ruk·si

🧮 Mathematics

Updated at 2011-01-05 17:00

Mathematics is an abstraction. Instead of thinking about particular numbers, mathematics focuses on the underlying patterns.

This note contains basic math formulas and terms that I mix up on a semi-regular basis.

Math:

  • Theorem: A pattern or rule.
  • Proof: Calculations that show that a theorem is always true.

Circle:

  • Center: Every point of a circle have the same distance from this point.
  • Edge: Points that form the outline of a circle.
  • Radius: Distance from the center to the edge.
  • Circumference: Distance of the edge.
  • Diameter: Distance from an edge point to opposite point. Twice the radius.
  • Pi: Ratio between circumference and diameter. Always 3.141559...

Average (Arithmetic Mean): The sum of a collection of values divided by the number of values in the collection.

sum(x) / x.length

Mid-range: Average of the minimum and maximum values in a collection.

( max(x) + min(x) ) / 2

Median: The middle value in an ordered collection of value. If there is a even number of numbers, median is average of the two middle numbers.

x = [a, b, c, d, e] ^ ^ ^ min. med. max.

Mode: The most common value in a collection of values.

x[a, a, b, c, c, b, b] = Mode is b

Quadratic is a generalization of conic sections such as ellipses, circles, parabolas and hyperbolas. Think of a 3D cone where you cut slices.

Transpose is flipping matrix rows to columns and columns to rows over its the diagonal, A vs A^T.

Ordinal data is a categorical data type where the variables have ordered categories and the distances between the categories are not known.