49 of the Maths AI glossary’s terms, each with the part of the syllabus where you first meet it.
A continuous probability distribution that is symmetric and bell-shaped about 0 like the standard normal distribution but has heavier tails, with a shape fixed by its number of degrees of freedom ; for a sample of size from a normal population, has a t-distribution with .
A confidence interval for the mean of a normal population with unknown standard deviation, given by
A test of whether the means of two populations are equal, using independent random samples from each; the pooled two-sample t-test assumes both populations are normally distributed with equal variances.
A table giving, for every pair of vertices in a graph, the weight of the shortest path between them.
A table that lists chosen inputs of a function alongside the corresponding outputs , giving points that lie on its graph.
The part of a distribution far from the mean on one side; the lower (left) tail holds the smallest values and the upper (right) tail the largest values.
The function defined by for every angle
For an acute angle in a right-angled triangle, .
The straight line that touches a curve at a point and has the same gradient as the curve at that point; it is the limiting position of the secants through that point.
One of the numbers in a sequence, written where the whole number is its position in the sequence.
The constant velocity that a falling object approaches when the resisting force on it balances its weight, so that its acceleration tends to zero.
A single value calculated from the sample data that measures how far the data are from what the null hypothesis predicts.
A method of checking reliability in which the same test is given to the same group of people on two occasions under the same conditions, and the two sets of scores are compared using a correlation coefficient; strong positive correlation indicates a reliable test.
A probability found by reasoning from a model of the experiment rather than from observed data; when the outcomes are equally likely it equals , the number of outcomes in the event divided by the number in the sample space.
An ordered triple that gives the position of a point in space as its distances along three mutually perpendicular axes that meet at the origin .
The equal ranks given to equal data values, each equal to the mean of the positions the tied values occupy together.
Replacing by in an equation of motion, which describes the same motion started units of time later; an object that starts from
A calculator or software tool that links the number of periods, the interest rate, the present value, the regular payment and the future value of an investment or loan, and finds any one of them from the others.
The turning effect of a force applied at position relative to a pivot, given by the vector product ; its magnitude
The law that water flows out of a small hole at depth below the surface with speed ; for a tank of constant cross-section it gives
The area of the region between a curve and an axis over an interval, counting every part as positive, found as or by adding the sizes of the integrals over the intervals between consecutive roots.
The length of the whole path an object covers in a time interval, counting movement in both directions as positive, given by
The difference between the total amount repaid on a loan and the amount borrowed; equivalently, the total cost of an item bought with a loan minus its price.
The problem of finding the point in a given region whose distance to the nearest site is as large as possible.
The sum of the entries on the leading diagonal of a square matrix; for the trace is
A walk in which no edge is repeated; vertices may be repeated.
The path traced in the phase plane by one solution of a coupled system as increases, with arrows showing the direction of motion.
A rule that moves every point of a graph or shape to a new position, such as a translation, a reflection or a stretch.
A matrix that defines a transformation of the plane by mapping each point with position vector to the point with position vector .
A directed graph whose vertices are the states of a Markov chain and whose edges are arrows labelled with the transition probabilities, including loops for staying in the same state.
The square matrix of a Markov chain whose entry in row and column is the probability of moving from state
The probability that a Markov chain moves from one given state to another given state in one step; denotes the probability of moving from state to state .
A transformation that moves every point of a graph the same distance in the same direction, without changing its shape, size or orientation.
A column vector that describes a translation of units parallel to the -axis and
A method of estimating by dividing the interval into strips of equal width and adding the areas of the trapezoids formed by joining neighbouring points on the curve with straight lines.
The problem of finding a route of least total weight that visits every vertex of a weighted graph and returns to the start. In the classical problem the graph is complete and the route is a Hamiltonian cycle of least weight; in the practical problem each vertex must be visited at least once.
A connected graph that contains no cycles, where a cycle is a closed route that returns to its starting vertex without repeating any edge or any other vertex.
A branching diagram for a sequence of events, in which each branch represents an outcome at one stage and is labelled with its probability given the outcomes on the branches before it.
A single performance of a random experiment.
The rule that to add two vectors, the second is drawn starting from the end of the first, and the sum is the vector from the start of the first to the end of the second.
A method of finding the positions of distant points by measuring the angles to them from the ends of a baseline of known length, and solving the resulting triangles.
An equation in which the unknown appears inside one or more trigonometric functions.
An equation involving trigonometric functions that is true for every value of the angle for which both sides are defined.
Shortening a number by removing all digits beyond a chosen position, without rounding; a positive number is never increased by truncation.
A point where a graph changes from rising to falling (a local maximum) or from falling to rising (a local minimum).
A test whose alternative hypothesis states only that a parameter differs from the value in the null hypothesis, in either direction.
A table that classifies a set of people or items by two features, with one feature in the rows, the other in the columns, a count in each cell and totals in the margins.
Rejecting the null hypothesis when it is true.
Not rejecting (accepting) the null hypothesis when it is false.