BetterExplained

This isn't answering your question but it seems others are and it's still good to say:

Spend some time learning maths.

I don't mean to say you shouldn't continue advancing in programming and I understand that you're in elementary school which is supposedly teaching you maths on a standard track but you are clearly a self-starter and would do well to advance independently.

Schools teach maths poorly. They generally focus on rote mechanics at a slow pace with very little to keep the interest of anyone and this is a big reason people (a) think they are bad at maths and (b) hate maths.

My elementary school barely advanced beyond arithmetic but, thanks in large part to programming, I independently advanced much faster than that. I still regret not pushing myself to go further but at least I got to spend most of my K-12 education ahead of the mathematics track.

I have no idea where you are in mathematics since "elementary school" is very broad, but BetterExplained (http://betterexplained.com/) is a great place to get some started. It can even give you a better grasp of addition and subtraction, let alone more advanced topics.

Summer of 1980, going into my senior year in high school, I mentioned I'd be taking Calculus next year to a co-worker a couple years older than I. He said he had the best book in the world on Calculus, and he loaned me his copy of Silvanus P Thompson's Calculus made easy. I thoroughly enjoyed that book, benefited from its intuitive explanations, and forever appreciated his recommendation.

If I may similarly influence anyone here, for themselves or someone they know, to read Calculus made easy to supplement their calculus coursework, I will be happy to have paid the favor forward in some small way.

By the way, Kalid Azad may be our modern day Silvanus P Thompson. And he has better tools[1], which he wields masterfully, than just pen and paper. Recommended too.

[1] https://betterexplained.com/

Two quick things I can recommend without hesitation, which focus on an intuitive understanding of concepts:

1. Essence of Linear Algebra mini-series - https://m.youtube.com/watch?v=kjBOesZCoqc

2. Better Explained website - https://betterexplained.com

YouTube has a lot of high quality math content, it definitely helped through university. It's also worth mentioning the Stanford U courses.

The main takeaway I have for you is learn the concepts intuitively first, then spend the time to play around with them on paper until they sink in. Some things will be easy, some will be frustrating, much like programming you will walk away from a frustrating problem and have an epiphany while doing something completely different.

All the best and have fun!

Great comment. I think the difficulty in defining what makes a good teacher is as difficult as what defines a good parent. In rough terms, I think a good parent means someone who raises a compassionate, honest child.

Similarly, a good teacher / education system is one that raises inquisitive students. I've long believed it's better to graduate kids who love algebra vs. those that know and hate calculus. Because in 10 years, the ones who loved algebra will probably end up loving calculus too (instead of developing a lifelong aversion to math, and learning in general).

So, my meta-reply would be to search for a system that tries to generate genuine interest in learning. (Plug: I try to blog in this manner at http://betterexplained.com).

I'd say my goal is not so much about avoiding math but more about learning intuition-first rather than equations-first. Top-down vs. bottom-up, maybe. Most of material that I've encountered about math-heavy stuff tends to do the latter.

I imagine there are many people who're great at picking apart an equation and deriving things from first principles; but for me, I find it more manageable to get the big picture first, visualize what's going on, and then finally learn the math behind it. So far the DSP Guide book is doing a great job of presenting things that way.

Another good example of this kind of style is https://betterexplained.com/ (some of their articles are great companions to these DSP topics actually!)

I'll go with an example to demonstrate why that's not always enough. Many people are quite keen to know what this (for example) is actually doing:

float InvSqrt(float x){ float xhalf = 0.5f * x; int i = *(int*)&x; i = 0x5f3759df - (i >> 1); x = *(float*)&i; x = x*(1.5f - xhalf*x*x); return x; } From https://betterexplained.com/articles/understanding-quakes-fast-inverse-square-root/

In my case I don't have a huge amount of time to chase down every rabbit hole, but I'd love to accelerate intuition for LLM's. Multiple points of intuition or comparison really help. I'm also not a python expert - what you see and what I see from a line of code will be quite different.