/sqt/ - Stupid Questions Thread: Ask the Math Oracle

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en.wikipedia.org/wiki/Zeta_function_universality
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Why ar u gai

How important is it to know statics well as a mech engr major?

If I finish this semester without properly having learned it, am I gonna pay for it later?

Ok I am totally new to math. And this will sound really stupid. But is there any equation with actual numbers that will actually get you pi? That is, where you can divide one number from another and actually get 3.1415926535....etc? I'm not talking about approximations like 22/7, but where you get the actual result of pi

How can repeating numbers exist?

does the definition of pi count? as in take any circle and divide its circumference by its diameter and you get pi.

if you're looking for a rational number a/b with a and b being whole numbers you won't find any since pi is irrational

they dont have to be whole numbers, could be really long decimal numbers. im just looking for an equation that will get you pi, with actual numbers

For a sequence such as [math]0, 1, 2, 3, 4, 5, 6, ...(n - 1) / 2[/math], what is the relationship called between any given term of the sequence and some kind of deterministic conversion, e.g. for a term [math]a: j = a * 2 + 3[/math] will produce all the odd numbers through the range of [math]n[/math] starting from 3.

Secondly, what would you call the "base" of the sequence? It's represented in base 10, but, for example, to convert [math] j^2[/math] to the sequence's "base", you'd need to take the relationship [math] (j^2 - 3) / 2[/math], so for example [math]j^2 = 49 = 7^2[/math], so to convert back to the sequence value, you take [math](7^2 - 3) / 2 =23 = An[/math]

...

ALGEBRAISTS IN HERE HELP A NIGGA OUT

So, hol up, lemme get this straight, if I want to create an extension field of Q to find a zero of (x^2-2), is this how I would do it::!!!

x^2-2 is irreducible over Q, with Eisenstein = 2, thus is a maximal ideal of Q[x], and Q[x]/ is a field. We identify q in Q with q + in Q[x]/. Hence we have an extension field of Q. Now, in Q[x]/, we let a = x + . Calculating a^2-2 we get 0, and baddabing baddaboom, we did it. Read the theorem, and I think I understood the construction well, and this is how it's done in practice, right?

>they dont have to be whole numbers, could be really long decimal numbers.

no

>im just looking for an equation that will get you pi, with actual numbers

define actual numbers, but, no

If someone knew nothing about math much at all, beyond the basics, how would you explain how this equation is considered so beautiful? What makes it so great?

tau/2

...

Bunch of very important, yet seeminly unrelated, numbers in math coming together in a very simple equation.

In reality it's just pure autism. Haven't seen a pure mathematician who could give less of a fuck about it.

seems about right.

just be careful when you conclude that is a maximal ideal. it's true in this case, but not just because the polynomial is irreducible. (e.g., consider that Z[x]/x is not a field even though the polynomial x is irreducible over Z). You need an additional property of Q[x], which is that it is a principal ideal domain.

>You need an additional property of Q[x], which is that it is a principal ideal domain.

Alright, thank you very much. The book I am self-studying with introduces principal ideal domains and those other things in a later chapter.

np senpai. i had a hell of a time keeping all those definitions straight when i was first learning this stuff.

Yes. Statics sets the foundation for dynamics, mechanics of materials, and machine design.

So as a student who passed without learning it beyond chapter 1, what's the best way to proceed?

I guess learning something tedious as that without the grade incentive

Go learn statics. First learn each coordinate system, then proceed. Just remember Sum of F = 0 and Sum of M = 0

:^(

Any book recommendations? I may have to return my rental soon, and I guess I could practice on a PDF

I just have to force myself into enjoying doing problems I guess

why do you use those faggy pictures from reddit for these threads

they are basically divergent roots of an expression

sin^-1(0)

There are arbitrarily many such formulas, although none of them could be evaluated in a finite amount of time.

You can only approximate pi arbitrarily well and we dont (and never will) now all its digits.

>sin^-1(0)
but that's not useful at all, that even includes 0

Of course it isnt usefull, but pi is still in its image, but that was never the point.

