math

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.

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.

Part 1 of a lecture by physicist Albert Bartlett on the exponential function and its consequences for population growth, resource use and energy. It argues that steady growth rates quickly lead to enormous quantities.

A short clip from Carl Sagan's Cosmos in which he explains how Eratosthenes measured the circumference of the Earth using shadows in two Egyptian cities. It is a clear, visual account of an ancient scientific feat.

A segment from Carl Sagan's original Cosmos explaining the fourth spatial dimension through analogy with a two-dimensional world and shadow projection.

A short animation reconstructing a planet's looping orbit using Ptolemy's epicycles and deferents, with the epicycles tracing out the face of Homer Simpson. It shows how enough circles can reproduce nearly any shape.

The introductory lecture of Stephen Boyd's Stanford Convex Optimization I course (EE 364A). It outlines convex sets, functions and problems, and the course's coverage of least-squares, linear and semidefinite programming, duality and interior-point methods.

The first lecture of Andrew Ng's Stanford CS229 Machine Learning course, giving an overview of the course. It introduces supervised and unsupervised learning, learning theory and reinforcement learning.

An excerpt from the 1983 BBC series Fun to Imagine in which Richard Feynman describes how he and a mathematician friend counted in their heads in different ways, one verbally and one visually. It shows that people can reach the same goal through quite different mental methods.

The first lecture of Leonard Susskind's Stanford Continuing Studies course on modern physics, beginning with classical mechanics. It is the start of a six-quarter sequence on the theoretical foundations of physics.

A score-following video of Iannis Xenakis's 1950s orchestral piece Metastasis, showing his graphic, mathematically derived notation as the music plays. It is a landmark of post-war modernist composition.

Second half of a demonstration of the 1982 Xerox Star user interface. It shows how the Star differed from the later Lisa and Mac interfaces, with strengths in networking and printing and little direct manipulation.