Mathematics. Dictionary
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In statistical significance testing, the probability of obtaining a test statistic at least as extreme as the one that was actually observed, assuming that the null hypothesis is true.
Lines or planes that never meet, staying the same distance apart at all points.
A convex quadrilateral in which each pair of opposite edges are parallel and of equal length.
Any measured quantity of a statistical population that summarises or describes an aspect of the population.
A set of equations that defines the coordinates of the dependent variables (x, y and z) of a curve or surface in terms of one or more independent variables or parameters.
A derivative with respect to one variable of a function of several variables with the other variables held constant.
A differential equation that involves the partial derivatives of a function of several variables.
The sum of the first n terms of an infinite series, where n is a finite number.
A polygon with five sides and five angles.
Any of the ninety-nine points that divide an ordered distribution into one hundred parts, each containing one per cent of the population.
A number that is the sum of all of its divisors except itself.
The sum of the distance of all the lengths of the sides of an object.
Any function whose value repeats after the regular addition of a period to its independent variable; i.e., a function ƒ such that, for some positive constant p, ƒ(x + p) = ƒ(x) for all x.
A one-to-one mapping from a finite set to itself.
A group whose elements are permutations (self-bijections) of a given set and whose group operation is function composition.
At or forming a right angle (to something).
A line that divides a line segment into two equal parts while also being perpendicular to said line segment.
An irrational and transcendental constant representing the ratio of the circumference of a Euclidean circle to its diameter; approximately 3.14159265.
The theorem which states that any partition of a finite set of n elements into m (< n) subsets (allowing empty subsets) must include a subset with two or more elements; any of certain reformulations concerning the partition of infinite sets where the cardinality of the unpartitioned set exceeds that of the partition (so there is no one-to-one correspondence).
The value of a digit of numbers. For example, ones, tens, hundreds in the decimal counting; ones, sixes, thirty-sixes in the senary counting.
A flat surface extending infinitely in all directions (e.g. horizontal or vertical plane); a bounded portion thereof.
The locus of points in the Euclidean plane that satisfies some geometric or algebraic definition; a curve in a plane (as opposed to higher-dimensional space).
The sign +, indicating addition or a positive number.
A decimal point (now especially when reading decimal fractions aloud).
The general field of topology, not restricting attention to specific classes of spaces, and not using algebraic topology.
The coordinates of a point in a plane, measured as its Cartesian distance from the origin and the angle measured counterclockwise from the x-axis to a line joining the point to the origin.
A plane figure bounded by edges that are all straight lines.
A solid figure with many flat faces and straight edges.
An expression consisting of a sum of a finite number of terms, each term being the product of a constant coefficient and one or more variables raised to a non-negative integer power, such as a_n x^n + a_{n-1}x^{n-1} + ... + a_0 x^0.
A ring (which is also a commutative algebra), denoted K[X], formed from the set of polynomial (usually of one variable, in a given set, X), with coefficients in a given ring (often a field), K.
The mean (usually arithmetic, but possibly geometric) of all members of a population or all possible values from which a sample can be taken, as opposed to a sample mean.
The probability that a statistical test will reject the null hypothesis when the alternative hypothesis is true.
Any infinite series of the general form \sum_{i=0}^\infty a_i (x-c)^i.
The generic term for symbolic formal systems like first-order logic, second-order logic, many-sorted logic or infinitary logic.
The factorization of a positive integer into its constituent prime numbers.
Any natural number greater than 1 that cannot be formed by multiplying two smaller natural numbers.
Any theorem that concerns the distribution of prime numbers.
For a given modulus n, a number g such that for every a coprime to n there exists an integer k such that g'k ≡ a (mod n); a generator (or primitive element) of the multiplicative group, modulo n, of integers relatively prime to n.
Chosen or assumed among a branch of possible values of a multi-valued function so that the function is single-valued.
A polyhedron with parallel ends of the same polygonal shape and size, the other faces being parallelogram-shaped sides.
A number, between 0 and 1, expressing the precise likelihood of an event happening.
Any function whose integral over a set gives the probability that a random variable has a value in that set.
A distribution of all possible values of a random variable together with an indication of their probabilities.
A measurable space having a unit measure
A quantity obtained by multiplication of two or more numbers.
The branch of mathematics that investigates those properties of figures that are invariant under homographies, special kinds of spaces called projective spaces, and the geometric structures that inhabit them.
A plane in which any pair of distinct point determine a line and any pair of distinct lines intersect at a point.
A sequence of statements consisting of axioms, assumptions, statements already demonstrated in another proof, and statements that logically follow from previous statements in the sequence, and which concludes with a statement that is the object of the proof.
The proof of a statement adduced by deriving a contradiction from the statement's negation.
A vulgar fraction in which the magnitude of the numerator is less than or equal to that of the denominator, such as 2/3.
A statement of equality between two ratios.
A formal deductive system in which formulae representing propositions can be formed by combining atomic propositions using logical connectives.
An instrument for measuring angles, usually a marked semicircle.
A surface generated by rotating a tractrix about its asymptote; a tractricoid
A solid with triangular lateral faces and a polygonal (often square or rectangular) base.
In mathematics, the Pythagorean theorem or Pythagoras's theorem is a fundamental relation in Euclidean geometry between the three sides of a right triangle. It states that the area of the square whose side is the hypotenuse (the side opposite the right angle) is equal to the sum of the areas of the squares on the other two sides. The theorem can be written as an equation relating the lengths of the sides a, b and the hypotenuse c, sometimes called the Pythagorean equation: a 2 + b 2 = c 2 .…
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