Game Theory The mathematics of strategic interaction — players, payoffs, and equilibrium — from von Neumann's minimax theorem to Nash equilibria and evolutionary stability.
Vectors and Matrices The basic objects of linear algebra: directed quantities with magnitude and direction, and rectangular arrays of numbers with defined arithmetic.
Fundamental Theorem of Calculus The theorem connecting differentiation and integration: the derivative of an integral recovers the integrand, and definite integrals equal differences of antiderivatives.
Standard Deviation A measure of how spread out a set of values is around its mean, expressed in the same units as the data.
Non-Euclidean Geometry Consistent geometries that reject or modify Euclid's parallel postulate: hyperbolic and elliptic geometry.
Fundamental Theorem of Arithmetic The theorem that every integer greater than 1 factors uniquely into primes, up to the order of the factors.
Central Limit Theorem The theorem that averages of many independent random variables become approximately normally distributed, regardless of the original distribution.
Pythagorean Theorem The central relation of Euclidean geometry: in a right triangle, the square of the hypotenuse equals the sum of the squares of the other two sides.