mathematica

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.

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.

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.

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.