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Wait, That’s It?

Wait, That’s It?

The companion to the YouTube channel: maths and deep learning, one idea an episode. Each episode has a page here, and each Deep Dive’s page has demos to drag, the questions students ask, and practice problems with answers.

Calculus

Big Idea 1The Derivative: Nobody Measured Usain Bolt's Top SpeedSpeed at one moment is the slope you get when you zoom in until the curve looks straight. That slope is the derivative.
Deep Dive 1.1The Limit: Is the Slope 6, or Nothing?The derivative isn't the slope of any chord; it's the number the chord slopes head for, found by doing the algebra while the gap is still not zero.
Deep Dive 1.2The Power Rule: Why the Power Comes DownMultiply out the rise, (x + h)ⁿ − xⁿ, and every term but one carries an extra h; the limit keeps only n·xⁿ⁻¹.

Big Idea 2Limits: Half Your Morning Coffee Is Still in You at LunchA limit is the exact number something closes in on. Name any tolerance, however small, and from some point on it stays closer than that. Your morning peaks close in on a hair over 1.037 cups and never pass it.

Deep Learning

Big Idea 2ReLU: The AI That Beat a Go Legend Ran on One RuleA neural network is a line with bends. Each neuron adds one bend with one rule (if it's negative, make it zero), and with enough bends the line can follow any curve.