Wow, this is by far the clearest I’ve ever seen this explained.

Once you get to integrals these become slightly less scary. Slightly.

While I acknowledhe that I had some pretty awful math teachers, I would like to add that explaining math concepts in an edited video that you could spend a lot of time making has different demands than babysitting/teaching 30+ students at different levels multiple times a day with little prep time.

Ok now try infinite for loops

freya is not a random internet people

People who are arguing that one way of expressing these concepts is easier to learn/understand than the other are missing the whole point. Mathematical notation was not designed to teach students how to do math or explain how to design algorithms. It was invented to communicate precise, abstract ideas concisely between mathematicians who already understand what the symbols mean.

Mathematicians require a notation that has the flexibility to manipulate mathematical objects/symbols in a way that naturally emphasizes their properties and relationships. Often they don’t even care whether the objects they’re studying are even computable or have a numerical representation. They just need them to have certain properties so that they can be manipulated appropriately.

Discrete sums are a rare example of when the mathematical notation overlaps with the description of an algorithm for computing its value (and the overlap is not even complete; infinite sums are easily represented in math notation but are practically uncomputable when implemented naively). Every other advanced mathematical concept puts a premium on ease of symbol manipulation over computability: integrals, derivatives, matrix multiplication, abstract algebra, etc.

TL;DR math notation is complex because its intended audience is people who already understand it, want maximum flexibility of symbol manipulation, and historically didn’t really care about practical computation.

I have no idea what these math things are but I understand the code perfectly lol

wow I wish we learned this kind of stuff in school

Freya is a really good programming maths communicator so it doesn’t surprise me

Ok but this is a bit of an unfair comparison given that Freya is pretty god tier at actually explaining math things.

Fuck! Im 40 and this is the first time I understand the sigma sign!! Thank you!

Couldnt they just show this to me at 7th grade or something when i already learned pascal?

I think gamedev or I guess graphics programming, visualize maths pretty well. I literally quit high school because I could never make any progress in several areas, including math class. But once I read/watch more about gamedev, programming, graphics programming on my own, I got to understand many mathematical terminologies better than I have ever been taught in any school.

test

Maybe it’s an unpopular opinion, but I assume students complaining about their teachers being bad because they are not as good as some internet people are usually pricks who aren’t really into learning and are more likely looking for an excuse not to learn. Those internet people aren’t going to give you an exam on what you actually pick up, nor are they going to have the data to see what the class is doing poor on and needs to learn.

Most of the shit you learn in school isn’t going to be used in real life, but that’s not the point of it. It is essentially a gym for your brain, so dissing your personal trainer just because there are athletes with advice that might be better for you is not a good look. This example really is only useful for people who have learned programming before math, and knows the differences and limits of the programming.

Sorta not really related but Freya’s video on splines (“The Continuity of Splines”) is a virtually perfect resource if you’re interested in learning about… well… splines.