Mathematics Topics

The number of radians in 1 degree.
Euler′s constant.
Catalans constant.
Square root of 2.
Brun′s constant, the sum of the reciprocals of all twin primes.
The base of natural (Napierian) logarithms
Pi is the number of times the diameter of a circle can be divided into the circumference.
The number of degrees in 1 radian.
Ab Initio
Latin meaning "from first principles".
The uppermost part of a colurnn capital or pilaster, on which the architrave rests. Also, a bead frame used as an arithmetic calculating aid.
Abelian Group
A mathematical group of transformations with the property that the end result of a series of transformations does not depend on the order in which they are performed.
The x coordinate on an (x, y) graph.
Absolute Value
The positive value for a real number, disregarding the sign.
Abundant Number
A positive integer that is smaller than the sum of its proper divisors.
Addition of Ordinates
A graphing technique where two or more functions are independently plotted on the same graph, then their y-coordinates are added together at each point to form the new graph.
Affine Cipher
Affine ciphers use linear functions to scramble the letters of secret messages.
Affine Space
A geometric structure that generalizes the affine properties of Euclidean space.
First major treatise written by Al-Khawarizmi in AD 810.
A logical sequence of instructions that explain how to accomplish a task. It must explain exactly how to go from one step to the next and have a finite amount of steps.
To adjust or set to a line or centre.
The first letter of the Greek alphabet.
A cryptarithm in which the letters, which represent distinct digits, form related words or meaningful phrases.
Altitude of a Conic Solid
The length of a segment whose endpoints are the vertex and a point on the plane of the base that is perpendicular to the plane of the base.
Altitude of a Cylindric Solid
The distance between the planes of the bases.
Amicable Numbers
Two numbers are said to be amicable if each is equal to the sum of the proper divisors of the other.
Lists all Analysis topics in the Encyclopaedia
Angular Frequency
The frequency of a steady recurring phenomenum in radians per second.
The region enclosed by two concentric circles.
To apodize is to remove or smooth a sharp discontinuity in a mathematical function, an electrical signal or a mechanical structure.
Arbitrary Unit
A unit that is not part of the standardized metric or other system.
Arc Length
The distance between the endpoints of an arc along the path of the circle.
The inverse of cosine. Note that arccos(A)=cos-1(x).
The inverse of cotangent. Note that arccot(A)=cot-1(x).
The inverse of cosecant. Note that arccsc(A)=csc-1(x).
Archimedes Constant
More commonly known as Pi.
Defined as 1/60 of a degree.
The inverse of secant. Note that arcsec(A)=sec-1(x).
Defined as 1/360 of a degree.
The inverse of sine. Note that arcsin(A)=sin-1(x).
The inverse of tangent. Note that arctan(A)=tan-1(x).
The type of mathematics that studies how to solve problems involving numbers, but not variables.
Arithmetic Coding
Arithmetic coding removes this restriction by representing messages as intervals of the real numbers between 0 and 1.
Arithmetic Operators
Symbols and signs used in mathematics.
A vector with magnitude equal to the maximum spatial rate of change of that function at a given point at a given time and directed toward increasing values of the function along the line of maximum change.
The inverse of sine. Note that asn(A)=sin-1(x).
Associative Property
When adding or multiplying three numbers, it doesn′t matter if the first two or the last two numbers are added or multiplied first.
An identifiable property of an object, set, or event that is subject to being measured.
An isomorphism from a set onto itslef.
A spectrum with the coefficients of the components expressed as the square of the magnitudes
A statistic calculated by summing a set of data values and dividing by the number of values.
Average Expected Payoff
An estimate of the amount that will be gained in a game of chance, calculated by multiplying the probability of winning by the number of points won each time.
In any process it is often necessary to average a number of measurements to gain any confidence in the measured value.
A statement assumed to be true without the need for proof.
Axiomatic Completeness
An axiomatic theory is complete if every syntactically correct statement in the theory can be proven either right or wrong.
The line, real or imaginary, passing through the centre of an object about which it could rotate; a point of reference.
Azimuth Angle
Azimuth measured from 0° at the north or south reference direction clockwise or counterclockwise through 90° or 180°.
Bar Chart
A strong graphical representation of data.
Substance which gives off hydroxide ions (OH-) in solution. In the expression xy, x is called the base and y is the exponent.
Basis Function
A mathematical function that can be used to build a description of wavefunctions for electrons in atoms or molecules.
Bayes Rule
A rule for finding conditional probability.
Behavioural Envelope
Envelope of response versus frequency.
Bell Curve
A continuous probability distribution that often gives a good description of data that cluster around the mean.
A letter of the Greek alphabet.
In the home entertainment context, pertaining to presentations involving the visual and auditory sensory modalities.
Pertaining to a characteristic that involves the selection, choice, or condition in which there are only two possibilities.
Binary Coded Decimal
A number system where each decimal digit is separately represented by a 4-bit binary code.
Binary Coded Digit
A digit of any number system that is represented as a fixed number of binary digits
Binary Notation
In order to understand how a number in binary notation is constructed, the decimal notation is first discussed.
Binary Number
A number written to base 2.
Binary Point
The radix point that separates powers of two and fractional powers of two in a binary number.
Binomial Coefficient
The coefficients of x in the expansion of (x+1)n.
Bisect means to cut something in half. For example, to bisect an angle, you would draw a line through the vertex of the angle such that the two angles created are equivalent in measure.
Black Box
A unit whose output is a specified function of the input, but for which the method of converting input to output is not necessarily specified.
Pertaining to the operations of formal logic.
The interior diameter of a cylinder.
Boundary Element Method
A mathematical formulation used to predict acoustic parameters such as pressure and power. This technique may be applied to interior and exterior acoustic problems.
A surface made up of rectangles; a rectangular parallelpided.
Box Plot
A graphic method that shows the distribution of a set of data by using the median, quartiles, and the extremes of the data set.
The symbols { and } used for grouping or to represent a set.
Braids Theory
Invented by Emil Artin and is a part of the Knot Theory. Braids are collections of lines whose ends are attached to two parallel straight lines.
Brun′s Constant
The sum of the reciprocals of all twin primes.
Cahen Constant
Defined as an infinite series of unit fractions, with alternating signs.
A machine for performing arithemtical calculations.
Caliban Puzzle
A logic puzzle in which one is asked to infer one or more facts from a set of given facts.
