/sci/ - Science & Math

We know how to count: 1, 2, 3, 4, etc.
For every [math]a[/math], [math]b[/math], [math]c[/math] [math]\in\mathbb{R}[/math]:
[math](a+b)+c=a+(b+c)[/math].
[math](ab)c=a(bc)[/math].
[math]a+b=b+a[/math].
[math]ab=ba[/math].
[math]a(b+c)=ab+ac[/math].
There exists [math]\mathit{0}[/math] such that for every [math]a\in\mathbb{R}[/math]:
[math]a+\textit{0}=a[/math].
There exists [math]\mathit{1}[/math] such that for every [math]a\in \mathbb{R}[/math]:
[math]\textit{1}a=a[/math].
For every [math]x\in\mathbb{R}[/math] there exists [math]y\in\mathbb{R}[/math] such that:
[math]x+y=\mathit{0}[/math].
For every [math]x \in\mathbb{R}^{\times}[/math] there exists [math]y\in \mathbb{R}^{\times}[/math] such that:
[math]xy=\mathit{1}[/math].
[math]\textit{0}\not\in\mathbb{R}^{+}[/math]
For every [math]a\in\mathbb{R}[/math] either [math]a\in\mathbb{R}^{+}[/math] or [math]-a\in\mathbb{R}^{+}[/math], but not both.
For every [math]a,b\in\mathbb{R}^{+}[/math]:
[math]a+b\in\mathbb{R}^{+}[/math].
[math]ab\in\mathbb{R}^{+}[/math].
Thread to start your mathematical journey from scratch.

We know how to count: 1, 2, 3, 4, etc.
For every [math]a[/math], [math]b[/math], [math]c[/math] [math]\in\mathbb{R}[/math]:
[math](a+b)+c=a+(b+c)[/math].
[math](ab)c=a(bc)[/math].
[math]a+b=b+a[/math].
[math]ab=ba[/math].
[math]a(b+c)=ab+ac[/math].
There exists [math]\mathit{0}[/math] such that for every [math]a\in\mathbb{R}[/math]:
[math]a+\textit{0}=a[/math].
There exists [math]\mathit{1}[/math] such that for every [math]a\in \mathbb{R}[/math]:
[math]\textit{1}a=a[/math].
For every [math]x\in\mathbb{R}[/math] there exists [math]y\in\mathbb{R}[/math] such that:
[math]x+y=\mathit{0}[/math].
For every [math]x \in\mathbb{R}^{\times}[/math] there exists [math]y\in \mathbb{R}^{\times}[/math] such that:
[math]xy=\mathit{1}[/math].
[math]\textit{0}\not\in\mathbb{R}^{+}[/math]
For every [math]a\in\mathbb{R}[/math] either [math]a\in\mathbb{R}^{+}[/math] or [math]-a\in\mathbb{R}^{+}[/math], but not both.
For every [math]a,b\in\mathbb{R}^{+}[/math]:
[math]a+b\in\mathbb{R}^{+}[/math].
[math]ab\in\mathbb{R}^{+}[/math].
For [math]a_{n}[/math], [math]a_{k} \in\mathbb{R}[/math] and [math]N, M[/math] counting numbers.
As definitions: [math]\sum_{n=1}^{0}a_{n}=\textit{0}[/math], [math]\sum_{n=1}^{1}a_{n}=a_{1}[/math]
and [math]\sum_{n=1}^{N+1}a_{n}=\left(\sum_{n=1}^{N}a_{n}\right)+a_{N+1}[/math].
[math]\prod_{n=1}^{0}a_{n}=\textit{1}[/math], [math]\prod_{n=1}^{1}a_{n}=a_{1}[/math]
and [math]\prod_{n=1}^{N+1}a_{n}=\left(\prod_{n=1}^{N}a_{n}\right)a_{N+1}[/math].
As theorems: [math]\sum_{n=1}^{N+M}a_{n}=\sum_{n=1}^{N}a_{n}+\sum_{n=N+1}^{N+M}a_{n}[/math]
[math]\prod_{n=1}^{N+M}a_{n}=\left(\prod_{n=1}^{N}a_{n}\right)\left(\prod_{n=N+1}^{N+M}a_{n}\right)[/math]
For every [math]\sigma\in\textrm{S}_{N}[/math]:
[math]\sum_{n=1}^{N}a_{\sigma(n)}=\sum_{n=1}^{N}a_{n}[/math].
[math]\prod_{n=1}^{N}a_{\sigma(n)}=\prod_{n=1}^{N}a_{n}[/math].
[math]\left(\sum_{n=1}^{N}a_{n}\right)\left(\sum_{k=1}^{M}b_{k}\right)=\sum_{n, k}a_{n}b_{k}[/math].
Thread to start your mathematical journey from scratch.

