what comes up in math from university

[modest ingot]

I am currently in ninth grade and like math very much.
I currently finished all the math my school would have taught me (it goes up to class 13).
since I am understanding everything from that and my hunger for Math hasn't calmed down I would like to know what Math is like in uni

I am asking this server because I couldn't find a reliable source online
-# websites to train that stuff would be appreciated

-# btw I am German so I may not understand every math word in English

[unborn aspen]

Kannst du keinen Universität-Mathematiklehrplan online finden?
-# Can't you find a university maths syllabus online?

[modest ingot]

lets stay english so other people can read everything

and no not really
I don't exactly know where to look
if you could send one that would help

[unborn aspen]

I meant this literally:

And in (my shoddy) German

[quartz pike]

||calculus||

[supple dagger]

calculus is but a rather small part of uni stuff and is the least of your worries

[modest ingot]

ok maybe I am just stupid
because I only typed in:
Math universitat

[modest ingot]

I know that a big part is analysis

-# atleast I think so

[unborn aspen]

That's just one part, though

Though it is still important

[supple dagger]

analysis is a rather important part but not the only route of attack

there's applied math, there's algebra, there's the god-forsaken geometry route...

[unborn aspen]

And by algebra, this refers to a massive variety

Much more broad than school algebra

[quartz pike]

Im curious, can you give an example?

[unborn aspen]

If you see "linear algebra" especially, this explicitly is university-level stuff

I've watched a clip of someone saying how she hated linear algebra at uni, only for several comments to think "ah that shit's easy" while not realising that the algebra in school is not linear algebra

[supple dagger]

well

there's linear algebra

there's group theory

[unborn aspen]

Think vector spaces, matrices, linear transformations [this is just lin. alg.]

[supple dagger]

there's ring theory

there's field theory

there's commutative algebra...

ok you get the point

[unborn aspen]

There's algebraic number theory, depending on how you classify it

[supple dagger]

there's algebruh, for cranks
but algebraic geometry as well

[unborn aspen]

That was a third-year course for me (and I both liked and hated it)

[supple dagger]

(no, algebraic geometry is NOT the high-school geometry)

please don't enter #algebraic-geometry with triangles and squares and cubes

[unborn aspen]

But please do enter it with tesseracts /s

Actually idk where Differential Equations really goes tbh
-# I mean, tbh it's in the applied route...

[modest ingot]

do you guys know any good online classes for all that stuff
-# so I don't need to learn from Wikipedia like I did with integers

[supple dagger]

Khan

and when you get to the hard shit, MIT OCW

[unborn aspen]

Or in fact any lecture notes from universities; in practice these are readily available online, freely

[supple dagger]

and when you get to the really hard shit, books

and lecture notes

but problem with lecture notes is that they are notes

[unborn aspen]

True

[supple dagger]

and thus only make complete sense when viewed with the accompanying lecture(s)

[unborn aspen]

They are... an thing

[supple dagger]

which is not always available

some notes can stand alone though