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2023-11: Warosu is now out of extended maintenance.

/sci/ - Science & Math

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5605676 No.5605676 [Reply] [Original]

Hey /sci/cologists.

I neglected math my whole life, now its time to start from scratch.
The easiest way for me to get into something is to cut it into 10 basic pieces and then learn each piece.

So in mathematics, starting from arithmetic (1), could you name the other 9 big levels of mathematics from simple to harder/complex?
I looked wikipedia but doesn't help in this aspect.

No uber/pure math though, am just a webdeveloper trying to understand as much math as i can.

>> No.5605677

ffs souce me up on that gif

>> No.5605680

>>5605677
welp i guess i'll have to use tripcode

>> No.5605682

>>5605677
also that gif is pretty much fake.

>> No.5605684

>>5605676
>>5605680
check the sticky

>> No.5605691

>>5605684
i just need the 10 words really, from people who know math, thats all.

>> No.5605692

>>5605691
arithmetic
algebra
trigonometry
precalc
calculus
advancd calc
extre calc
calc calc
calc x1000
calc universe boom omg lol godlike lelele

>> No.5605694

>>5605692
>science and math

>> No.5605700
File: 89 KB, 590x518, 1363019204285.jpg [View same] [iqdb] [saucenao] [google]
5605700

>girl will never rape you in school restroom

>> No.5605706
File: 814 KB, 3045x2300, Math Tree.jpg [View same] [iqdb] [saucenao] [google]
5605706

>>5605676
The TREEEE OF MATHSSSS

>> No.5605711

There are no easy steps, only some with less prerequisites than others.
A logical progression would be:
Arithmetic > Basic logic (proof techniques and reasoning) and set theory : Sets, operations on sets, mappings, binary relations (you'll need that if you expect to go anywhere beyond arithmetic..) > Combinatorics and elementary number theory > Basic abstract algebra: groups, rings, fields > Linear algebra: Linear spaces, subspaces, linear mappings, matrices, polynomials > Affine and euclidian geometry > Basic point-set topology > Analysis > More linear algebra > More abstract algebra

>> No.5605724

>>5605676
http://www.math.com/tables/index.html
Your welcome faggot

>> No.5605733

>>5605711
Saved.
Seems rather interesting, look completely difference than i expected.

>> No.5605735

>>5605733
Yes, this is pretty much how we're taught in the first years of superior education in France. It is organized in such a way that we only have to skip a very small amount of proofs

>> No.5605775

>>5605735
If forgot everything and wanted to learn math from 0 would you follow that progression?

>> No.5605778

>>5605735
>french
>cis scum

>> No.5605792

>>5605775
Well I think so, maybe move number theory and euclidean geometry right after arithmetic because they don't really have any prerequisites but I still think this is an intellectually satisfying progression. Actually, I did try to teach myself math in middle school (ie from 0) using the internet and I learned some of these at random but I realized by the end of high school that I might have had a much deeper understanding if I had had a plan like this.

>> No.5605822

>>5605792
one more question, is khan academy's progression tree any good?

>> No.5605844

>>5605711
A person of average intellect that knows only arithmetic and studying about 3 hours per day, how much would take him to learn all 10?

>> No.5605853

>>5605844

Not the guy you're talking to, but unless you could instantly understand every new piece you read... I would imagine more than half a decade to get all of that down.

>> No.5605855

>>5605822
Are you talking about >>5605706 ? (I hadn't heard that name before) I will comment on it
I don't think there is anything wrong with this but it doesn't cover much, it just links some formulas together, which is interesting, but there is more to math than formulas and calculus.
I think Khan Academy in general is a great help but it can't substitute for a rigorous course

>> No.5605871

>>5605855
I was just mentioning the progression tree layout they have on their practice program.

Sure, learning seems to be better the more mediums you use, be it an app, courses, reading, writing, discussing etc.

>> No.5605873

>>5605844
We do this in two fairly intensive year (about two or three hours in classroom per day from monday to friday plus two or three problems from one day to the next) but it may take more time without this framework (really, having a teacher you see everyday helps a lot)

>> No.5605886

>>5605844
>A person of average intellect that knows only arithmetic and studying about 3 hours per day, how much would take him to learn all 10?

(I'm not the author of >>5605711)

Depends on how long you study each subject, you can make it as hard or as easy as you want. Best would be to read a good book, in my opinion. A course in Pure mathematics by Hardy is a good one (but it doesn't cover every subject).

By the way, I would divide math roughly in these subjects:

- Arithmatic and it's algebra
- Logic and set theory, proofs and function theory
- Combinatorics, discrete probability, discrete mathematics and number theory
- Groups, rings, Galois theory, etc.
- Linear Algebra (applied to R^n)
- Trigonometry and geometry, maybe a bit of topology
- Limits, series, calculus(derivatives and integrals) and continous probability, analysis, convergence, all that stuff (but this could be split up into two, three, maybe even four subjects as well: it's a huge category. I just feel they are very related)
- Complex functions
- Graph theory
- Algorithms
- Differential equations, transformations

I tried to seperate the topics as well as I could, but it's kind of impossible.

There are many fields based on a generalization of an idea. Vectorspaces, Banach spaces, Hilbert spaces, all kind of weird spaces or generalizations of a general idea. These are pretty technical and boring, but they learn you that if you can identify something as an instance of a certain idea, you can apply all theory to it, and you know a great deal about the properties of the instance.

For example: Fourier theory can be understood very quickly if one knows properties about Hilbert spaces, and realizes that the theory can be applied to Fourier series.

>> No.5605894

>>5605886
>arithmetic and it's algebra
>arithmetic and it is algebra

>> No.5605924

>>5605886
>limit series calc
Yeah when i had finished highschool i was somewhere in there.

Maybe am confused but isn't trigonometry kinda one of the first things you learn? like after logic/set theory.

First half is very similar to this:
>>5605711

But i see you're more advanced in the latter stages, i trust you know better.
W-when it will be m-my turn to d-differential and transfor-rm

>> No.5605926

>>5605894
Lol, that's a stupid type indeed.

>> No.5605927

>>5605926
>type

>> No.5605930

>>5605924
Well, you can probably take it a lot further if you start studying series and especially analysis: it is a deep subject.
But it's all a matter of how far you want to take it. Some advanced things sound exciting but are utterly boring in reality (a good example is functional analysis: it seems completely artificial and applicationless at first)

>> No.5605932

>>5605927
FUUUUUUUUUUUUUUUU-