Random internet people explaining math better then math teacher

Its got to be a relatively small group who knows enough to understand loops and is also afraid of math symbols.

Not really sure if this answers your question (I agree with you, ultimately), but here’s my experience:

At the college I attended, these sigma/pi expressions weren’t taught until the end of Calculus 2, but I wanted to take an Algorithms class - which had calc 2 as a prerequisite.

I got an exception from my advisor which allowed me to take Algorithms before the pre-req. In my experience, these concepts were easily learned in the context of algorithmic complexity.

Some might be barred from learning important theory in computer science by “brutal” math classes at university. They might find solace in this post which translates sigma into ‘for’

They are the same difficulty level, sure, but that's like saying f(x) and f'(x) are at the same difficulty level. Coming from one to the other in a process is the difficult part, and the code offers instructions to follow this process.

I'm a subscriber to her YouTube(one of my favourite videos of hers) and she has a bunch of videos aimed at helping game developers learn the maths concepts they need for making games, so her audience is mostly people with a coding background, I'm guessing.

So it's less that code is simpler than math notation, more that the maths notation looks scary to people without a maths background, but here's a link to a different complex symbolic abstraction that you might already know

I forget what the symbols mean but I'm sure not gonna forget what a for loop means

Math notation is just terrible in general because a lot of it is shorthand made up by someone who likes single-letter variables. A symbol you can't type, something above, something below.

A for loop is clear and descriptive.
Or if you're feeling fancy, you could go functional with reduce(add, range(0, 5), 0).

It's a Meme? Do you ask the same under other memes as well "What is the reason?"

Turning 35 in a month and I've just started learning maths again after being afraid of it because of a similar situation to yours.

Sorry you were put through that. Aggressions are no place for learning

My family and school were god awful at teaching. It was all forced (rote memorisation) learning and not me actually learning. I needed things taught slowly and broken down. I have wanted to learn the more advanced technical maths long ago, but now I am an adult and need to find a safe, quite and gentle environment where i can

anybody reading this, please do not give suggestions or advice in replies. thank you.

i completely agree. this sentiment was echoed pretty well in a (nontechnical and accessible) paper i read a few years ago. he says the current approach is like forcing people to learn music, but only teaching them how to read sheet music and not letting them touch any instruments. it hides the creativity and problem-solving of the discipline and reduces it to memorizing formulas.

Idk man I've been doing my Cal 3 and 4 this semester and fuck me it's hard. Yeah sure it's cool sometimes but wrapping my head around it and often trying to think about things geometrically hurts. I sat there for a full hour trying to figure out why I couldn't picture the equation I was trying to take a triple integral of only to realize it's 4 dimensional and I almost cried

Im sorry you had awful teachers, but not all of them are bad. I had amazing teachers that were very worried for the students to learn. In contrast I had very shitty classmates that just didn't care and would blame the teachers for their laziness.

It's not about being frightened, it's just that i know only a handful (mostly esoteric) languages with worse syntax.

Fear fear fear. The same old, actually hollow from the inside, villian that bugs me everywhere

I liked this so much I tried to find more. A few seconds googling turned up a lot, but this is the first hit: https://amitness.com/2019/08/math-for-programmers/

You are right the symbols weren't created so students can learn them, but students have to learn them at one point and for me personally, a student that knows how to program, figuring out that these symbols kind of represent for loops made them easier to understand.

Quaternions are the closest you'll ever get to lovecraftian horror in real life.

one specific programming language

I think you'd be hard pressed to find someone with any sort of programming background, even just as a hobbyist, who doesn't understand that for loop notation, whether or not they know the specific language it's from. (I couldn't even tell you what specific language that's from, because that notation matches so many different ones.)

I have a 15 year old son; he definitely has not seen summation in math classes yet, but he has far more than enough programming experience (even just from school) to understand the for loop.

I think the concept of a for loop is easier to learn, even for non-programmers, as biased as I may be.

not to resurrect a dead thread but yeah anyone remotely into computer science should be able to read pseudo code notation. it being variable in how people write it is part of what makes it a nice tool. this code could work in many contexts in many languages. it’s pretty precise for pseudo code, even.

That does not help. What does non-discrete mean?

if you take a modular approach and allow different measures to be used, it also lets the integral sign be a discrete for-loop

Theyarethesame.png

Came here to say the same!

