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The first chapter of 3Blue1Brown's Essence of Linear Algebra series, introducing vectors with animated geometric visuals. It begins a series that builds intuition for linear algebra from the basics.
Jim Weirich's RubyConf 2012 talk derives the Y combinator step by step, live-coding in Ruby lambdas. It builds up an understanding of functional programming and lambda calculus from first principles.
3Blue1Brown's first chapter on deep learning explains what neurons and layers are and the math underlying a basic neural network, using handwritten digit recognition with visual animations.
Freya Holmer explains how Bezier curves work, from the helper-line construction to their uses in animation, text rendering and shapes. It uses visuals from her Unity Shapes plugin and was a SoME1 contest winner.
Monty Montgomery of Xiph.org gives real-time demonstrations of sampling, quantization, bit depth and dither using real audio equipment, including both digital analysis tools and vintage analog bench gear. It shows that sampled audio is not stair-stepped and corrects common misconceptions about digital audio.
Freya Holmer's 74-minute video essay on splines, covering Bezier curves, B-splines, derivatives and the different levels of continuity (C0, C1, C2), built with custom animation tools. She notes she did not cover non-uniform splines.
The full-length Numberphile interview with mathematician and hedge fund founder Jim Simons. He discusses his path from mathematics and codebreaking to founding Renaissance Technologies, his use of algorithms in markets, and his philanthropy.
An 88-minute Microsoft Research talk that explains how quantum computers beat classical ones using basic linear algebra, qubits, superposition and gates. It works through the Deutsch oracle problem and ends with entanglement, teleportation and a live demo.
The first lecture of Gilbert Strang's MIT 18.06 Linear Algebra course, covering the geometry of linear equations. It opens a full 35-lecture university course.
3Blue1Brown explains the math and mechanics behind Bitcoin visually: ledgers, digital signatures, proof of work and the blockchain, building up a decentralized payment system from first principles.
A short Dyalog demonstration building Conway's Game of Life in a single line of APL, step by step. It shows how array operations replace loops.
Dyalog
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