Maths Glossary

Algorithm : A fixed process which if caried out systematically produces a desired result.Thus the "Euclidean algorithm" is a set of rules which when applied to two integers produces their common divisor.

Complex Number : A 2 dimensional number comprising a real and imaginary component of the form A+Bi,where i is the square root of -1.Such numbers are mapped on the Argand plane and form a matrix of numbers,the imaginary numbers being at right angles to the real ones.The conjugate takes the form a-bi.

Continuum Hypothesis : In Cantorian set theory,the cardinal number of a set designates its "manyness". The cardinality of the set of integers 1,2,3,... is designated by
À0.The cardinality of the set of real numbers is 2À0.The continuum hyopothesis asserts that there is no set whose cardinal falls between À0 and 2À0.

Cube : 1. A number raised to the power 3,ie 2 x 2 x 2 = 23 = 8
            2. A 3 dimensional figure with the height,width and depth having the same lengths,and all at right-angles to each other.

Denominator : The lower number in a
fraction, Numerator/ Denominator.

Diophantine Equation : An equation which is required to be solved by integers.Thus the diophantine equation 2x2 - 3y2 = 5 has the integer solution x=2,y=1.


Eigen (value or state) : Possible values for a parameter of an equation for which the solutions will be compatible with the boundary conditions.In quantum mechanics the energy eigenvalues for the Schrödinger equation are the possible energy levels for the system.


Factor: A number that divides into another number.EG 3 and 2 are factors of 6.

Fermat's theorem : The statement that the equation xn + yn = xn has no positive integer solution x,y,z if n is an integer greater than 2.Fermat's last problem is currently one of the most famous of the unsolved problems.

Four Colour Theorem : It is desired to colour a political map on a plane so that countries sharing a common boundary are coloured differently. Experience of map-makers has shown that four colours suffice.This assertion in its precise formulation was an unsolved problem in mathematics for over a hundred years.It has now been "proved" by an assist from a computer.

Fraction : A number made up of two numbers,a numerator and denominator,the former divided by the latter.

Imaginary Number : A number forming the latter component of a complex number of the form A+Bi,where i is the square root of -1.

Integer : The positive integers are 1,2,3,,...The negative integers are -1,-2,-3...Then there is 0 ,the zero integer. Numbers with no fractional part.

Irrational Number : A number which cannot be represented in fractional form,such as PI (3.14159..).

Numerator : The top number of a fraction,Numerator/ Denominator


Perfect Number : A number that is the sum of its factors.EG 6=1+2+3

Prime Number : A number that is only divisible by 1 and itself.

Pythagoras Theorem : The Square on the Hypotenuse is equal to the sum of the squares of the other to sides.[H2=Ö(a2 + b2) ]

Rational Number : A number that is capable of being represented as a fraction,via a numerator and denominator.

Real Number : Any of the conventional numbers,including fractions and irrationals.

Reciprocal : A number that is made into a fraction.The reciprocal of 2 is 1/2.

Root : The Nth root of a number,is that which when multiplied by itself N times produces the desired number.The square (2nd) root of 4 is 2 (2 x 2 = 4).The cube (3rd) root of 27 is 9 (3 x 3 x 3 =9).

Russell's Paradox : Popularly : The Cretan who said that all Cretan's are liars - is a liar - was he lying or telling the truth?
In a mathematical context : the set of all sets that are not members of themselves.This concept embodies a contradiction.

Square : 1. A number raised to the power 2,ie 2 x 2 = 22 = 4
               2. A 2 dimensional figure with the height and width having the same lengths,and at right angles to each other.


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The Mathematical Experience File Info: Created 25/4/2001 Updated 22/1/2002 Page Address: http://members.fortunecity.com/templarser/mathglos.html