Areas of math

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Yes I am brainlet.


Usually when you are learning some subject you are learning basic, fundamentals and then you are learning more advanced stuff, after you learn advanced stuff it turns out that there is even more advanced stuff.

Now in math its completely different, you can learn basic stuff like +/-/:/* and then you are learning lets say calculus, but if you want to learn statistic or discrete math, calculus is not going to help you.

Is there a way to connect everthing?

Usually when I learn something, First I have big picture of problem in my head and then I study piece after piece.

This way allows me to understand real application of the thing I study and expand it in future.


but in math?

I feel like different areas are barely connected or not connected at all.

I would expect that all derived from one main root?

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Algebra is the one thing that's behind everything

Calculus is in statistics, mate.

Start with set theory (ZFC or even ZF until you need the C) and logic and go from there.

I am a computer science student and for me this disjunction(don't know if this is the correct term) is a true gift as I don't have to study all the topics.

>tfw all that shit in the middle of the math circle is useless and only the small intersections with other things will ever help you get a job

>I would expect that all derived from one main root?
Yes, axiomatic set theory, more specific ZFC. Nearly everything in mathematics is build on that.

If you have set theory you can start to define things as "functions","numbers", "addition", "groups" and so on which are the foundations of the rest of mathematics.

But that is not the way you can actually teach mathematics. If you started in first grade trying to explain to a 6 year old how the definition of real numbers works will not get you very far.

This, fucking this someone gets it

thx

I was looking on Veeky Forums wiki but there are no book on set theory

anybody knows some good set theory + proofs book for a brainlets?

>I was looking on Veeky Forums wiki but there are no book on set theory

Veeky Forums-science.wikia.com/wiki/Mathematics#Proofs_and_Mathematical_Reasoning
Veeky Forums-science.wikia.com/wiki/Mathematics#Introductory_Set_Theory

This, algebra is logic intrinsic to every operation

I was looking on wiki from pinned post on top on Veeky Forums

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>ADHD, ODD, ANXIETY, OCD, DCD AND DEPRESSION checking in

...

>schitzotypy

>but if you want to learn statistic or discrete math, calculus is not going to help you.

The only statistics without calculus is the brainlet crap for high schoolers/business majors/CS. Real discrete math uses calculus too.

>Is there a way to connect everthing?

Pretty much all of math is heavily interconnected.

>I feel like different areas are barely connected or not connected at all.

Go deeper. Remember precalculus where you learned complex numbers, trigonometry, and exponentials/logarithms and thought it was all disconnected stuff lumped together. Then in calculus you learn about e^ix=cos(x)+i*sin(x) and how they are all linked together.

"Disjoint"

>communication skills

FUCKING NIGGER SHIT PISS

>is there a way to connect evrything

There are two interpretations of your questions that must be considered.

>Is everything interconnected in a logical way
Yes, the foundation of mathematics is the study of the logical systems that can be used as a rigourous system to develop mathematics

>how can i connect everything connected to understand it
Thats a different question, and you (theoretically) could start learning set theory, logic, or category theory and "go from there", but I doubt thats the path to an understanding of mathematics.

I believe abstract thought must be developed to appreciate the deep consequences of the given forman system, so i believe is better to give the learning process a context.

For example, learning math in an order that roughly corresponds to the way it was historically developed. (not saying this is the only way)

I like how this chart implies that people with anxiety can never be gifted, people with OCD can never be depressed, and so on.