algorithms

Erik Demaine's MIT 6.006 lecture introducing dynamic programming through Fibonacci numbers and shortest paths. It covers memoization, subproblems and optimal substructure.

Donald Knuth's 2017 Christmas Tree Lecture at Stanford about a combinatorial geometry problem whose computed numbers matched a striking formula. He tells the story of the conjecture and its sequel.

Erik Demaine's MIT 6.851 Advanced Data Structures lecture introducing succinct data structures, covering rank, select and tries. It is part of the Spring 2012 course.

A 2013 lecture in which Vitalik Buterin explains what quantum computers are and what they can and cannot do. He then discusses what they could mean for Bitcoin's cryptography.

The first lecture of David MacKay's Cambridge course on information theory, pattern recognition and neural networks. It introduces the core ideas of his book Information Theory, Inference, and Learning Algorithms.