Glossary of Mathematical Terms
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Data structure.
Data structure is both a programming language construct that unifies several related attributes and a basic data type. Realization of the utility of data structures in programming led eventually to the modern object oriented trend. Among the basic data types are the stack, list, queue, tree.

Equation.
An equation is a statement that two mathematical object, e.g. algebraic expressions, are equal under certain conditions. Equations are usually and sometimes tacitly accompanied by the requirement to establish these conditions. In the case where mathematical objects contain arbitrary variables, such a requirement may mean finding those values of the variables that turn the equation into equality. Equations are written as two mathematical objects connected by the equality sign "=". Equations are sometimes called more explicitly as conditional equations.

Equality.
An equality is a statement of two mathematical objects being equal. Like equations, equalities are written as two mathematical objects connected by the equality sign "=". The meaning of two objects being equal depends very much on the nature of the objects. E.g., two matrices are equal iff they have identical dimensions and all their corresponding elements are equal. Two triangles are equal if there exists a distance preserving transformation that maps one on the other (Nowadays equal triangles more often than not are called congruent.) Equalities are sometimes called unconditional equations.

Edge
The line segment where two faces of a polyhedron meet.

Equation
A mathematical sentence containing an equal sign.

Equiangular or equilateral triangle
See regular polygon regular polygon.

Estimation
Determining an approximate amount, value or size of something.
Quantitative estimation is determining the approximate number of items in a group.
Computational estimation is determining the approximate result to an arithmetic calculation.
Measurement estimation is determining the approximate length, perimeter, area, volume or other measurement of a geometric figure.

Extreme value, local or global.
A function f:A->B is numeric if B is a set of numbers. For a numeric function it's possible to compare its values at different points aA. Extreme is a value which, in some sense is either maximum or minimum. If f(a) exceeds all other values of f then we say it's a global extreme, maximum. If it's only larger than values of f for points near a, the maximum is local.

Exterior angle of a polygon

The angle outside a polygon formed by extending one of its sides.

 

Field.
A field is a ring in which multiplication is a group operation. In France (and sometimes elsewhere in Europe), the multiplicative group need not be commutative. In the US and Russia it must be.


Floor.
For a real number r, its floor value [r] is defined as the largest integer no greater than r. Thus [5]=[5.1]=5 and [-5]=-5 while [-5.1]=-6.

Fractional Part.
For a real number r, its fractional part is defined as {r}=r-[r], where [r] is the floor value of r.

Free group.
Groups have generators, such elements that all other elements of a group could be obtained from generators and their inverses using the group operation. A group is said to be free if no relation exists between its generators other than between an element and its inverse. The additive group of integers is free with a single generator 1. The multiplicative group of all positive rational numbers has prime numbers as its generators. From the Fundamental Theorem of Arithmetic representation of integers in the form paqb...rc where p, q, ..., r are all different primes, is unique. Therefore the group is free. The group of sliding motions in the sliders puzzle is not free. Indeed, for the sequence Sj+S+iSj-S-i we obviously have the following identity (Sj+S+iSj-S-i)3=Id, where Id is the unit element of the group, i.e. the element that leaves all the counters unchanged.

 
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