Canonical Form
In a mathematical context this term is taken to mean a generic or basic representation.
Cardinal Number
A number that indicates the quantity but not the order of things.
The curve described by a point on a circle of radius r as it rolls on the outside of another circle of radius r.
Cartesian Coordinates
Coordinates where the position of a point is described by the distance it is from 2 lines in 2 dimensional space or from 3 planes in 3 dimensional space.
Cartesian Plane
A coordinate plane.
Catalans Constant
= 0.915965594177219015
Cauchy Sequence
A sequence x0, x1, ... of elements of a metric space is said to be a Cauchy sequence if differences |xn+m-xn| are uniformly small in m (i.e. do not depend on m) and tend to 0 as n grows.
Ceiling Function
The ceiling function of x is the smallest integer greater than or equal to x.
A number equal to 10303.
Central Limit Theorem
A random sample of observations from any distribution with a finite mean and a finite variance, the average will tend to follow a normal distribution for large samples.
Central Tendencies
A number which in some way conveys the "centre" or "middle" of a set of data. The most frequently used measures are the mean and the median.
A point or axis around which anything revolves or rotates.
The centre of mass of a figure.
The breakdown of predictability, or a state of disorder.
Codes for writing secret messages.
Closed Interval
An interval that includes it′s endpoints.
A coefficient is a constant multiplicative factor of a certain object.
In the same line.
Points are said to be collinear if they all lie on the same line.
A combination is the set itself without reference to order.
Describes an operator that gives the same result irrespective of the order of arguments.
The complement of a subset of a given set is the collection of all elements of the set that are not elements of the subset.
Complementary Rules
Rules in Boolean Algebra derived from the combination of a single variable with the inverse of itself.
An object is complete if nothing needs to be added to it.
Complex Conjugate
A complex number whose imaginary part is the negative of that of a given complex number, their real parts being equal.
Complex Numbers
A complex number consists of a real and imaginary part.
Complex Numbers, Exponential Form
Exponential expression of complex numbers.
Complex Numbers, Polar Form
Complex numbers written in polar form.
Composite Number
A natural number that is not prime.
Compund Event
Two or more events that happen simultaneously.
To solve problems that use numbers.
Curved from the inside.
Concave Up
A curve is "concave up" when it is a concave shape, meaning curved like the inside of a bowl, with the two ends of the curve pointing up.
Pertaining to the occurrence of two or more events or activities within the same specified interval of time.
Conic Section
The cross section of a right circular cone cut by a plane.
A statement that may seem to be true, but has yet to be proven.
The operation of replacing i by -i in a complex number.
Consecutive Vertices
Endpoints of a single side of a polygon.
Consistent Linear System
A system of linear equations is consistent if it has at least one solution.
A quantity that does not change. This quantity may be a number or a variable.
Constant Functions
Functions that stay the same no matter what the variable does are called constant functions.
Continuous Graph
In a graph, a continuous line with no breaks in it forms a continuous graph.
The outline of an object.
A reduction in size.
Control Chart
A chart used to determine whether the distribution of data values generated by a process is stable over time.
Control Group
The subjects in a controlled experiment who do not receive the treatment.
The curved surface of a cylinder, as a sphere when viewed from without.
Coordinate Plane
A plane with a point selected as an origin, some length selected as a unit of distance, and two perpendicular lines that intersect at the origin, with positive and negative direction selected on each line.
Numbers that specify the position of a point or the position or orientation of a geometric object.
A set of points or lines that are all on a common plane.
Integers m and n are coprime if the greatest common divisor of m and n is 1.
Corollary to a Theorem
A corollary is a proposition that follows with little or no proof from one other theorem or definition.
Correlation Coefficient
A numerical value, between +1 and -1, that identifies the strength of the linear relationship between variables.
Trigonometric function.
Trigonometric function.
A measure of the joint variability of a pair of numeric variables.
Cross Correlation
The cross-correlation function gives a measure of the extent to which two signals correlate with each other as a function of the time displacement between them.
Cross Spectrum
The cross spectrum Fxy(f) of fx(t) and fy(t) is the forward Fourier Transform of the cross correlation function Rxy(T). The cross spectrum is in general complex.
A number puzzle.
Field of mathematics and computer science concerned with information security and related issues, particularly encryption and authentication.
Abbreviation of the trigonometric function cosecant.
Cumulative Frequency
The number of observations falling in a given class in a frequency table, plus all observations falling in earlier classes.
Cumulative Relative Frequency
The number of observations falling in a given class in a frequency table, plus all observations falling in earlier classes, divided by the total number of observations.
Departure from flatness of a surface. Defined as the reciprocal of the radius of curvature.
Curve Sketching
When sketching a curve there are a number of general features to look for.
The curve described by a point on a circle as it rolls along a line.
A right angle circular cylinder.
A number equal to 1033.
Pertaining to the number representation system with a radix of ten.
Decimal Number
A number written to the base 10.
Decimal Point
The period in a decimal number separating the integer part from the fractional part.
A conclusion derived by reasoning.
Defective Matrix
A matrix A is defective if A has an eigenvalue whose geometric multiplicity is less than its algebraic multiplicity.
Deficient Number
A positive integer that is larger than the sum of its proper divisors.
Del Operator
The del or grad operation means to take the derivative with respect to distance, in 3 dimensions.
de Moivre
Named after the analyst and probability theorist Abraham de Moivre.
Dense Line
The line that contains the shortest path between two points.
Density Function
A mathematical function used to determine probabilities for a continuous random variable.
Dependent Variable
The dependent or response variable is the variable whose behaviour is to be measured as a result of an experiment.
The Discrete Fourier Transform, the digital version of the fourier transform.
Diagonal Matrix
A diagonal matrix is an n x n matrix with every off diagonal element equal to zero.
A cryptarithm in which digits represent other digits.
In the decimal system, one of the numbers 0, 1, 2, 3, 4, 5, 6, 7, 8, 9.
The indication of how far something extends in space.
Dimension of a Subspace
The dimension of a subspace W is the number of vectors in any basis of W.
Diophantine Equation
An equation which is required to be solved by integers.
Dirac Delta Function
The limiting case of a pulse with unit area that is infinitely short and at the same time infinitely high.
Direct Measurement
A process of obtaining the measurement of some entity by reading a measuring tool, such as a ruler for length, a scale for weight, or a protractor for angle size.
Direct Proportion
Two variables are said to be in a direct proportion if the proportions of corresponding pairs of values are always equal.
