What do you wish more people knew about?

submitted by panel30 from self.AskSaidIt

sorted by:
top
newinsightfulfun
you are viewing a single comment's thread.

view the rest of the comments →

[–][deleted] 2 insightful - 1 fun2 insightful - 0 fun3 insightful - 1 fun -  (5 children)

Integral equations.

Could stop a lot of wars from happening, even without putting pointwise convergence into these.

Integrals basically are "easy" to understand, while limites and differentials are quite "hard", even as a concept.

[–]panel30[S] 1 insightful - 1 fun1 insightful - 0 fun2 insightful - 1 fun -  (4 children)

is there a good starter or summary for this, and how it would help with avoiding wars?

[–][deleted] 2 insightful - 1 fun2 insightful - 0 fun3 insightful - 1 fun -  (3 children)

Remember summation from elementary school. Usually, when you sum something. , you do it with discrete values. Seemingly easy, but not well understood since applications of these arithmetic only help in everyday-life when using countable values: like money, apples or the world-famous watermelons. Since many text-book examples are quite out of touch with reality and most curricula soon after that focus on solving equations, the concept of functions themselves seldom pops up during middle-school education.

Integration is generalized summation of continuous functions, but since functions are only seldom done in middle-school, it is kind of hard to dive more deep into this topic.

Facts are:

  • almost all mathematical operations itself are functions
  • integration has weak requirements to be applicable on some function
  • you need at least some knowledge about sets to be able to comprehend, why integration is mightier than differentiation.

So: From my personal pov, it is taught the wrong way around. But I also am able to admit, that not every student is eligible to look at this, like it "really" is.

My school-days are mostly done, but i know from firsthand that there are people out there, being able to comprehend concepts "way-beyond" understanding.

Like summation over dimensions or tensors itself, which explain most.

Integration only needs weak assumptions (from a mathematical-pov) to be to put to actual useful purposes.

While number-theory itself, the same as "standard"-algebra, needs a lot of them, especially, when questioned.

I just wish, I learned about integration a lot earlier. That's it.

[–]panel30[S] 1 insightful - 1 fun1 insightful - 0 fun2 insightful - 1 fun -  (2 children)

Thank you for coming back to reply, it was really nice of you to!

I don't feel like I really understand a whole lot about math stuff. I wasn't taught about calculus stuff until high school and college. I was taught some but I don't think I understand a whole lot, like what it means, what it's useful for. I think I understand maybe basic stuff, like how long a package of food will last if I eat a certain amount per day. I think it maybe makes more sense to me if I understand it on a more practical level, like I understand what I'm trying to use the numbers to help me with.

I tried to find a wiki article for integration, is this the concept you mean? It has a section that looks like it's about how this concept can be useful. Maybe sadly, I don't think I've ever tried to use something like this outside of a math classroom. It sounds like this concept seems really valuable though. What makes it so valuable? If it can contribute to avoiding wars that sounds like something good to understand if possible.

[–][deleted] 2 insightful - 1 fun2 insightful - 0 fun3 insightful - 1 fun -  (1 child)

As I tried to explain: Understanding functions as a concept ain't "easy" but mighty nonetheless.

So even nowadays, I wouldn't put calculus the same as most mathematics on middle-school curricula.

e.g.: See, addition itself is a function.(Even more in fact, it is an operator in a mathematical sense: So once, we have associativity (left or right, this is a simple decision by definition) "out of our way", we could dive into, how to sum up most curves, values and basically everything continuous, which 99.5% of useful appliances in fact are because continuity is a very weak assumption about a function. (Especially once you got some corollaries in your arsenal, that are as easy to prove, as to understand)

When compared with differentiability, which usually is taught first, it is in fact quite easy to understand, but kind of hard to grasp, once you look at applications. Differentiability itself nonetheless is kind of a "hard" assumption, that puts about 80% of "real" applications out of its focus, as long as you have to apply it on a middle-school or undergrad-level.

So, if you want to hear my unsolicited opinion:

I'd divide math-classes in middle-school, about 9th grade.

Those "who want" and those "who don't" and I'd go easy on both of these groups.

[–]panel30[S] 2 insightful - 1 fun2 insightful - 0 fun3 insightful - 1 fun -  (0 children)

unsolicited opinion

I solicited your opinion! Thank you for sharing it.

I don't understand a whole lot about math right now, but I think maybe I understand a little bit about what you're trying to explain. That changing the way these concepts are taught could help interested students learn them better. Maybe if somebody else with a background in math education reads this later they will be able to understand better. Or maybe I'll understand better later if I look back on this after exploring math more at some point, if I do that.

I wanted to understand why you feel this would be so valuable. Could stop a lot of wars from happening sounds really good! Unless I misunderstood what you meant. I think I don't have a good grasp of how math stuff generally can be a big help.