah, why, why, why.

if not to draw stupid geometries.

can´t see the point.

this is a trial and error.

manipulating equation and look what happens and the trying to analyze what happens.

@limber roost

how shall we study this math ?

[native pine]

I found this is good board guide for maths

https://www.neilwithdata.com/mathematics-self-learner

[limber roost]

@native pine cool article.

[limber roost]

Calculus in the sense of what they teach in school is quite boring imo but it's still useful as a crutch going into analysis

[limber roost]

It seems you are mainly coming across lots of different complex maps so ig maybe atleast start off with complex analysis

But for more deeper geometry questions stuff gets very complicated blisteringly fast so be wary

@limber roost nah, just obsessed with it since some weeks

but without geometry mathematics would make no sense to me

You mentioned projective geometry too outside of the elementary stuff that is WAYY out of my paygrade

I think Abstia is taking some classes on algebraic geometry but still a lot of those topics are way too advanced

[limber roost]

If you do wanna self study you'll prob find abstract algebra a lot more fun compared to analysis atleast for the inherent beauty in it

@limber roost yeah, that is true, but i try to learn more about algebra too. but this is a project for years. since some things can´t be understood from today to tommorow.

some weeks ago i read an artikle about a german abitur question. it was called der octaeder des Grauens.

lot´s of student´s struggeled with this task

so calculus is big in school but when it comes solving relativly simply geomtric tasks, students struggle

i don´t know excatcly where the reasons for this are. but i think studying the platonic soldis carefully isn´t a thing done in school.

i don´t know why this is. or why it is better to do so much analyzis instead.

as if some areas under some fuctions would be the most important thing in life.

hmm.

[limber roost]

Hmm many years for research level mastery maybe but not for an introductory course in say group theory following lectures online maybe just 2 or 3 months

But yea the motivation and exposition is what is really lacking

[limber roost]

Hmm i can't speak on this really i hardly know what they do anymore but i think basic geometry is usually covered at an early stage

[limber roost]

Ahh that's too reductionist no

@limber roost o.k. fair point.

but i can tell you lot´s of people with abitur wouldn´t be able to do simple geometry (like early age stuff) at the age of 30. or 40.

[limber roost]

Although part of the fun is being able to see the beauty in it yourself through your own efforts

[limber roost]

Ahhh i don't doubt that 😂

@limber roost yeah, that´s true, for me it´s just nice to sit arround and draw stuff, to keep my brain somehow alive, for work it isn´t required.

but the projective geometry stuff will maybe follow me some years.

cause there is always new things to discover.

huge field.

[limber roost]

I was trying to find a nice intro video have a look at this gives some nice motivation to study group theory nothing super deep
https://youtu.be/Vjio1cwylTs?si=5WyrsYwXaOhDzIca