211–220 of 268 posts
For anyone coming back to math I can't recommend enough the book "Journey through Genius: The Great Theorems of Mathematics". It's interesting how much of algebra came originally from geometry and the path to developing these fields makes it so much more intriguing / understandable vs just learning math to learn math.
If OP still wants to learn the mathematical foundation of transformers, I built a free alternative learning tool: https://afaik.io/nebula?mode=nebula&category=blueprint&id=ed... It's also based on an underlying knowledge graph, connecting concepts across various subjects like maths, machine learning, physics, etc. You can check the graph for transformer here: https://afaik.io/nebula?category=brickset&id=VLlOnZLl&mode…
I find the concept of "underlying knowledge graph" interesting. What does it mean? I assume it means such a graph connects the topics together as "pre-requisites". To understand A you need to already understand B and C, and to understand B you need to understand D and ... etc. But the thing about such a graph is that really it must be a tree, not just a directed graph. Why? Because there cannot be cycles in it. If to…
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Hi, I'm Alex, curriculum director at Math Academy. Thanks for your comments. In response to the things you'd like us to have: "ability to skip lessons" - we plan on introducing "mini-diagnostics" sometime soon, hopefully within the next few months. This will allow students to "place out" of certain content they know. The primary diagnostic assessment will have done most of the grunt work here, but mini-diagnostics ca…
> "a reference page to track unlocked material" If this is implemented to resemble an "upgrade tree" found in games, I bet it could work as an extra motivator for the kid audiences.
Tangential, but: the notes that this post refers to are probably not the best way to learn how transformers work. If you want mathematical precision, those notes are based on this paper from DeepMind: https://arxiv.org/abs/2207.09238 The paper provides mathematically precise definitions of all the parts of a transformers, though it's showing its age (ha!) in that it doesn't include some formalizations that are common…
>> The ‘Foundation Series‘ is what I’m starting with. It’s for adults to help streamline learning (it skips the stuff that kids need, but adults don’t) and work back up through college-level math relatively quickly (emphasis on relatively ). I'm curious to know what 'stuff' he's referring to. And what about it makes it such that kids need it but adults don't. And if that's true, are we SURE kids need it? I had horrib…
OP here. My understanding is that it's the stuff kids are tested on in school to pass (like standardized tests), but not necessarily needed for an adult to meet their learning goals.
Like, if your kid was using it they'd take take the grade level courses, but if you wanted to work up to Math for Machine Learning like I am you'd take the Foundation courses, which are streamlined.
One cool thing I like that I shared a screenshot of in the post is the knowledge graph that shows all the topics and how they are connected to make all of the lessons feel more purposeful. And if you get stuck somewhere there's an easy way to brush up on past lessons (dependencies).
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> it must be a tree, not just a directed graph It may be a tree. But it must be a DAG (directed acyclic graph).
Heh knowledge graphs sometimes don’t feel acyclic, at least not to me anyway. Sometimes I’m stuck bouncing back and forth :)
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I find the concept of "underlying knowledge graph" interesting. What does it mean? I assume it means such a graph connects the topics together as "pre-requisites". To understand A you need to already understand B and C, and to understand B you need to understand D and ... etc. But the thing about such a graph is that really it must be a tree, not just a directed graph. Why? Because there cannot be cycles in it. If to…
> it must be a tree, not just a directed graph It may be a tree. But it must be a DAG (directed acyclic graph).
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> set her nose to the grindstone Worth calling out the key observation: it takes practice, and lots of it (for most people, anyway) to get good at math. Just reading about it does zilch.
please tell me that how can I get question for practice in math of university level? most of textbook even don't contain answers of practice in the book...
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> set her nose to the grindstone Worth calling out the key observation: it takes practice, and lots of it (for most people, anyway) to get good at math. Just reading about it does zilch.
OP described a specific type of practice to get good test grades using 'Anki cards' . Standardized tests test for grinding and dedication not expertise or 'getting good'.
Sometimes, you just know a thing or don't, and for me, spaced repetition cards helped a ton with the static things you just have to memorize (or derive). Knowing definitions is important—you're absolutely right that it's just one piece of the puzzle though.
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This is just not true. Reading is necessary but hardly about as important. If you are lucky and get a good text, the exercises guide you to "invent" the important parts of the theory. Otherwise its just definitions and theorems, and its up to you to make your own examples to gain an intuition, which to be fair is closer to life outside of a classroom.
Could you elaborate on this please: "the exercises guide you to "invent" the important parts of the theory." BTW: I think time not doing exercises is just as important; it's when your mind tries to piece together the data. Coincidentally(?) time resting, after physically exercising, is when your muscles strengthen.