The way a number goes - positive or negative.
A circle together with its interior.
A break in sequence or continuity of anything.
Discontinuous Graph
A line in a graph that is interrupted, or has breaks in it forms a discontinuous graph.
A type of random variable which may take on only a limited set of values, such as 1,2,3,...,10.
Disjoint Events
Two events are disjoint if they can't both happen at the same time.
Distance Between Two Points
The straight line distance between two points in cartesian coordinates.
Distributive Law
States that if a group of terms connected by like operators contains the same variable, the variable may be removed from the terms and associated with them by the appropriate sign of operation.
The divergence operation is performed on a vector and produces a scalar.
A number or quantity that is to be divided by another number or quantity.
A number or quantity that is to be divided into another number or quantity.
The set of all allowable inputs for a function.
Domain of the Function
The set of numbers x for which f(x) is defined.
A description of a point in which the point has a definite size.
Duodecimal Number System
The system of numeration with base 12.
Natural base of logarithms e=2.718281...
Possible values for a parameter of an equation for which the solutions will be compatible with the boundary conditions.
A member of or an object in a set.
Elementary Matrix
A matrix that is obtained by performing an elementary row operation on an identity matrix.
A plane through a right angle cone.
Engineering and Physical Sciences Research Council
EPSRC funds research and postgraduate training in engineering and the physical sciences at universities and other organisations throughout the UK.
The curve described by a point on a circle of radius b as it rolls on the outside of a circle of radius a.
Engineering and Physical Sciences Research Council
The relationship between two quantities that have the same value or values.
Equally Likely
In probability, when there are the same chances for more than one event to happen, the events are equally likely to occur.
The same distance from something.
Equal in length.
Equivalent Linear Systems
Two systems of linear equations in n unknowns are equivalent if they have the same set of solutions.
Around 230BC developed a method for finding all prime numbers.
No measurement is exact, they all contain some degree of errors.
Values for C in the Julia Set or Mandelbrot set where at each iteration the resulting value grows larger and larger, approaching infinity.
An indication of the value of an unknown quantity based on observed data.
The process by which sample data are used to indicate the value of an unknown quantity in a population.
Any quantity calculated from the sample data which is used to give information about an unknown quantity in the population.
Greek mathematician.
Euclidean Algorithm
A set of rules which when applied to two integers produces their common divisor.
Eulers Constant
γ = 0.5772156..
Even Function
A function f(x) is called an even function if f(x)=f(-x) for all x.
Even Node
A node that has an even number of arcs.
Even Number
An integer that is divisible by 2.
In probability, an event is a set of outcomes from a given experiment.
Exclusive Or
One or the other, but not both.
An increase in size.
In the expression am, m is the exponent and a is the base. am is the mth power of a. If this is set equal to y (y=am) then this is called an exponential function.
Exponential Form of Complex Numbers
Exponential expression of complex numbers.
A validated series of variables, constants, and functions that can be connected by operating symbols to describe a desired computation.
Numbers or other things that get multiplied.
A polynomial has been factored or is in factored form, when it is written as a product of lower degree polynomials.
Definition of factorial.
Famous Scientists & Engineers
Lists all the Famous Scientists & Engineers in the Encyclopaedia
Farey Sequence
The sequence obtained by arranging in numerical order all the proper fractions having denominators not greater than a given integer.
Feigendaum Constants
Two mathematical constants.
Fermat Number
The integers Fn=22n+1 are Fermat numbers.
Fermat′s Last Theorem
States that xn+yn=zn has no whole number solutions for n greater than 2.
An abbreviation of Fast Fourier Transform, an algorithm, or digital calculation routine, that efficiently calculates the discrete Fourier transform from the sampled time waveform.
His book "Liber Abaci" he introduced Arabic notation for numerals and their algorithms for arithmetic.
Fibonacci Number
A member of the sequence 0, 1, 1, 2, 3, 5,... where each number is the sum of the previous two numbers.
Figurate Numbers
Polygonal numbers.
A geometric form consisting of any combination of points, lines, or planes.
Finite Group
A group containing a finite number of elements.
Floor Function
The floor function of x is the greatest integer in x, i.e. the largest integer less than or equal to x.
Four Colour Theorem
It is desired to colour a political map on a plane so that countries sharing a common boundary are coloured differently.
Discovered by Benoit Mandelbrot in 1964.
Frequency View
An approach taken by mathematicians and scientists to determine the chances of an event happening by repeating the experiment many times and using the results to calculate the probability.
Galileo Galilei
Astronomer, mathematician and physicist he dwelt, not on the useless question, why do things happen? but, how do things happen?
Game Theory
A branch of mathematics that seeks to model decision making in conflict situations.
The Greatest Common Factor of two numbers is the largest number that divides into both numbers evenly, with no remainder. For example, the greatest common factor of 60 and 84 is 12.
Generalised Coordinates
The minimum number of independent coordinates necessary to completely describe a systems position constitutes a set of generalized coordinates.
The bent line-segment or figure that replaces the initiator at each iteration of a fractal.
Genetic Algorithm
A type of optimization algorithm that uses Darwinian principles to evolve a solution to a mathematical model based on survival of the fittest.
A flat board into which nails have been driven in a regular rectangular pattern.
The arc on a surface of shortest length joining two given points.
The study of the shape of the Earth, e.g. its deviations from an exact sphere.
Geometric Multiplicity of an Eigenvalue
For an eigenvalue c of a matrix A this is the dimension of the eigenspace of c.
Geometric Progression
A sequence in which the ratio of each term to the preceding term is a given constant.
Geometric Sequence
A set where each element is a multiple of the previous element.
Geometric Series
A series in which the ratio of each term to the preceding term is a given constant.
Geometric Solid
The bounding surface of a 3-dimensional portion of space.
The branch of mathematics that deals with the nature of space and the size, shape, and other properties of figures as well as the transformations that preserve these properties.
Information assumed to be true in a proof.
Gnomon Magic Square
A 3 X 3 array in which the elements in each 2 X 2 corner have the same sum.
Golden Mean
The proportion of the division of a line so that the smaller part is to the larger part what the larger part is to the whole. This may be applied to the lengths of the sides of a rectangle.
Golden Rectangle
A rectangle whose sides are in the golden ratio.
A number equal to 10100.
A number equal to 10googol. Where a googol is 10100.
