tuition

A 10-minute 3Blue1Brown chapter explaining the determinant as the factor by which a linear transformation scales area or volume. It builds the idea geometrically with animations before any formulas.

3Blue1Brown walks through a very hard Putnam competition problem and its elegant solution, emphasizing the visual intuition and the thought process behind solving it.

3Blue1Brown's chapter on eigenvectors and eigenvalues in the Essence of Linear Algebra series. It builds a visual intuition for what they mean, why an eigenbasis is useful, and ends with a puzzle.

Cody's Lab builds a 200-billionth-scale model to show how far away the nearest stars are, using parallax and light speed. A short astronomy explainer on interstellar distances.

A short 3Blue1Brown video explaining Euler's formula e^(i*pi) = -1 through dynamics, treating velocity as the thing that moves a point to a new position. It builds geometric intuition for why an exponent with i produces rotation.

2swap explains how he solved the Klotski sliding-block puzzle by mapping its full state space as a graph and visualizing it. The video includes footage of the Guinness world-record solve and links to an interactive graph.

PBS Infinite Series explains how Shor's algorithm lets a quantum computer break RSA encryption, building on earlier episodes about cryptography and the math of quantum computers. It works through the idea step by step.

Matt Parker on Numberphile explains the strange properties of spheres in higher dimensions, such as how they poke out of their bounding boxes. It uses Pythagoras to build intuition for 4D and beyond.

3Blue1Brown's chapter 4 on deep learning gives a more formal, symbol-based account of backpropagation calculus, connecting the intuition from the previous chapter to the math found in textbooks and code.