mathematics

11 articles · All tags

• What Is Linear Regression? How Least Squares Works
  Linear regression fits a straight line through data to predict one quantity from another, and least squares picks the line with the smallest squared errors.
• Gödel's Incompleteness Theorems: What They Prove
  Gödel's incompleteness theorems show that no consistent formal system for basic arithmetic can prove every truth about numbers, or prove its own consistency.
• The Fibonacci Sequence and the Golden Ratio Explained
  Each Fibonacci number is the sum of the previous two, and their ratio approaches the golden ratio, about 1.618. See the math, the history, and the myths.
• Game Theory
  The mathematics of strategic interaction — players, payoffs, and equilibrium — from von Neumann's minimax theorem to Nash equilibria and evolutionary stability.
• 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.
• Vectors and Matrices
  The basic objects of linear algebra: directed quantities with magnitude and direction, and rectangular arrays of numbers with defined arithmetic.
• 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.
• Standard Deviation
  A measure of how spread out a set of values is around its mean, expressed in the same units as the data.
• 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.