Graceful Graph
A graph is said to be graceful if you can number the n vertices with the integers from 1 to n and then label each edge with the difference between the numbers at the vertices, in such a way that each edge receives a different label.
Grad Operator
The del or grad operation means to take the derivative with respect to distance, in 3 dimensions.
Grade of a Slope
The pitch of a slope, and is often expressed as a percent tangent, or rise over run.
The rate of change of a quantity.
A pictorial presentation of the relation between two or more variables.
Graph Completeness
A graph is complete if any two of its vertices are connected by exactly one edge. A complete graph with N vertices is often denoted as KN.
Graph Paper
Paper that is printed with fine lines making up a regular grid.
Graph Theory
The mathematics of complicated networks.
Greater Than
An inequality that says the variable on the left is greater than the variable to the right of the inequality.
Greater than or Equal to
An inequality that says the variable on the left is greater than or equal to the variable to the right of the inequality.
Greatest Common Divisor
The greatest common factor of two numbers is the largest number that divides into both numbers evenly, with no remainder.
Greatest Common Factor
The greatest common factor of two numbers is the largest number that divides into both numbers evenly, with no remainder. For example, the greatest common factor of 60 and 84 is 12.
Greatest Lower Bound
The greatest lower bound of a set of real numbers, is the largest real number that is smaller than each of the numbers in the set.
A tesselation of congruent squares sometimes used to measure distance.
One of two equal parts.
Hankel Matrix
A matrix in which all the elements are the same along any diagonal that slopes from northeast to southwest.
Heaviside Function
Also known as the unit step function.
Heaviside Oliver
An English electrical engineer who introduced Laplace transforms into electrical engineering.
Counting system based on 16.
Hexagonal Number
A number of the form n(2n-1).
Hidden Line
Broken line used to signify a line that normally would not be seen in a drawing.
Torus has a hole, sphere does not. If every curve on a surface can be continuously shrunk into a point the surface has no holes.
A one-to-one continuous transformation that preserves open and closed sets.
Homogeneous Equations
A differential equation may be described as homogeneous.
Homogeneous Linear System
A system of linear equations Ax = b is homogeneous if b = 0.
A function that preserve the operators associated with the specified structure.
Horizontal Line
A line whose slope is zero.
Horizontal Plane
A plane parallel to the surface of the earth.
A funnel-shaped section.
Huffman Coding
For a given character distribution, by assigning short codes to frequently occurring characters and longer codes to infrequently occurring characters, Huffman's minimum redundancy encoding minimizes the average number of bytes required to represent the characters in a text.
An open curve with two branches, all points of which have a constant difference in distance from two fixed points called focuses.
Hyperbolic Spiral
The curve whose equation in polar coordinates is r*theta=a.
A geometric solid whose equation is x2/a2+y2/b2-z2/c2=1 or x2/a2+y2/b2-z2/c2=-1.
The longest side of a right triangle.
A hypothesis is a proposed answer to a problem, or an explanation that accounts for a set of facts and that can be tested by further experimentation and observation.
Hypothesis Tests
Tests based on a sample of data to determine which of two different states of nature is true.
i denotes the imaginary number formed by square rooting negative one.
Idempotent Law
Combining a quantity with itself either by logical addition or logical multiplication will result in a logical sum or product that is the equivalent of the quantity.
A number that when an operation is applied to a given number yields that given number. For multiplication, the identity is one and for addition the identity is zero.
Identity Law
States that any expression is equal to itself.
If and only if.
Imaginary Axis
The y-axis of an Argand diagram.
Imaginary Number
i denotes the imaginary number formed by square rooting negative one.
Imaginary Part
The imaginary part of a complex number.
Inclusive Or
One or the other, or both.
Inconsistent Linear System
A system of linear equations is inconsistent if it has no solutions.
An unspecified amount, having no exact limits.
Independent Events
Two events A and B are independent if the probability that they happen at the same time is the product of the probabilities that each occurs individually.
Independent Variable
One that is associated with the inputs to a function.
A relationship between two expressions that are not equal.
Becoming large beyond bound.
A variable that approaches zero as a limit.
A reference to a quantity larger than any specific integer.
A point of inflection of a plane curve is a point where the curve has a stationary tangent, at which the tangent is changing from rotating in one direction to rotating in the oppostie direction.
A line-segment or figure that begins as the beginning geometric shape for a fractal.
Inner Product
The inner or dot product of two vectors is obtained by adding the products of the respective components of the vectors.
The number or value that is entered, for example, into a function machine.
A whole number.
The point where two lines drawn on a graph cross each other.
Intersecting Planes
Planes that share a line.
Intersection Law
States that if one input to an AND gate is already TRUE, then the output will depend upon the state of the other inputs only.
Inverse of a Matrix
The matrix B is an inverse for the matrix A if AB = BA = I.
Inverse Proportionality
A relationship in which a quantity is related to the reciprocal of a second quantity.
Inverse Square
A relationship in which a quantity is related to the reciprocal of the square of a second quantity.
Inverted or reversed in position or relationship.
To change a physical or logical state to its opposite state.
A function, f(x), is invertible if there is a function, g(x), which is its inverse.
Invertible Matrix
A matrix is invertible if it has an inverse.
Irrational Number
Any number that cannot be expressed as the ratio of two integers.
Irregular Fractals
Complex fractals whose dimension is often difficult to determine and in some cases is unknown.
A transformation that keeps the same size and shape of a figure but moves it to a new location.
A mapping between objects which shows a relationship between two properties or operations.
Repeating a set of rules or steps over and over.
j is used in engineering and physics to represent i the imaginary number.
Joint Variation
A variation in which the values of one variable depend upon those of 2 or more variables.
Jordan Curve
A simple closed curve.
Jordan Matrix
A matrix whose diagonal elements are all equal (and nonzero) and whose elements above the principal diagonal are equal to 1, but all other elements are 0.
Julia Set
The set of all the points for a function of the form Z^2+C.
Jump Discontinuity
A discontinuity in a function where the left and right-hand limits exist but are not equal to each other.
Kalman Filter
A technique for estimating an unknown state of a linear dynamic system given observations of the system which have additive (Gaussian) noise.
Knight′s Tour
A knight's tour of a chessboard is a sequence of moves by a knight such that each square of the board is visited exactly once.
Laplace Transform
The Laplace transform is used to convert certain types of inital value problems into algebra problems.
The divergence of a gradient.
