The higher you go up in math, does it get more difficult to understand?

>>8905605
Things become more difficult in that you need to actively "work" or "hold" more concepts in your head.

>maths
>hard to understand
Its only difficult if you arnt trying. Wikipedia and some other sites have literally all youd ever need to know to understand most of the shit.

The only actually difficult parts of math are the theoretical ground breaking parts describing things we dont even know exist. But thats all done by actual smart people. I.e. no one who would ever come to this board

>>8905649
t. Engineering undergrad student

>>8905649
>math isn't difficult if you ignore the difficult parts

Really made me think

>>8905650
>>8905651
>t. angry undergrad matletes
Im grad school nuclear physics but ok bois

>>8905605
It does get more difficult to understand. When you start most definitions are very self explanatory. but eventually you reach a point where you can read a definition and understand it logically but have no idea about what it really, really means. At this point is when you have to learn how to poke around to see what happens and maybe learn some theorems that come from the definitions. Personally, the topological definition for differentiability left me completely confused thinking what the fuck is this shit until I saw it used to prove a theorem. Then it clicks like "Oh, so that is why this was defined the way it is".

>>8905658
>numerically solves PDEs using software
>thinks their opinion on higher maths is at all relevant

>>8905658
i mean.. taking out the rigor makes it a lot easier to understand, so yea

>>8905682
So what is the point where it gets hard?

High school algebra 1? Calculus 3? Ring theory stuff? Abstract Topological whatever-the-fuck-ebra?

>>8905605
Math, the higher up you go, will be more and more about rigorous proving, using only axioms and statements that we know to be true.

You will need background knowledge, sure.
You will need to know all the most important definitions but fortunately you're not going to use all that many at any one time and once you've trained with the formal definitions enough, you can forget about them, knowing that you can quite easily reverse engineer them based on your intuition.

Also, to be honest, the chore of memorizing formulas that you don't quite understand but which apparently work is not going to completely go away. Fortunately, with increased math skills, you will at least be able to prove for some of them that they work and find some solace in that.

In any case, I think higher math is much more about understanding and much less about remembering formulas than it previously was. And I love it like that.

>>8905686
I didn't like Calc 2. I got a B in it, do maybe that is where it starts. But that's just me and I know other people who loved Calc 2 and hated Calc 1.

>>8905649
>theoretical ground breaking parts describing things we dont even know exist.
do you mean pure math ?

>>8905686
general topology is really unintuitive at first

>>8906543
Why thought?

If preschoolers were taught a dumbed down version of it first, would it be easier?

>>8906543
I think you mean always :P (unless you're gonna do topology on a manifold, then im chill with it)

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Nope. If you proceed naturally, the degree of difficulty should be somewhat constant. If you skip something essential in between, then it will get more difficult to understand.

>>8905605
It gets conceptually harder, but at least at the undergrad level nothing you can't understand if you work at it.
t. brainlet with bachelor's in math

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>>8905739
>>Math, the higher up you go, will be more and more about rigorous proving, using only axioms and statements that we know to be true.
this is what undergrad believe

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>tfw you have to deal with sets of sets of sets of sets and it's hard to even keep track of what level of sets you're on

>>8905605
Cramming is always painful and difficult, and in the subjects where I've had to read a whole book in a couple of weeks because of bad planning, it really feels like it gets absurdly hard towards the last few pages. But that isn't how you generally study, and I suppose a student studying the same thing evenly throughout a semester would feel that the progression was natural and smooth.
Cramming really isn't the same as learning. If you study eagerly and work at your own pace, the difficulty curve should have about the same slope. That is how I would define "your own pace" anyway.
Since most of the maths you learn is just there so that you can use it to learn more, higher levels of maths, the difficulty will always depend on how well you've been keeping up until then. If you spend enough time studying this current sort of simple thing, the next one will be just as easy.

>>8905605
more difficult.

things become infinitely more complex.

>>8905605
>higher you go up in math
No.

Math doesn't have a low or high point of any kind. It is all the same. It is merely more or less complex in its attempt to mimic things in the real world.

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>>8908367
Assign each set a color.