You can only approximate pi anyways.

>>>/reddit/

We are in sci not Reddit. I think you are lost. SQT officially features the math oracle.

I want to get far in optimization (in real domain).
Currently I have studied real analysis, convex optimization.
I'm thinking about getting to work on some differential geometry books.
Will they help?

bump since other thread hit bump limit

Not in the way you're probably thinking of. Pi is non-algebraic, meaning there is no finite polynomial of algebraic numbers which gives pi. These types of numbers are a special case of irrational numbers—which can't be expressed as fractions—such as [math]\sqrt{2}[/math]. Observe that [math]\sqrt{2}[/math] is algebraic, as it can be expressed as a polynomial of other algebraic numbers, namely, 2 to the 1/2. There is no similar formula which gives pi.

Can I get an engineering masters degree in EE (in europe) if I have a BS in applied math?
please respond

you realize you'd have to look at the website of the universities you want to go to to figure this out right?

thanks for the tips at least

Why do I sometimes see shit like
[math]a_1, a_2, a_3,... a_n[/math]
Shouldn't there be notation for something like this?

that is the notation... for n elements

Here's a stupid question:
What got the get?

I'm currently working through the notation definitions of Understanding Machine Learning by Shwartz and Ben-David, and I'm confused by their set theory.

I actually have two question, but I'll separate them into two posts. My first question is regarding these three fragments of text

"We use uppercase letters to denote matrices, sets, and sequences. The meaning should be clear from the context."

Then,

"As we will see momentarily, the input of a learning algorithm is a sequence of training examples. We denote by [math]z[/math] an
abstract example and by [math]S = z_{1}; : : : ; z_{m}[/math] a sequence of m examples."

The "training examples" being vectors. Later on, they talk about

"Throughout the book, we make use of basic notions from probability. We
denote by D a distribution over some set for example, Z"

If they use uppercase letters to denote structures made up of the lowercase counterpart, this implies that D is over a set of [math]z_{1}; : : : ; z_{m}[/math]. But they already defined a sequence of multiple [math]z[/math] as being S. Why did they now call it Z? I wondered if maybe there's a difference between the complete set, which might be S, and a mere part of it, Z, but this has happened again already on the same page and I'd rather not go on with what feels like speculation.

The second example is here

A sequence of m vectors is denoted by [math]x_{1}; : : : ; x_{m}[/math].
The ith element of [math]x_{t}[/math] is denoted by [math]x_{t,i}[/math].

What do you guys think?

Sorry, those [math]:::[/math] are supposed to be [math]...[/math], I missed them when I was making the LaTex. I should also clarify, in the second example of this problem I don't know why they're using both [math]_{t}[/math] and [math]_{m}[/math] as subscripts for [math]x[/math].

Also no second question, in writing it out I think I understood what they mean.

Anyone know any way to test or check general math knowledge? Like to know things I've missed or forgot.
It could be for particular subjects, but I'm interested in general undergraduate math courses.

How does one calculate a definite integral on the function
[math]f: \mathbb{R} \rightarrow \mathbb(H)[/math]

I meant [math]\mathbb{H}[/math]

what function?

I just wonder if gamma function is defined for [math] \mathbb{H} [/math]

I think he means, any function that turns a real number into a quaternion

why do real riemann zeta functions of x to any power always intersect exactly at (0, -0.5) when the complex zeta function doesnt do anything special at real part -0.5?

integrate the components along 1,i,j and k separately, as you would for any vector-valued function

>why do real riemann zeta functions of x to any power always intersect exactly at (0, -0.5)

...

well zeta(0)=-1/2 so it shouldn't be surprising that your f(0)=g(0)=h(0)=p(0)=zeta(0)=-1/2

i don't know what you mean by the 'complex' zeta, it's the same function, it still satisfies zeta(0)=-1/2

now why the fuck didnt i think of that
thanks anyways

Is there a job where I can apply uni-level math and do programming on a day to day basis?

if you want something cool to read
en.wikipedia.org/wiki/Zeta_function_universality

you could work at maplesoft or any of the other math software development companies