Latin Square
An n by n array of numbers in which only n numbers appear. No number appears more than once in any row or column.
The angular distance of a point on the Earth from the equator.
Lattice Point
A point with integer coordinates.
Least Significant Bit (LSB)
The bit within a digital word that represents the smallest possible coded value.
Least Upper Bound
The least upper bound of a set of numbers is the smallest number that is larger than every member of the set.
The plural of Lemma.
A proposition that is useful mainly for the proof of some other theorem.
Lempel-Ziv Welch Compression
Algorithm used by the Unix compress command to reduce the size of files, eg. for archival or transmission.
Leonardo of Pisa
Fibonacci was also known as Leonardo of Pisa.
A distribution that is more peaked than a normal distribution.
Less Than
An inequality that says the variable on the left is less than the variable to the right of the inequality.
Less than or Equal to
An inequality that says the variable on the left is less than or equal to the variable to the right of the inequality.
The number you approach as you plug values into a function, and the values get closer and closer to a given number.
Line is one of the basic undefined terms in Euclidian geometry, but one intuitive definition is as follows: A straight set of points that continue on to infinity in both directions. Although a line is of infinite length, it has thickness and width of zero.
Line Graph
A diagram showing a system of connections or interrelations between two or more things by using lines.
Line of Best Fit
A straight line used as a best approximation of a summary of all the points in a scatter-plot.
Line of Reflection
The line that is reflected over in a reflection.
Line Plot
A graphical display of a set of data where each separate piece of data is shown as a dot or mark above a number line.
Line Segment
A piece of a line which includes two definite endpoints and all points in between them.
Having an output that varies in direct proportion to the input.
Linear Combination of Vectors
A vector v is a linear combination of the vectors v1, ..., vk if there exist scalars a1, ..., ak such that v = a1v1 + ... + akvk.
Linear Regression
An attempt to model the relationship between two variables by fitting a linear equation to observed data.
Linear Space
A collection of vectors which means that the space is an additive Abelian group and, in addition, its elements can be multiplied by scalars.
Abbreviation of Natural Logarithm.
The set of all points meeting some specified condition.
Abbreviation of Logarithm.
The study of the formal laws of reasoning.
Logistic Equation
A classical starting point for the dynamics of quasiperiodic and chaotic systems.
Lorentz Transformation
A set of equations which are used, in relativity problems, to transform measurements from one frame of reference to another.
Lowest Terms
A fraction is said to be in lowest terms if its numerator and denominator have no common factor.
Abbreviation of Least Significant Bit, the bit within a digital word that represents the smallest possible coded value.
Lucas Number
A member of the sequence 2, 1, 3, 4, 7,... where each number is the sum of the previous two numbers.
The portion of a sphere between two great semicircles having common endpoints, including the semicircles.
Magic Square
A square array of n numbers such that sum of the n numbers in any row, column, or main diagonal is a constant.
Magic Tour
If a chess piece visits each square of a chessboard in succession, this is called a tour of the chessboard.
Main Diagonal
In the matrix [aij], the elements a11, a22, ..., ann.
Major Axis
The major axis of an ellipse is it′s longest chord.
Mandelbrot Set
The most famous fractal, named after Benoit Mandelbrot. It is created by iterating an equation many times.
Mathematical Model
A mathematical representation of a process or physical object.
Mathematical Symbols
Common symbols used in mathematics.
A rectangular array of elements.
The maxima are points where the value of a function is greater than other surrounding points.
In a sample of data, the largest observation.
A statistic which measures the centre of a set of data by finding that value which divides the data in half.
Mersenne Number
A number of the form 2p-1 where p is a prime.
Mersenne Prime
A Mersenne number that is prime.
A distribution that is normal.
Metric Completeness
A metric space is complete if all Cauchy sequences of its elements converge.
Metric Space
A space X is metric if there is defined a real non-negative function of two variables d(A, B).
The minima are points where the value of a function is less than other surrounding points.
In a sample of data, the smallest observation.
Minor Axis
The minor axis of an ellipse is its smallest chord.
A number from which another number is to be subtracted.
The symbol: -
Mixed Numbers
Numbers that have both whole numbers and fractions, such as 3 3/4.
Modular Arithmetic
This is can be used as method for finding remainders where all the possible numbers (the numbers less than the divisor) are put in a circle, and then by counting around the circle the number of times of the number being divided, the remainder will be the final number landed on.
Modular Number System
A number system represented best by numbers on a circle because the numbers repeat.
The integers a and b are said to be congruent modulo m if a-b is divisible by m.
The absolute value of a quantity, not considering it's sign or direction.
Monic Polynomial
A polynomial in which the coefficient of the term of highest degree is 1.
An algebraic expression consisting of just one term.
A sequence is monotone if its terms are increasing or decreasing.
Designating sequences, the successive members of which either consistently increase or decrease but do not oscillate in relative value.
A sequence is monotone if its terms are all increasing or all decreasing.
Moving Average
The average of the most recent n data values.
Natural Number
Any one of the numbers 1, 2, 3, 4, 5, ..
The process of inverting the value of a function or variable.
A quantity or value that is less than zero.
Negative Numbers
Numbers that are less than zero are negative numbers.
A group of nodes and arcs.
Newton, Isaac
Newton was a mathematician and natural philosopher (physicist).
A graphical device used for computation which uses a straight edge and several scales of numbers.
Nonagonal Number
A number of the form n(7n-5)/2.
Associated with 9.
Nondimensional Number
A pure number not involving any physical dimensions.
Nondimensional Parameter
Any parameter of a problem which has the dimensions of a pure number, usually rendered so deliberately.
A number equal to 1030.
Nonsingular Matrix
A square matrix A is nonsingular if the only solution to the equation Ax = 0 is x = 0.
A characteristic of a time series for which the distribution changes over time.
not equal to
A definite statement that the quantity on the left hand side is not equal to the quantity on the right hand side.
Null Hypothesis
Proposes a general or default position, such as that there is no relationship between two measured phenomena, or that a potential treatment has no effect.
Nullity of a Linear Transformation
This is the dimension of its null space.
A mathematical entity that may indicate quantity or amount of units.
Number Line
A line on which each point represents a real number.
Number Representation
The representation of numbers by agreed sets of symbols according to agreed rules.
Number System
Any system for the representation of numbers.
A numeral is just an object or symbol that stands for a number. For example, 5 is the Arabic numeral for five, and V the Roman numeral for five.
