Calculus made easy

okkayyy...let's just stick to the process and wait for this whole thing to blow over

This is such a classic engineer brain solution to the problem. It just warms my heart.

I also studied chemical engineering, and throughout high school and university that was exactly it. Calculus was a kind of magic, and you just had to learn all the spells.

With this book I finally understood why the derivative of x^2 is 2x.

I read a short paper called "Lockheart's Lament", but I didn't realize he had expanded on it. I might have cried about that one. Thanks for the reccomendations!

He defiantly used it properly, definitely.

Irreverent not irrelevant

"All the, derivatives. True care. Truth brings."

Jargon is the little-death

Somewhere in France someone is getting really excited about learning jargon.

Definitely are.

In a way it makes sense because the industry loves its acronyms and you'll be using them.

On the other hand, I have the ability to search. I'm an IT professional, I will have a computer. Let me let the computer do the lookup. Its the old "you won't have a calculator with you all the time" argument that was dated when my teachers told it to me.

Absolutely! One of the difficulties that I have with my intro courses is working out when to introduce the vocabulary correctly, because it is important to be able to engage with the industry and the literature, but it adds a lot of noise to learning the underlying concepts and some assessments end up losing sight of the concept and go straight to recalling the vocab.

Knowing the terms can help you self-learn, but a textbook glossary could do the same thing.

Yeah, I may be wrong but I think it usually comes down to a very specific kind of precision needed. It's not meant to be hostile, I think, but meant to provide a domain-specific explanation clearly to those who need to interpret it in a specific way. In law, specific jargon infers very specific behaviour, so it's meant to be precise in its own way (not a law major, can't say for sure), but it can seem completely meaningless if you aren't prepped for it.

Same thing in other fields. I had a professor who was very pedantic about {braces} vs [brackets] vs (parentheses), and it seemed totally unnecessary to be so corrective in discussions, but when explaining where things went wrong with a student's work it was vital to be able to quickly differentiate them in their work so they could review the right areas or understand things faster during a lecture later down the line.

But that noise takes longer to teach through, so if it is important, it needs it's own time to learn, and it will make it inaccessible to anyone who didn't get that time to learn and digest it.

I feel like this isn't quite fair to math, most of these can apply to school math (when taught in a very bad way) but not even always there imo.

Its true that math notation generally doesn't give things very descriptive names, but most of the time, depending on where you are learning and what you are learning, symbols for variables/functions do hint at what the object is supposed to be E.g.: When working in linear algebra capital letters (especially A, B, C, D as well as M) are generally Matrices, v, w, u are usually vectors and V, W are vector spaces. Along with conventions that are largely independent of the specific math you are doing, like n, m, k usually being integers, i or j being indices, f and g being functions and x, y, z being unknowns.

Also math statements should be given comments too. But usually this function is served by the text around the equations or the commentary given along side them, so its not a direct part of the symbolic writing itself (unlike comments being a direct part of source code). And when a long symbolic expression isn't broken up or given much commentary that is usually an implicit sign that it should be easy/quick for the reader to understand/derive based on previously learned material.

Finally there's also the Problem with having to manipulate the symbols. In Code you just write it and then the computer has to deal with it (and it doesn't care how verbose you made a variable name). But in math you are generally expected to work with your symbolic expressions and manipulate them. And its very cumbersome to keep having to rewrite multi-letter names every time you manipulate an expression. Additionally math is still generally worked on in paper first, and then transferred into a digital/printed format second, so you can't just copy + paste or rely on auto completion to move long variable names around, like you might when coding.

Very well put.

Functional programming is much more math oriented and I think works well here, as it likes to violate a lot of these rules as a rule. I think it's what makes it so challenging and so obvious for different folks.

You can't except learning the science of abstraction by making it concrete. Exampled are not more than examples and if one field required abstract theory, it is indeed the mathematics.

but teaching math through “how you would implement it in code” seems really interesting.

This is near exactly how I handled learning advanced mathematics back in the late 80s and early 90s. This method takes the abstract and makes it practical, which is what many people really need in order to effectively learn.

I know this is just a simple example but sum() doesn't teach you about the concept of sums. It would have to be something like:

def sum_up(my_list):
    result = 0
    for item in my_list:
        result = result + item
    return result

Then you could run that through a debugger and see how the variables change at every step. That way you can develop an understanding of what's going on there.

calculus made easy?

To be fair, a formula that foreboding should only be approached indirectly, no matter what you're armed with. I recommend sneaking up behind it.

Now it only rest to include Gravity. Well, tomorrow maybe

All of geometry is a cult. The only kind I like. Math cult. Good people. Great orgies.

It’s all triangles.

Sure. They relate different properties of triangles or periodic phenomena.

But can you explain what a "sine" operation is actually doing? Algebra and calculus can pretty much all be explained in terms of basic operations like addition, subtraction, multiplication, and division. But I'm in the same boat as @rekabis@lemmy.ca - trig operations feel like a black box where one number goes in and a different number comes out. I am comfortable using them and understand their patterns, but don't really get them.

I mean, the idea is simple enough to understand. The actual execution is what fucks idiots like me, especially when the exam is full of shit like integral sin(e ^ (x^2 * cos(e)) * tan(sqrt 5x)