(Here the `take 30` just stops the computer from trying to give us all infinity of the results!) For the first element, it just subtracts 0, so it doesn't do anything. I'm going to teach you one list-operator, it's a function which subtracts each number in a sequence from the one that comes before it in that sequence. We might number these sequences and then write down rules for them for example we might write $x_n = (n + 1) ^2$ to denote the sequence of square numbers starting with 1, `map (^2) ` if you're not familiar with these then we'll write out the first five as: A sequence starts with a value, and then there is another value, and so on, and so on. We're going to start thinking of infinite sequences. I'd love to chat more if you like! Just ping me at often thought that you could give people a huge leg up on calculus if you could first explain to them the discrete calculus, possibly with a programming language like Haskell. (Why are we so enamored with video? We can't fix our inevitable mistakes!) As long as we're dealing with text, it's infinitely editable and updatable. In my experience it's the other way around.)įor scaling, getting the first few right should hopefully make a template others can take and run with. (The hypothetical student should study limits for weeks, then derivatives, then integrals. "imagining" what a hypothetical student needs. I'd prefer to organically grow the guide out of our shared experience vs. (I don't have one built yet for the Fourier Transform.) Make it easy to contribute an insight.Ĥ) Weave the final result into an honest, realistic guide from curiosity to mastery. My idea:ġ) Have a topic like the Fourier Transformģ) Collect feedback, examples, diagrams, etc. to help aggregate this, but it was over-engineering. Previously I'd tried to make apps, forums, etc. * Generic, boring, academic "tone of voice" (kills the fun for me) Even excellent contributors have to fight to get changes in. * Too much detail for beginners (to be fair, it's a reference, not a tutorial) I've been kicking around ideas for an "intuitive wikipedia", guides explicitly (and realistically) designed to get you from curiosity to mastery. For me, investing a few hours of exploration before the formalities is well worth it. Ultimately, we have to acknowledge the approach that helps us. Not if I was honest about my motivations. Just like learning music, I'd listen to the song, then clap along to it, then play a few chords along with the band, then learn a bit of music notation, and then practice playing it. What would a learning plan look like, assuming limited motivation, a need for genuine understanding, and goal of starting with appreciation and moving to proficiency? I decided to Elon Musk It™ and reason from first principles ( ). (Yes, I could memorize rules but could I visualize the product and quotient rule?) I had similar confusions despite years of engineering classes, I didn't build an intuition for Calculus until a decade later. Kalid from BetterExplained here, glad you like it!
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