The quantity or value on the top of a fraction.
Numeric Coding
A system of coding in which information is represented by digits.
Numerical Analysis
The study of methods for approximation of solutions of various classes of mathematical problems including error analysis.
Oblate Spheroid
An ellipsoid produced by rotating an ellipse through 360 about its minor axis.
Oblique Coordinates
A coordinate system in which the axes are not perpendicular.
Observations refer to repeated values of a data variable. The rows of a column represent the observations.
A number system using the base-8, i.e., each digit can be any of 8 values, represented by the digits 0-7.
Any one of the 8 portions of space determined by the 3 coordinate planes.
A number equal to 1027.
Odd Function
A function f(x) is called an odd function if f(x)=-f(-x) for all x.
Odd Number
An integer that is not divisible by 2.
of the order of
Used when estimating a quantity and means that it is roughly equal to.
Offset Binary Coding
For bipolar signals, offset binary is a digital coding scheme in which the most negative value is represented by all zeros (00000000) and the most positive value is represented by all ones (11111111).
One to One
A function f is said to be one to one if f(x)=f(y) implies that x=y.
Open Interval
An interval that does not include its two endpoints.
Opposite Faces
Faces that lie in parallel planes.
Ordered Pair
A pair of numbers in which one number is distinguished as the first number and the other as the second number of the pair.
Ordinal Number
A number indicating the order of a thing in a series.
The y-coordinate of a point in the plane.
In Cartesian coordinates, it is the point (0, 0) and located at the intersection of the x- and y-axes.
The point of intersection of the altitudes of a triangle.
Mutually perpendicular.
Orthogonal Matrix
A matrix A is orthogonal if A is invertible and its inverse equals its transpose; i.e., A-1 = AT.
Orthogonal Set of Vectors
A set of vectors in Rn is orthogonal if the dot product of any two of them is 0.
Orthonormal Set of Vectors
A set of vectors in Rn is orthonormal if it is an orthogonal set and each vector has length 1.
Any one of the possible results of an experiment.
Outcome Space
Another name for Sample Space.
A data value which is unusual with respect to the group of data in which it is found.
The number or value that comes out from a process.
A positive integer whose digits read the same forward and backwards.
A positive integer is said to be palindromic with respect to a base b if its representation in base b reads the same from left to right as from right to left.
Pandiagonal Magic Square
A magic square in which all the broken diagonals as well as the main diagonals add up to the magic constant.
A decimal integer is called pandigital if it contains each of the digits from 0 to 9.
A paraboloid of revolution is a surface of revolution produced by rotating a parabola about its axis.
A statement that appears to contradict itself, for example, suggesting a solution which is actually impossible.
Parallel Planes
Planes that have no points in common.
A prism whose bases are parallelograms.
A quadrilateral in which opposite sides are parallel.
The symbols ( and ) used for grouping expressions.
Applies to situations where two items or their properties may be juxtaposed as being opposites (in a certain context) of each other.
Pascal′s Triangle
Each number is the sum of the two numbers above. The sum of each row is equal to a power of 2.
Recognizable regularities in situations such as in nature, shapes, events, sets of numbers.
Extreme value of a varying quantity, measured from the zero or mean value.
Pearson Product Moment Correlation Coefficient
A dimensionless index that reflects the extent of a linear relationship between two data sets.
Pell Number
The nth term in the sequence 0, 1, 2, 5, 12,... defined by the recurrence P0=0, P1=1, and Pn=2Pn-1+Pn-2.
Penrose Impossible Staircase
A four sided staircase that always goes up if you travel around it in one direction and always down if you travel in the opposite direction.
Pentagonal Number
A number of the form n(3n-1)/2.
A star shaped figure constructed by extending all of the sides of a regular pentagon until they meet at the points of the star.
A ratio that compares a number to one hundred.
A value on a scale that indicates the percent of a distribution that is equal to it or below it.
Perfect Number
A positive integer that is equal to the sum of its proper divisors.
Perfect Power
An integer is a perfect power if it is of the form mn where m and n are integers and n>1.
Perfect Square
An integer is a perfect square if it is of the form m2 where m is an integer.
The distance around the outside of a shape.
Permutations and Combinations
A permutation is a particular sequence of a given set of objects. A combination is the set itself without reference to order.
At right angles to. A line at right angles to another line or to a plane.
A feeling of depth.
Perspective Drawing
A drawing in which, in order to show perspective, oblique parallel lines will meet.
A letter of the Greek alphabet. The lowercase is used to denote the number of times the diameter of a circle can be divided into the circumference.
Pie Chart
A strong representation of data with the size of the slice representing the fraction of the total.
Piecewise Function
A function is piecewise-defined, if its rule is given by more than one other formula for different sets of input.
Place Value
Within a number, each digit is given a place value depending on it′s location within the number.
A two-dimensional group of points that goes on infinitely in all directions; made up of infinite lines.
Plane Section
The intersection of a figure with a plane.
A Greek philosopher, pupil of Socrates and Aristotle′s teacher.
A distribution that is less peaked than a normal distribution.
The symbol: +
A zero-dimensional figure.
Poisson Equation
A fundamental equation of mathematical physics, describing the spatial variation of a potential function for given source terms.
Polar Axis
In the polar coordinate system, a ray from the pole in a fixed direction, analogous to the x-axis in the Cartesian system.
Polar Coordinates
The position of a point is defined as the distance from the origin and an angle relative to the x axis.
Polar Form of Complex Numbers
Complex numbers written in polar form.
In the shape of a solid formed by plane faces, as in a prism.
A function that is a sum of power functions, with positive integer exponents, multiplied by constants.
Positional Notation
A numbering system in which a number is represented by means of a stated set of symbols or digits, such that the value contributed by each symbol or digit depends upon its position as well as upon its value.
Positional Weighting
The value given a digit based on the digit′s position within a given number.
A quantity or value that is greater than zero.
Positive Logic
The form of logic in which the more positive logic level represents 1 and the more negative level represents 0.
Positive Number
A number larger than 0.
A statement assumed to be true without proof.
Practical Number
A positive integer m such that every natural number n not exceeding m is a sum of distinct divisors of m.
Prime Numbers
A prime number has only two different factors. They are 1 and the number itself. 13 is a prime number because the only factors of 13 are 1 and 13. Note that 1 is not a prime number.
