Maths AI terms: E

E

Edge (graph)HL only · also edges

A connection between two vertices of a graph, drawn as a line (straight or curved) joining them.

Introduced in 3.14 Graph theory

Edge (Voronoi diagram)also Voronoi edge, Voronoi edges, edges of a Voronoi diagram, boundary between cells

A boundary between two neighbouring cells of a Voronoi diagram; it is a line segment or ray lying on the perpendicular bisector of the two sites whose cells it separates.

Introduced in 3.6 Voronoi diagrams

Effective annual ratealso AER, annual equivalent rate, effective rate, effective interest rate

The percentage by which a balance actually grows in one year once compounding within the year is included; for a nominal rate $r\%$ compounded $k$ times a year it equals $\left(\left(1 + \frac{r}{100k}\right)^{k} - 1\right) \times 100\%$.

Introduced in 1.4 Financial applications of geometric sequences

EigenvalueHL only · also eigenvalues, λ, lambda, characteristic value

A number $\lambda$ for which a square matrix $M$ has a non-zero vector $\boldsymbol{v}$ with $M\boldsymbol{v} = \lambda\boldsymbol{v}$; it is the factor by which $M$

EigenvectorHL only · also eigenvectors, characteristic vector

A non-zero vector $\boldsymbol{v}$ for which multiplying by a square matrix $M$ gives a scalar multiple of $\boldsymbol{v}$, so that $M\boldsymbol{v} = \lambda\boldsymbol{v}$ for some number

Element of a matrixHL only · also entry, element, elements, entries, a_ij

One of the numbers in a matrix; the element in row $i$ and column $j$ of matrix $A$ is written $a_{ij}$.

Introduced in 1.14 Matrices

Empirical rulealso 68–95–99.7 rule, 68-95-99.7 rule, three-sigma rule

For any normal distribution, about 68% of values lie within one standard deviation of the mean, about 95% within two standard deviations and about 99.7% within three standard deviations.

Introduced in 4.9 The normal distribution

Encoding matrixHL only · also key matrix, coding matrix, decoding matrix, encryption matrix, encoding matrices

A non-singular square matrix used to convert a message, written as columns of numbers, into code by multiplication; its inverse is the decoding matrix that recovers the message.

Introduced in 1.14 Matrices

EnlargementHL only · also enlargements, dilation

A transformation that maps every point $P$ to the point $P'$ on the line through a fixed centre $C$ and $P$ with $\overrightarrow{CP'} = k\,\overrightarrow{CP}$

Equal matricesHL only · also equality of matrices, equal matrix

Two matrices that have the same order and whose corresponding elements are all equal.

Introduced in 1.14 Matrices

Equal vectorsHL only

Vectors that have the same magnitude and the same direction; in component form, vectors whose corresponding components are all equal.

Introduced in 3.10 Vectors

Equally likely outcomesalso equally likely, equiprobable outcomes, equally likely outcome

Outcomes that all have the same probability of occurring, so that with $n(U)$ such outcomes each has probability $\frac{1}{n(U)}$.

Introduced in 4.5 Concepts of probability

Equation of a normalalso normal equation, equation of the normal, equation of the normal line

The equation of the line through $(a, f(a))$ perpendicular to the tangent there, $y - f(a) = -\frac{1}{f'(a)}(x - a)$

Equation of a tangentalso tangent equation, equation of the tangent line, equation of a tangent line

The equation of the straight line that touches the curve $y = f(x)$ at $(a, f(a))$ with gradient $f'(a)$

Equidistance linealso median line, equidistance boundary, equidistance lines

A boundary on which every point is the same distance from the nearest points of two coastlines or regions; between two single points it is their perpendicular bisector.

Introduced in 3.5 Perpendicular bisectors

Equidistantalso equidistance, equal distance, equally distant

At the same distance from two or more given points or objects.

Introduced in 3.5 Perpendicular bisectors

Equilibrium pointHL only · also equilibrium, fixed point, critical point of a system, equilibrium points, equilibrium solution

A point in the phase plane at which every rate of change of a system is zero ($\dot{x} = 0$ and $\dot{y} = 0$ simultaneously), so that a solution starting there stays there for all time.

Introduced in 5.17 Phase portraits

EstimateHL only · also point estimate, estimated value, estimates

The single numerical value that an estimator gives for one particular sample, used as a best guess of a population parameter.

Introduced in 4.14 Linear transformations of random variables

Estimated meanalso estimate of the mean, estimated mean of grouped data, mean of grouped data

An approximation to the mean of grouped data, calculated with the mean formula using the mid-interval value of each class in place of the unknown individual values.

Introduced in 4.3 Measures of central tendency and dispersion

Estimated parameterHL only · also parameter estimated from the data, estimated parameters, estimating a parameter

A value of a distribution's parameter, such as a mean, a standard deviation or a probability of success, that is calculated from the sample data because it is not known or given in advance.

Introduced in 4.12 Data collection and reliability

Estimationalso estimating, rough calculation

Finding an approximate value of a calculation or quantity, usually by rounding the numbers involved to 1 significant figure, in order to judge whether an exact result is reasonable.

Introduced in 1.6 Approximation and error

EstimatorHL only · also estimators, point estimator

A rule or formula, applied to sample data, that is used to estimate a population parameter; because the sample is random, an estimator is itself a random variable.