We know how to count: 1, 2, 3, 4, etc.
For every [math]a[/math], [math]b[/math], [math]c[/math] [math]\in\mathbb{R}[/math]:
[math](a+b)+c=a+(b+c)[/math].
[math](ab)c=a(bc)[/math].
[math]a+b=b+a[/math].
[math]ab=ba[/math].
[math]a(b+c)=ab+ac[/math].
There exists [math]\mathit{0}[/math] such that for every [math]a \in \mathbb{R}[/math]:
[math]a+\textit{0}=a[/math].
There exists [math]\mathit{1}[/math] such that for every [math]a \in \mathbb{R}[/math]:
[math]\textit{1}a=a[/math].
For every [math]x \in\mathbb{R}[/math] there exists [math]y \in \mathbb{R}[/math] such that:
[math]x+y=\mathit{0}[/math].
For every [math]x \in\mathbb{R}^{\times}[/math] there exists [math]y \in \mathbb{R}^{\times}[/math] such that:
[math]xy=\mathit{1}[/math].
[math]\textit{0}\not\in\mathbb{R}^{+}[/math]
For every [math]a\in\mathbb{R}[/math] either [math]a\in\mathbb{R}^{+}[/math] or [math]-a\in\mathbb{R}^{+}[/math], but not both.
For every [math]a,b\in\mathbb{R}^{+}[/math]:
[math]a+b \in\mathbb{R}^{+}[/math].
[math]ab \in\mathbb{R}^{+}[/math].
For [math]a_{n}[/math], [math]a_{k} \in\mathbb{R}[/math] and [math]N, M[/math] are counting numbers.
As definitions: [math]\sum_{n=1}^{0}a_{n}=0[/math], [math]\sum_{n=1}^{1}a_{n}=a_{1}[/math] and [math]\sum_{n=1}^{N+1}a_{n}=\left(\sum_{n=1}^{N}a_{n}\right)+a_{N+1}[/math].
[math]\prod_{n=1}^{0}a_{n}=1[/math], [math]\prod_{n=1}^{1}a_{n}=a_{1}[/math] and [math]\prod_{n=1}^{N+1}a_{n}=\left(\prod_{n=1}^{N}a_{n}\right)a_{N+1}[/math].
As theorems: [math]\sum_{n=1}^{N+M}a_{n}=\sum_{n=1}^{N}a_{n}+\sum_{n=N+1}^{N+M}a_{n}[/math]
[math]\prod_{n=1}^{N+M}a_{n}=\left(\prod_{n=1}^{N}a_{n}\right)\left(\prod_{n=N+1}^{N+M}a_{n}\right)[/math]
For every [math]\sigma\in \textrm{S}_{N}[/math]:
[math]\sum_{n=1}^{N}a_{\sigma(n)}=\sum_{n=1}^{N}a_{n}[/math].
[math]\prod_{n=1}^{N}a_{\sigma(n)}=\prod_{n=1}^{N}a_{n}[/math].
[math]\left(\sum_{n=1}^{N}a_{n}\right)\left(\sum_{k=1}^{M}b_{k}\right)=\sum_{n, k}a_{n}b_{k}[/math].
The thread to start your mathematical journey from scratch.

This is not a homework question, but a genuine question about math. I'm currently interested to learn again about math, but I lack the direction to which area to start and where to go after those. I'm planning to master math as a whole (if possible), and the thing I lack was the direction needed of what to learn and what to learn after said area.

Please help. I have this pic that I can't even comprehend and struggling to take directions from it. I'm an ESL so if my request is confusing, I'm very sorry in advance.

>>11628445
From what book is this figure?

Is it possible to make contributions to physics by learning and using only math without studying physics? I mean, there's a mathematical formulation of quantum mechanics, so technically it's possible to take these as axioms and start building from there, right?

This is more and less accurate, right?

This is more and less accurate, right?

>>8274251
It's not quite as impressive though.

Alright /sci/, mathematical physics can pretty much describe everything in the universe, with a few exceptions of course.

But what exactly is the most fundamental aspect of mathematical physics? Is it the notion of metric spaces, topologies?

Is it the notion of sets, and functions?

Is it the notion of tensors, number theory, analysis with geometry?

Or perhaps abstract algebra and logic creates all of the universe?

Just wondering what you all think is the best or most "fundamental" math that best describes the universe. I am aware it all draws upon each other, but perhaps there is a theory of everything for mathematics.

Lastly, how could such a theory be applied to serve humanity and life on Earth?

Alright, /sci/, hear me out...

I feel more comfortable studying by myself, and feel a lot more progress that way. I'm just out of high school and learning nothing for 4 years was terrible, in this past semester I taught myself more than I learned throughout all 4 years of school.

So here I ask, how seriously is an online degree taken? What are its benefits, what are its drawbacks? I'm willing to do a lot of work, I love science and mathematics and actually would like to study it just about 24/7, not take random classes with potentially slow professors and lame homework assignments and all.

Thanks for any feedback /sci/, I really appreciate it.