Primitive Root of Unity
The complex number z is a primitive nth root of unity if zn=1 but zk is not equal to 1 for any positive integer k less than n.
Principal Component Analysis
Constructing new features which are the principal components of a data set.
Principal Curve
A nonlinear principal component axis.
Prolate Spheroid
An ellipsoid of revolution, the longer axis of which is the axis of revolution.
Pronic Number
A number of the form n(n+1).
Proper Divisor
The integer d is a proper divisor of the integer n if 0
A statement of equality between two ratios.
A relationship in which a quantity is related to the second quantity.
A tool used to measure angles.
A method of scaling the amplitude axis of spectra of random rather than deterministic signals.
A letter of the Greek alphabet.
Greek philosopher and mathematician; held that numbers were basic to matter.
Pythagoras Theorem
The Square on the Hypotenuse is equal to the sum of the squares of the other two sides.
Pythagorean Triple
An ordered set of three positive integers (a,b,c) such that a2+b2=c2.
Abbreviation for quod erat demonstrandum, used to denote the end of a proof.
In Cartesian Coordinate geometry, the coordinate plane is divided into four quadrants.
Square free.
Quadric Curve
The graph of a second degree equation in two variables.
Quadric Surface
The graph of a second degree equation in three variables.
A four sided polygon.
A number equal to 1015.
A unit of volume.
One of four equal parts. An outdated British unit of weight 1 quarter = 28 pounds (lb).
A polynomial equation of degree 4.
A polynomial equation of degree 5.
Statistics which divide the observations in a numeric sample into 5 intervals.
A number equal to 1018.
Quod Erat Demonstrandum
Normally abbreviated as QED and used to denote the end of a proof.
The result when one number or quantity is divided by another.
An abbreviation of radian the SI unit of plane angle.
A direction perpendicular to the centreline of a shaft.
Plural of radius.
The number of distinct symbols used in a number system.
Random Noise
A noise signal, commonly used in measurements, which has constantly shifting amplitude, phase, and a uniform spectral distribution of energy.
Random Number Generators
A device used to produce a selection of numbers in a fair manner, in no particular order and with no favour being given to any numbers.
Random Process
A random process is a collection of time-history records that can be described by appropriate statistical parameters, such as averaged properties of these records at a number of fixed times.
Random Sampling
A sampling method in which all elements in the population have an equal chance of being selected.
Rate of Change
The speed at which a function is changing.
The quotient of two numbers.
Rational B-Spline
equation that permits the modeling of free-form curves between two endpoints as a function of a set of intermediate points whose values influence the shape of the curve.
Rational Number
Any number that can be expressed as the ratio of two integers.
Rayleigh′s Method
A method used for calculating approximate natural frequencies for a vibrating system assuming a deflected shape and balancing kinetic and strain energies.
Real Axis
The x-axis of an Argand diagram.
Real Number
Any of the conventional numbers, including fractions and irrationals.
Real Part
The real number x is called the real part of the complex number x+iy where x and y are real and i=sqrt(-1).
Real Variable
A variable whose value ranges over the real numbers.
Recency Effect
An increase in correct recall rate for the most recently presented items of a list compared with those presented earlier in the list.
A number that is made into a fraction.The reciprocal of 2 is 1/2.
Rectangular Coordinates
Coordinates where the position of a point is described by the distance it is from 2 lines in 2 dimensional space or from 3 planes in 3 dimensional space.
Given some starting information and a rule for how to use it to get new information, the rule is then repeated using the new information.
In a tessellation, reflect means to repeat an image by flipping it across a line so it appears as it would in a mirror.
Relative Frequency
A count of the number of occurrences of a data value in a sample, or the number of values falling within a fixed range, expressed as a proportion of the total number of observations.
Relatively Prime
If the greatest common divisor of a and b is 1 then a and b are known as relatively prime.
An integer all of whose digits are the same.
Repeating Decimal
A decimal whose digits eventually repeat.
An integer consisting only of 1′s.
A rotary, electromechanical device used to perform trigonometric computations by varying the magnetic couplings between its primary and secondary windings.
A rotation through a full circle, or 360 degrees.
A parallelogram with four equal sides.
Roman Numerals
The roman number system with decimal equivalents.
A root of a polynomial function, f, is just a solution to the equation f(x) = 0, that is an input that yields an output of 0.
Root of Unity
A solution of the equation xn=1, where n is a positive integer.
Rosenbrock Function
A non-convex function used as a performance test problem for optimization algorithms introduced by Rosenbrock in 1960.
Round Off Error
This is error introduced into a calculation by rounding off the results of intermediate steps to values which are close, but not exactly correct.
A numerical value means replacing it by another value that is approximately equal but has a shorter, simpler, or more explicit representation.
Round-Off Error
The error accumulated during a calculation due to rounding intermediate results.
Row Equivalent Matrices
Two matrices are row equivalent if one can be obtained from the other by a sequence of elementary row operations.
Ruled Surface
A surface formed by moving a straight line.
Sample Space
The set of all possible outcomes of a given experiment.
Scalar Product
The scalar or dot product of two vectors is obtained by adding the products of the respective components of the vectors.
The process of drawing a figure either enlarged or reduced in size from its original size.
Scatter Plot
A graphical representation of the distribution of two random variables as a set of points whose coordinates represent their observed paired values.
Scientific Notation
Numbers entered as a number from one to ten multiplied by a power of ten.
Secant Line
A line that intersects a curve or circle in two places.
Second Derivative
The derivative that comes after the first derivative and before the third derivative. Obtained by taking the derivative of a function twice in a row.
A non-overlapping piece of an object.
Self Similarity
Two or more objects having the same characteristics.
Semi-Magic Square
A square array of n numbers such that sum of the n numbers in any row or column is a constant (known as the magic sum).
Separable Equations
A differential equation is separable if it can be written: y′=A(x)B(y)
A unit of quantity equal to 7.
A number equal to 1024.
An ordered set whose elements are usually determined based on some function of the counting numbers.
The sum of a finite or infinite sequence.
The same as Hexadecimal.
In the sexagesimal system calculations are done in the base 60 as used by the Ancient Babylonians.
A unit of quantity equal to 6.
A number equal to 1021.
Shapiro-Wilks Test
A test to determine whether or not a sample comes from a normal distribution.
The sympol that states whether a number is positive (+) or negative (-). If a sign is not placed immediately before a number, it is taken as positive.