Introduced in 4.14 Linear transformations of random variables

Euclidean distancealso straight-line distance, Euclidean metric

The length of the straight line segment joining two points, calculated in two dimensions as $\sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}$

Euler's formulaHL only · also Euler formula, e^(iθ) = cos θ + i sin θ

The identity $\mathrm{e}^{\mathrm{i}\theta} = \cos\theta + \mathrm{i}\sin\theta$, valid for every real $\theta$ measured in radians.

Introduced in 1.13 Polar and Euler form

Euler's identityHL only · also Euler identity, e^(iπ) + 1 = 0

The equation $\mathrm{e}^{\mathrm{i}\pi} + 1 = 0$, the case $\theta = \pi$ of Euler's formula.

Introduced in 1.13 Polar and Euler form

Euler's methodHL only · also Euler method, forward Euler method, Euler's method for coupled systems

A numerical method for a first-order differential equation that starts from a known point and repeatedly moves a fixed distance along a straight line whose gradient is given by the differential equation at the current point.

Introduced in 5.16 Euler’s method

Euler's numberalso e, the number e, Napier's constant

The irrational constant $\mathrm{e} = 2.718\,281\,828\ldots$, the value that $\left(1 + \frac{1}{n}\right)^n$

Eulerian circuitHL only · also Euler circuit, Euler tour

A circuit that uses every edge of a graph exactly once, starting and finishing at the same vertex.

Introduced in 3.16 Tree and cycle algorithms

Eulerian graphHL only · also Eulerian graphs

A connected graph that has an Eulerian circuit, which happens exactly when every vertex has even degree.

Introduced in 3.16 Tree and cycle algorithms

Eulerian trailHL only · also Euler trail, Eulerian path, Euler path

A trail that uses every edge of a graph exactly once.

Introduced in 3.16 Tree and cycle algorithms

Even vertexHL only · also even vertices, vertex of even degree

A vertex whose degree is an even number, including 0.

Introduced in 3.14 Graph theory

Eventalso events

A set of outcomes from the sample space, usually described in words and named with a capital letter; the event occurs when the outcome of a trial is one of its outcomes.

Introduced in 4.5 Concepts of probability

Exact valuealso v_E, true value, accepted value, actual value

The true or accepted value of a quantity, written $v_E$, against which an approximation is compared.

Introduced in 1.6 Approximation and error

Exam modealso examination mode, press-to-test, exam mode for IB

A setting on a GDC that temporarily blocks stored files, notes, programs and selected functions so that the calculator meets examination rules, usually shown by an indicator on the screen until it is switched off.

Exchange ratealso exchange rates, currency conversion, conversion rate, rate of exchange

The amount of one currency that is equal in value to one unit of another currency.

Introduced in 1.4 Financial applications of geometric sequences

Expected frequencyalso expected frequencies, f_e

The number of observations predicted for a category if the null hypothesis were true, written $f_e$; it is the total frequency multiplied by the probability of the category under the null hypothesis.

Introduced in 4.11 Hypothesis testing

Expected number of occurrencesalso expected number, expected occurrences, expected count

The average number of times an event is expected to occur in $n$ trials, equal to $n \times \mathrm{P}(A)$ when the event has probability $\mathrm{P}(A)$ in each trial.

Introduced in 4.5 Concepts of probability

Expected valuealso E(X), expectation, mean of a random variable, expected value of a random variable

The long-run mean value of a random variable over a very large number of repetitions; for a discrete random variable $X$ it is $\mathrm{E}(X) = \sum x\,\mathrm{P}(X = x)$, the sum of each value multiplied by its probability.

Introduced in 4.7 Discrete random variables

Exponentalso index, indices, exponents

The number written as a raised superscript on a base, which, when it is a positive integer $n$, counts how many copies of the base are multiplied together: $a^n = a \times a \times \cdots \times a$ with $n$

Exponential decayalso exponential decay model, decays exponentially

Change in which a quantity is multiplied by the same factor between 0 and 1 over every interval of equal length, so that it decreases by a constant percentage of its current size.

Introduced in 2.5 Modelling with functions

Exponential equationalso exponential equations

An equation in which the unknown appears in an exponent.

Introduced in 1.5 Exponents and introduction to logarithms

Exponential formHL only · also Euler form, re^(iθ), r e^(iθ)

The form $z = r\mathrm{e}^{\mathrm{i}\theta}$ of a non-zero complex number, where $r = |z| > 0$ is its modulus and $\theta$

Exponential growthalso exponential growth model, grows exponentially

Change in which a quantity is multiplied by the same factor greater than 1 over every interval of equal length, so that it increases by a constant percentage of its current size.

Introduced in 2.5 Modelling with functions

Exponential regressionHL only · also exponential regression curve, ExpReg, exponential fit

Fitting a model of the form $y = ab^x$, or equivalently $y = a\mathrm{e}^{kx}$, to bivariate data with positive $y$

Extrapolationalso extrapolate, extrapolating, extrapolated, dangers of extrapolation

Using a model to predict a value for an input that lies outside the range of the input values used to build or test the model; such predictions rely on the pattern continuing and are often unreliable.

Introduced in 2.6 The modelling process