/sci/ - Science & Math

A theorem proved in a variety of ways can be interesting. The Fundamental Theorem of Algebra comes to mind.

>>6478942
Gauss rated him bro. Get with the program.

>You will never be Gauss

>Einstein or Newton
>On Gauss' level

Pick 1

Next week I need to do a talk about an interesting math subject, suitable for +/- 17 year olds. I was thinking about something in algebra / number theory, what are particularly interesting subjects in these fields?

Hey /sci/ what are you learning currently?

I just learned gauss's law this week and it blows my mind how elegant it is. Also learned how to read phase diagrams, basic circuit analysis, intro statics problems and just learned most of the integration techniques in calc 2.

pic related

Student A's score follows a normal distribution N(160, 15)
Student B's score follows a normal distribution N(170, 10)

What is the probability that student A gets a better grade than student B?

In the vein, how can you believe number theory, statistics, analysis, differential geometry, geodesy, geophysics, electrostatics, astronomy and optics, if they're just theories (by Gauss)?

I am wondering if there is a single term for this mathematical concept I'm thinking of. The problem is that I'm not sure how to express it. So I guess it would be nice to have a more concise way of expressing this in addition to having a name.

Note: I'm pretty sure everyone who reads this is going to say to themselves either "what is this I didn't..." or "Wow, this idiot has no clue how to wield mathematical notation."

Let <span class="math">\mathcal{P}_n=\{P|a\in P\to a\in \mathbb{Z}^+\backslash \{1\};a,a'\in P\to gcd(a,a')=1; \sum\limits_{a\in P}a=n\}[/spoiler] be a class containing sets of integers who partition n such that none of these sets contain 1 and all elements of each of these sets are coprime.

Now, let <span class="math">\Pi_n=\{\prod\limits_{a\in P}a|P\in \mathcal{P}_n\}[/spoiler].
That is, I <span class="math">\Pi_n[/spoiler] is the set of products of the elements of each set of <span class="math">\mathcal{P}_n[/spoiler].

What I am interested in is <span class="math">sup(\Pi_n)[/spoiler].
So in whole, I want to take a integer and find the partition containing no 1s or summands which share a common factor which has the greatest value when the sum is replaced by the product.

Ok, I kind of lied. I do have a simple way to express the concept. I just don't like how it's an indirect way of expressing it. Given a symmetric group, <span class="math">S_n[/spoiler], the maximal order of all elements <span class="math">a \ S_n[/spoiler].

>>1385023
You spent five fucking years summing one series. You can suck my ass Euler.
Leave math for the real mathematicians.

gauss fuck yea