/sci/ - Science & Math

Very important.

If you can algebraically solve a problem/represent a situation, but have no meaning for the numbers, then you are trapped by that singular representation and cannot even properly apply each of the missing concepts.

Also, you're just doing finances with higher equations, so...

>>4126795

How do you go about studying math like this?

I'd like to understand the problems I'm solving to the point where if I completely forgot the formulae I could figure out a method for solving it myself.

>>4126801

Try moving between representations of the problem.

> Graphical
> Algebraic
> Tabular/Numerical
> Conceptual
> Verbal

>>4126801
Study the derivation of the algorithm that leads to the solution rather than the algorithm itself

>>4126809

How? Just look for proofs or what?

>My question is how important is it to intuitively understand every step of every problem you do?
Get more sleep. This ONLY ever happens to me when I'm too tired during lecture to grasp the concept when its introduced.

>>4126790
not important at all
you just need to know the logic is correct, ie, your inference is valid
mathematicians wouldn't get very far if they constrained themselves to the 'intuitive'

I would say not very.
In all honesty, if you work with something simple enough long enough, you'll eventually begin to understand the underlying concepts. Whether you want to or not.
Until that happens, just plug and chug.

>>4126834
Knowing the history of the problem helps. If you can get into the mindset of Newton or whoever who developed the method for solving the problem, you can obtain a much stronger grasp on what the problem and the solution actually mean. Then you can compare that solution to more sophisticated solutions that might have developed when, for example, computers were developed and understand why one solution is more useful than the other.

>>4126857

So then math should just be remembering formulas?

>>4126877

Good advice.

>>4126790
you're a robot.

well what do you mean by intuition? Unless you're working on equations whose fundamental constants / operators have physical meaning (applying math to science), then the underpinnings of math are really meant to be abstract and capable of describing a highly versatile field of phenomena.

I wouldn't worry; just keep studying your maths OP

>>4126897

Thanks, this satisfies my question. I'll go do that.

>>4126892

If I was a robot I wouldn't care.

>>4126857
follow-up: existence proofs
do irrationals <span class="math">a[/spoiler], <span class="math">b[/spoiler] exist where <span class="math">a^b[/spoiler] is rational? yes!
proof: <span class="math">\sqrt{2}[/spoiler] is irrational. if <span class="math">\sqrt{2}^{\sqrt{2}}[/spoiler] is irrational, then<div class="math">\left(\sqrt{2}^{\sqrt{2}}\right)^{\sqrt{2}} = \sqrt{2}^{\sqrt{2} \sqrt{2}} = \sqrt{2}^2 = 2</div>is rational. thus, <span class="math">\sqrt{2}^{\sqrt{2}}[/spoiler] is rational or <span class="math">\sqrt{2}^{\sqrt{2}}[/spoiler] is irrational and <span class="math">\left(\sqrt{2}^{\sqrt{2}}\right)^{\sqrt{2}}[/spoiler] is rational. either way, irrationals <span class="math">a[/spoiler], <span class="math">b[/spoiler] exist where <span class="math">a^b[/spoiler] is rational. QED
notice we don't know <span class="math">\sqrt{2}^{\sqrt{2}}[/spoiler] is rational or irrational, yet we still know the conclusion is true. intuition doesn't matter

>>4126888
>So then math should just be remembering formulas?
no, it's a competent command of logic. I try to remember as little as possible and infer everything possible

>>4126946
>no, it's a competent command of logic. I try to remember as little as possible and infer everything possible

Really?
Do you derive the Peano axioms anytime you have to do basic math?
Do you derive the power, product, quotient, and chain rules before you take a derivative?
Do you prove the pythagorean theorem and the cosine law each time you do something with a triangle?
Do you independently rediscover Euclidean geometry each time you need to approximate something on earth?
Do you rediscover logarithms when needing to add trig functions?

>>4126975
>as little as possible
really
if I use a
>rule
>logarithm
>trigonometry
>geometry
then I've proved it once before, seen the proof, or can look it up. not that hard.
no one proves axioms

>>4126975
>Do you derive the Peano axioms anytime you have to do basic math?

Not important at all. It's just important to know what kind of equations are solvable.

>>4126975
>derive
>axiom

>>4126975
yes