No it's not harder to grasp, just less concise. Summation and Product notation exist for the same reason we don't say "a discernible but subtle level of humidity" and just use "moist" instead - it's more convenient. People can be taught to readily understand "moist" or the summation notation. It's much harder to teach people to read the longer notation more quickly.

Meme is gud, title is stupid

This thread makes me sad as fuck.

Obviously you can integrate using Sigma notation, if it’s a definite integral.

Also the viewers are actively looking for that content

The sigma sign shows up as "sum" quite a bit but I didn't know about the for-loop thing.

I was into coding (javascript) but nope they are unwilling to find creative new ways to help teach people, gotta be a nonseical "one size fits all"

The hardest thing for me about math was the symbols. Greek, Roman, English.

Once you get past that, the numbers are easy.

Her videos about splines are god-tier

This isn't even god tier, it's just that more people are familiar with the basics of programming than higher level math, which is honestly a good thing.

What's wrong with list comprehensions? Do I just have Stockholm Syndrome at this point?

I would skip the square brackets and just use a generator expression: sum(3*n for n in range(5)).

Yes, the classic readability of c style for loops.

How about some Haskell

let numbers = [1, 2, 3, 4, 5] let sumOfNumbers = sum numbers

I don't think you can use python list comprehensions in this case, since you don't want a new list, but rather reduce it to a single value.

It's about math teachers, not English teachers.

and then you grow a bit older and realize that coding has nothing to do with math, instead it's got everything to do with problem solving.

Wait until you realize what math is all about

Coding has nothing to do with math yet the entire basis of computing and programming is Boolean algebra.

coding has nothing to do with math

A monad is just a monoid in the category of endofunctors, what's the problem?

I mean, coding does have to do with math, it's usually just different notation. i = i + 1 in math notation is just i := i + 1.

Not knowing about Splines before

Feeling like understanding Splines afterwards 🥰

She has a youtube channel

I've only watched a couple of her videos--on Splines and Bezier curves--and her explanations and animations were intuitive and beautiful to watch, but ultimately her target audience is game devs... So the answer to your question is "technically yes*"

*it's with the intent of learning to code the math

I don't know anything about the original post author, but product notation is the same as summation notation except that instead of adding each new term to the running total, you're multiplying each new term. You don't have to know programming to see from the code samples that the only difference in the code is += vs *= (well, maybe it would help to know that * means multiply; I honestly dont rember how common-knowledge that is).

I think it would be much better to write it in another language, but here's another way to do the second one (this is on Visual Basic):

Dim n as long
Dim product as long
Product = 1

For n = 1 to 4
Product = product * 2 * n
Next n

Sort of; a lot of what she does is computer graphics, which just happens to be applications of math she explains. There is still code, but sometimes the "code" is a flow graph in Unreal Engine or Blender.

Nah, look at the implementation above:

n <= 4

Means it’s inclusive.

You’re probably referring to some other implementation that doesn’t involve such fine control, like Python where range(4) means [0 1 2 3]

i thought this was pretty weird too when i found out about it. i’m not entirely sure why it’s done this way but i think it has to do with conventions on where to start indexing. most programming languages start their indexing at 0 while much of the time in math the indexing starts at 1, so i=0 to n-1 becomes i=1 to n.

I think this is pretty much the imperative equivalent of foldl (\acc i -> acc + 3*i) 0 [1..4].

Can you explain this out a bit more? I'm a self-taught programmer, of sorts, and I'm not quite getting this...

Definitely, although I’m sure that under the hood it’s all the same. Some (albeit high-level) languages also support a sum function that takes a generator as an input, which seems pretty close to this math notation.

while

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Sounds as a conspiracy theory

there is no reason for a (non-foreach) for loop to be any more or less finite than a while loop.

for (a; b; c)
{
  d;
}

is just syntactic sugar for

{
  a;
  while (b)
  {
    d;
    c;
  }
}

in most or all languages with c-like syntax.

for (i=0; true; i++)

There's nothing special about a generic for loop (at least in C-like languages). There's no reason you couldn't do something like for (i = 0; true; i++) to make it infinite. Some languages even support an infinite list generator syntax like for i in [0..] (e.g. it lazily generates 0, then 1, then 2, etc. on each iteration) so you can use a for-each style loop to iterate infinitely.

Now, whether or not you should do such things is another question entirely. I won't pretend there aren't any instances where it's useful, but most of the time you're better off with a different structure.

I wanna see how you get a while loop to actually go to infinity. I'll wait...

on second thought, no I won't.