Significant Digits
The number of digits to consider when using measuring numbers.
Signs and Symbols
A list of signs and symbols.
The relationship between two objects that have exactly the same shape but not necessarily the same size.
Singular Matrix
A square matrix A is singular if the equation Ax = 0 has a nonzero solution for x.
Having the form of a sine wave.
Skeleton Division
A long division in which most or all of the digits have been replaced by asterisks to form a cryptarithm.
An expression of the so-called "third moment".
Skewness defines the degree of asymmetry of the distribution around its central value.
Slide Rule
A calculating device consisting of two sliding logarithmic scales.
The measure of the tilt of a line, the rise over run or how much the line moves up for every movement to the right.
Slope of a Linear Function
The slope of the line y = mx + b is the rate at which y is changing per unit of change in x.
Smoothing techniques are used to reduce irregularities in time series data.
Greek philosopher; emphasized the study of human nature in relationship to society.
Solid of Revolution
A solid formed by rotation a plane figure about an axis in three-space.
The set of all possible points; made up of infinite planes.
Special Constants
A list of Mathematical constansts and their formulations.
Spherical Coordinates
A point is located in space by the distance from the origin and two angles.
A number raised to the power 2 ie 2 x 2 = 22 = 4. Also, a 2 dimensional figure with the height and width having the same lengths,and at right angles to each other.
Square Free
An integer is said to be square free if it is not divisible by a perfect square, n2, for n>1.
Square Root
The square root of a number is a number that when multiplied by itself equals the number that the square root is being taken of.
Square Root of 2
Square Root of Negative One
The square root of -1 is i.
Standard Integrals
A listing of the standard indefinite and definite integrals.
Standardized Kurtosis
A standardized form of the kurtosis statistic which renders the statistic free of scale.
Standardized Skewness
A standardized form of the skewness statistic which renders the statistic free of scale.
Lists all Statistics topics in the Encyclopaedia
Statistics Books
Lists all Statistics Books in the Encyclopaedia
Statistics Calculations
Lists all Statistics Calculations in the Encyclopaedia
Statistics Conversions
Lists all Statistics Conversions in the Encyclopaedia
Statistics Weblinks
Lists all Statistics Weblinks in the Encyclopaedia
Straight Line
A straight set of points that continue on to infinity in both directions.
A number that is to be subtracted from another number.
The result of the addition of numbers.
Numbers or letters written above and to the right of other numbers or letters or symbols indicating how many times the latter is to be used as a factor.
Used in mathematics to describe an irrational quantity.
Surface Area
The total area of the surface of a solid.
Symbolic Logic
A mathematical form in which propositions and their relationships may be represented symbolically.
Symmetric Matrix
A matrix A is symmetric if it equals its transpose.
A number equal to 103.
The measure of an angle as compared to a horizontal line.
A brief overview of the major milestones in science and engineering.
Toeplitz Matrix
A matrix in which all the elements are the same along any diagonal that slopes from northwest to southeast.
Mathematical techniques for reconstructing three dimensional volumes from the integrated projections along rays.
The configuration of a surface, including its relief and the position of its natural and man-made features.
Topological Space
Every point has a collection of neighbourhoods to which it belongs.
The overall sum of numbers or a quantity.
The trace of a matrix is the sum of the terms along the principal diagonal.
Not algebraic.
A transform is a mathematical operation that converts a function from one domain to another domain with no loss of information.
A change in the size, shape, location or orientation of a figure.
In a tessellation, to translate an object means repeating it by sliding it over a certain distance in a certain direction.
A line that intersects 2 others.
A network in which all arcs can be traced without going over one more than once.
Tree Diagram
A schematic way of showing the number of ways a compound event may occur.
A unit of quantity equal to three.
Triangular Number
A number of the form n(n+1)/2.
In general, the unique location of the source from some combination of at least three ranges and/or bearings in three dimensional space.
Lists all Trigonometry topics in the Encyclopaedia
Method of surveying wherein the lengths of the triangle sides are measured.
A number equal to 1012.
A group of three items.
To eliminate without round-off some low-order bits, often after performing an arithmetic computation.
Truncated Paraboloid
A paraboloid reflector that has been cut away at the top and bottom.
Truncation Error
Error resulting from the use of only a finite number of terms of an infinite series or from the approximation of operations.
Twin Primes
Two prime numbers that differ by 2. eg 11 and 13.
Unilateral Surface
A surface with only one side, such as a Moebius strip.
A finite sequence is unimodal if it first increases and then decreases.
Unimodular Matrix
A square matrix is unimodular if its determinant is 1.
Unitary Divisor
A divisor d of c is called unitary if gcd(d,c/d) = 1.
Unitary Matrix
A nonsingular matrix whose Hermitian adjoint equals its inverse.
Universal Statement
A conditional that uses the words "all" or "everything".
Vanishing Line
The horizon; in a drawing it is at the height of viewer′s eye.
Vanishing Point
The point in space where two parallel lines seem to meet.
A letter that is used to represent a numerical quantity whose value may or may not yet be known.
Random variable.
Venn Diagram
A diagram where sets are represented as simple geometric figures, with overlapping and similarity of sets represented by intersections and unions of the figures.
As a function of, as distance versus time.
The direction of gravity at the point of observation.
Vertical Axis
On a graph, the straight line axis that is plotted from bottom to top, the y axis.
Vertical Line
A line that goes straight up and down, and whose slope is defined as infinite or undefined.
Vertical Plane
An imaginary plane that is perpendicular to the horizontal plane.
Related to intervals of 20.
The horizontal bar in a fraction separating the numerator from the denominator.
Warning Limits
Limits placed on a control chart for variables or attributes at 1 and 2 sigma to help determine how far points lie from the centerline.
Waterfall Plot
A series of spectral maps taken at regular intervals of time or at regularly spaced shaft speeds, similar to the flow of a waterfall.
Weak Inequality
An inequality that permits the equality case. For example, a is less than or equal to b.
Winding Number
The number of times a closed curve in the plane passes around a given point in the counter clockwise direction.
Roman numeral for 10.
x axis
The horizontal axis in the plane.
The point at which a line crosses the x-axis.
y axis
The vertical axis in the plane.
The point at which a line crosses the y-axis.
Z Axis
Axis perpendicular to both X and Y axes.
Zero Element
The element 0 is a zero element of a group if a+0=a and 0+a=a for all elements a.
The point at which a line crosses the z-axis.

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