Course Highlights This course includes interactive demonstrations which are intended to stimulate interest and to help students gain intuition about how artificial intelligence methods work under a variety of circumstances. Course Description This course introduces students to the basic knowledge representation, problem solving, and learning methods of artificial intelligence. Upon completion of 6.034, students should […]

# Adventures in Group Theory

Adventures in Group Theory: Rubik’s Cube, Merlin’s Machine, and Other Mathematical Toys David Joyner 5-15-2008 Published on Jan 15, 2016 The vast majority of people who tackle the Rubik’s cube never succeed in solving it without looking up somebody else’s solution. In this video the Mathologer reveals a simple insight that will enable all those […]

# systematically generate all permutations

In mathematics, the notion of permutation relates to the act of arranging all the members of a set into some sequence or order, or if the set is already ordered, rearranging (reordering) its elements, a process called permuting. These differ from combinations, which are selections of some members of a set where order is disregarded. […]

# general circulation model (GCM)

A general circulation model (GCM), a type of climate model, is a mathematical model of the general circulation of a planetary atmosphere or ocean and based on the Navier–Stokes equations on a rotating sphere with thermodynamic terms for various energy sources (radiation, latent heat). These equations are the basis for complex computer programs commonly used […]

# Revenue equivalence theorem

Revenue equivalence is a concept in auction theory that states that given certain conditions, any auction mechanism that results in the same outcomes (i.e. allocates items to the same bidders) also has the same expected revenue. An auction is a special case of a mechanism. In this case, the mechanism takes buyers’ bids and decides […]

# Markov decision processes

Markov decision processes (MDPs), named after Andrey Markov, provide a mathematical framework for modeling decision making in situations where outcomes are partlyrandom and partly under the control of a decision maker. MDPs are useful for studying a wide range of optimization problems solved via dynamic programming andreinforcement learning. MDPs were known at least as early […]

# Alpha–beta pruning

The Alpha-Beta algorithm (Alpha-Beta Pruning, Alpha-Beta Heuristic [1] ) is a significant enhancement to the minimax search algorithm that eliminates the need to search large portions of the game tree applying a branch-and-bound technique. Remarkably, it does this without any potential of overlooking a better move. If one already has found a quite good move […]

# Spectral theorem

Spectral theorem From Wikipedia, the free encyclopedia In mathematics, particularly linear algebra and functional analysis, the spectral theorem is any of a number of results about linear operators or about matrices. In broad terms the spectral theorem provides conditions under which an operator or a matrix can bediagonalized (that is, represented as a diagonal matrix in some basis). This concept of diagonalization is relatively straightforward for operators on finite-dimensional spaces, but […]

# Horner scheme

http://en.wikipedia.org/wiki/Horner_scheme In numerical analysis, the Horner scheme (also known as Horner algorithm), named after William George Horner, is an algorithm for the efficient evaluation of polynomials in monomial form.Horner’s method describes a manual process by which one may approximate the roots of a polynomial equation. The Horner scheme can also be viewed as a fast algorithm for dividing a polynomial by a […]

# Jacobi Method

In numerical linear algebra, the Jacobi method is an algorithm for determining the solutions of a system of linear equations with largest absolute values in each row and column dominated by the diagonal element. Each diagonal element is solved for, and an approximate value plugged in. The process is then iterated until it converges. This […]