Maths AI terms: O

O

ObjectHL only · also original shape, pre-image

The point, line or shape to which a transformation is applied, before it is moved.

Introduced in 3.9 Matrix transformations

Objective functionalso objective functions, function to be optimised, quantity to be optimised

The function that gives the quantity to be maximised or minimised, written in terms of a single variable.

Introduced in 5.7 Optimisation

Observed frequencyalso observed frequencies, f_o

The number of observations actually recorded in a category of a sample, written $f_o$.

Introduced in 4.11 Hypothesis testing

Obtuse anglealso obtuse angles, obtuse

An angle greater than 90° and less than 180°.

Introduced in 3.2 Trigonometry in triangles

Odd vertexHL only · also odd vertices, vertex of odd degree

A vertex whose degree is an odd number.

Introduced in 3.14 Graph theory

One-sample t-testHL only · also one-sample t test, single-sample t-test, one sample t-test

A hypothesis test for the mean of a normal population with unknown standard deviation, using the statistic $t = \frac{\bar{x} - \mu_0}{s_{n-1}/\sqrt{n}}$

One-tailed testalso one-tailed, one-sided test, one-tailed alternative

A test whose alternative hypothesis states the direction of the difference from the value in the null hypothesis.

Introduced in 4.11 Hypothesis testing

One-to-one functionalso one-to-one, injective function, one to one function

A function in which every output comes from exactly one input, so that different inputs always give different outputs.

Introduced in 2.2 Functions, domain and range

Opposite sidealso opposite, opp

In a right-angled triangle, the side across from a given acute angle, which does not form either arm of that angle.

Introduced in 3.2 Trigonometry in triangles

Optimal valuealso optimum, optimal solution, optimum value, best value

The greatest or least value of the objective function that can be achieved within the constraints, together with the value of the variable at which it occurs.

Introduced in 5.7 Optimisation

Optimisationalso optimization, optimise, optimize, optimising, optimizing, optimisation problem

The process of finding the value of a variable that makes a quantity as large as possible (a maximum) or as small as possible (a minimum), usually subject to conditions set by the context.

Introduced in 5.7 Optimisation

Order of a differential equationHL only · also first-order differential equation, first order DE, order of a DE, first-order DE

The order of the highest derivative that appears in a differential equation: first order if only the first derivative appears, second order if the second derivative is the highest, and so on.

Introduced in 5.14 Setting up differential equations

Order of a matrixHL only · also order, dimensions, m × n, size of a matrix

The number of rows and the number of columns of a matrix, written $m \times n$ for a matrix with $m$ rows and $n$ columns.

Introduced in 1.14 Matrices

Order of magnitudealso orders of magnitude

The power of ten that describes the size of a quantity, usually the exponent $k$ when the quantity is written in standard form $a \times 10^{k}$; two quantities differ by $n$ orders of magnitude when one is about $10^{n}$

Ordinal dataalso ordinal, ordinal scale, ordinal variable

Data whose values can be placed in a meaningful order, but where the differences between values are not equal or not measured.

Introduced in 4.10 Spearman’s rank correlation

Ordinary annuityalso payments at the end of the period, END mode, end-of-period payments, annuity in arrears, ordinary annuities

An annuity in which each payment is made at the end of a payment period.

Introduced in 1.7 Amortisation and annuities

Ordinatealso ordinates, y-values, y-value at a strip edge

The $y$-coordinate of a point on a curve; in the trapezoidal rule, the ordinates $y_0, y_1, \ldots, y_n$

OrientationHL only · also orientation-reversing, orientation-preserving, reverses orientation

The direction, clockwise or anticlockwise, in which the labelled vertices of a shape occur; a transformation with a positive determinant preserves it and one with a negative determinant reverses it.

Introduced in 3.9 Matrix transformations

Out-degreeHL only · also out degree, outdegree

The number of edges of a directed graph that start at (point out of) a vertex.

Introduced in 3.14 Graph theory

Outcomealso outcomes

One possible result of a single trial of a random experiment.

Introduced in 4.5 Concepts of probability

Outer functionHL only · also outside function

In a composite function $y = g(f(x))$, the function $g$ that is applied last, to the output $u$ of the inner function, giving $y = g(u)$

Outlieralso outliers, 1.5 × IQR rule, outlier rule, fences

A data value that is more than $1.5 \times \mathrm{IQR}$ below the lower quartile or more than $1.5 \times \mathrm{IQR}$ above the upper quartile.

Introduced in 4.1 Collecting data and sampling

Outstanding balancealso balance, amount owed, remaining balance, outstanding balances

The amount of a loan still owed at a given time, after the payments made so far.

Introduced in 1.7 Amortisation and annuities

OverdampedHL only · also over-damped, overdamping, heavily damped

Describes a damped system $\ddot{x} + a\dot{x} + bx = 0$ whose auxiliary equation has two distinct negative real roots ($a^2 > 4b$

OverdispersionHL only · also over-dispersion, overdispersed, over-dispersed

The situation in which count data have a variance noticeably larger than their mean, which suggests that a Poisson model is not suitable because the events are clustered or the rate varies.

Introduced in 4.17 The Poisson distribution

Overestimatealso overestimates, over-estimate, too large an estimate

An approximation that is greater than the true value it approximates.

Introduced in 5.8 The trapezoidal rule