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I'm going to say a strong no to that. The programming parts are fine, but on a quick skim, the mathematics is written in a way they will likely find very confu
by seanhunter 2y ago
I'm going to say a strong no to that. The programming parts are fine, but on a quick skim, the mathematics is written in a way they will likely find very confusing unless they already know calculus and leave them thinking they are bad at maths whereas actually the author is just not really trying to explain the maths to someone who doesn't already know it.
For example look at the diagram on[1]. It has unlabled axes of a shaded L-shaped box with a curve going through it and then it is followed by a bunch of equations where he derives the formula for integration by parts using a set of parametric equations with multiple substitutions etc. I know what integration by parts is and how it works really well. This is possibly the most confusing way you could possibly derive the formula and/or explain it, and this diagram really adds absolutely nothing unless you already know and understand the concept. If you have seen the exceptional diagrams and illustrations and clarity of explanation in a book like "Calculus" by James Stewart the contrast is so stark it really jumps out.
The normal way of explaining integration by parts starts the way the author does (with the product rule for derivitives) and shows a few examples of taking the derivitive of things using the product rule so you get an intuition for what the form of the resulting antiderivitive looks like. You then go through the derivation of the formula for integration by parts by using the product rule for derivitives, integrating both sides and splitting the resulting integral[2]. Its very clear and easy to follow. And if they want to actually help the student to do this they teach something like the tabular/"DI" method so the student isn't tearing their hair out getting the signs mixed up when integrating by parts multiple times.
[1] https://jverzani.github.io/CalculusWithJuliaNotes.jl/integrals/integration_by_parts.html https://jverzani.github.io/CalculusWithJuliaNotes.jl/integra...
[2] My own notes on this derivation which I took when learning this are here. Note that this isn't me really trying to explain it to a beginner - it's just my personal notes but it's still a lot easier to follow than the example given https://publish.obsidian.md/uncarved/3+Resources/Public/Integration+by+parts https://publish.obsidian.md/uncarved/3+Resources/Public/Inte...
- barrenko 2y agoHi sean, we have the same end-goal possibly.
- seanhunter 2y agoThat's awesome. Hope your studies are going well and you achieve what you are hoping for. I'm finding it fantastic so far I have to say. Super-interesting and always more to discover.
- barrenko 2y agoDefinitely, good luck!
- ultrasounder 2y agoWow! My secret plan is also to grok the math behind the Transformer while helping my HSchooler out. And I think your resource is super good.
- seanhunter 2y agoThat's awesome. Very happy you found it useful. Bear in mind of course that while I do try to get it right, there will be errors etc. If you find it helpful there is a lot more to come - I have a bunch more notes that I need to edit and make new diagrams for but I should be publishing soonish, and then I am learning all the time. Please let me know if there's anything that you found confusing/hard to understand[1] or if you see any errors. [1] because that indicates I don't understand it well enough myself and I need to work on it more and then fix the note.