finite fields

Christof Paar's university lecture introducing Galois fields and finite-field arithmetic as used in AES. It covers the mathematics behind the AES S-box.

David Tong, a Cambridge theoretical physicist, explains at the Royal Institution that the fundamental building blocks of nature are quantum fields rather than particles. He covers what we know about these fields and how they fit into the Standard Model.

Sean Carroll's 2013 Fermilab Users Meeting lecture on particles, fields and the future of particle physics. He explains that particles are vibrations in underlying quantum fields and touches on the Higgs, neutrinos and dark matter.

The first lecture of Michael Sipser's MIT 18.404J Theory of Computation course, covering course mechanics, finite automata, regular languages and regular expressions. It proves closure of regular languages under union and begins concatenation.

Stanford physicist Leonard Susskind explains what the Higgs mechanism is and what it means to give mass to particles. He also covers what is at stake for physics and cosmology.

A lecture by Richard Feynman on how computers work, using the analogy of a filing clerk that becomes progressively dumber and faster. It also covers heuristics and how computers handle data and solve problems in finite time.

Physicist Al Bartlett's well-known lecture on the arithmetic of exponential growth, applied to population, energy consumption and resource depletion. He argues that steady percentage growth cannot be sustained on a finite planet and that most public discussion ignores this.

Utah State plant scientist Bruce Bugbee presents his analysis of the energy and environmental costs of vertical and indoor farming. He argues artificial lighting cannot compete with sunlight in fields or greenhouses.

A recording of physicist Albert Bartlett's well-known lecture on the arithmetic of exponential growth, applied to population and energy use. He argues that steady percentage growth in a finite world cannot continue and sneaks up suddenly.

An RSA Animate in which Steven Pinker explains how the mind builds infinite meanings from finite language, and why people often speak indirectly. It covers ambiguity, politeness and mutual knowledge, including the emperor's new clothes example.

Vladimir Voevodsky's IAS lecture starts from Godel's second incompleteness theorem to explore whether first-order arithmetic could be inconsistent. It motivates his vision of univalent foundations and computer-checked proofs.

Physicist Albert Bartlett's full-length lecture on how steady exponential growth in population and energy use collides with finite resources. It uses examples like bacteria in a bottle and covers peak oil.

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.