AC

Axiom of Choice.

adj

adjugate of a matrix.

Ai

Airy function.

Alt

alternating group (Alt(n) is also written as A_n.)

arccos

inverse cosine function.

arccosec

inverse cosecant function. (Also written as arccsc.)

arccot

inverse cotangent function.

arccsc

inverse cosecant function. (Also written as arccosec.)

arcosech

inverse hyperbolic cosecant function. (Also written as arcsch.)

arcosh

inverse hyperbolic cosine function.

arcoth

inverse hyperbolic cotangent function.

arcsch

inverse hyperbolic cosecant function. (Also written as arcosech.)

arcsec

inverse secant function.

arcsin

inverse sine function.

arctan

inverse tangent function.

arg

argument of a complex number.

arg max

argument of the maximum.

arg min

argument of the minimum.

arsech

inverse hyperbolic secant function.

arsinh

inverse hyperbolic sine function.

artanh

inverse hyperbolic tangent function.

Aut

automorphism group.

Bi

Airy function of the second kind.

Card

cardinality of a set.(Card(X) is also written #X, #X or |X|.)

cdf

cumulative density function.

char

characteristic of a ring.

Cl

topological closure.

cos

cosine function.

cosec

cosecant function. (Also written as csc.)

cosech

hyperbolic cosecant function. (Also written as csch.)

cosh

hyperbolic cosine function.

cot

cotangent function.

coth

hyperbolic cotangent function.

cov

covariance of a pair of random variables.

csc

cosecant function. (Also written as cosec.)

csch

hyperbolic cosecant function. (Also written as cosech.)

curl

curl of a vector field. (Also written as rot.)

deg

degree of a polynomial. (Also written as ∂.)

del

del, a differential operator. (Also written as ∇.)

det

determinant of a matrix or linear transformation.

dim

dimension of a vector space.

div

divergence of a vector field.

dom

domain of a function.(Or, more generally, a relation.)

End

categories of endomorphisms.

Ei

exponential integral function.

erf

error function.

erfc

complementary error function.

exp

exponential function. (exp x is also written as e^x.)

Ext

Ext functor.

ext

exterior.

FOL

first-order logic.

Frob

Frobenius endomorphism.

Gal

Galois group. (Also written as Γ.)

gcd

greatest common divisor of two numbers. (Also written as hcf.)

GL

general linear group.

grad

gradient of a scalar field.

hcf

highest common factor of two numbers. (Also written as gcd.)

Hom

Hom functor.

iff

if and only if.

Im

image of a function or imaginary part of a complex number

inf

infimum of a set.

int

interior.

Ker

kernel.

lcm

lowest common multiple of two numbers.

lg

common logarithm (log₁₀) or binary logarithm (log₂).

LHS

left-hand side of an equation.

Li

offset logarithmic integral function.

li

logarithmic integral function or linearly independent.

lim

limit of a sequence, or of a function.

ln

natural logarithm, log^e.

log

logarithm. (If without a subscript, this may mean either log₁₀ or loge.)

LST

language of set theory.

Lub

least upper bound.(Also written sup.)

max

maximum of a set.

Min

minimum of a set.

mod

modulo.

Mx

matrix.

NTS

need to show.

Ord

ordinal number of a well-ordered set.

Pdf

probability density function.

Pf

proof.

PGL

projective general linear group.

Pmf

probability mass function.

Pr

probability of an event.

PSL

projective special linear group.

Ran

range of a function.

Re

real part of a complex number.

resp

respectively.

RHS

right-hand side of an equation.

Rk

rank.

Rng

non-unital ring.

Rot

rotor of a vector field.

RTP

required to prove.

sec

secant function.

sech

hyperbolic secant function.

seg

initial segment of.

sgn

signum function.

sin

sine function.

sinh

hyperbolic sine function.

SL

special linear group.

Sp

linear span of a set of vectors. (Also written with angle brackets.)

Spec

spectrum of a ring.

st

such that or so that.

STP

[it is] sufficient to prove.

sup

supremum of a set.(Also written lub.)

supp

support of a function.

Sym

symmetric group (Sym(n) is also written as S_n.)

tan

tangent function.

tanh

hyperbolic tangent function.

TFAE

the following are equivalent.

Thm

theorem.

Tor

Tor functor.

Tr

trace, either the field trace, or the trace of a matrix or linear transformation.

var

variance of a random variable.

walog

without any loss of generality.

wff

well-formed formula.

wlog

without loss of generality.

WO

well-ordered set.

wrt

with respect to or with regard to.

WTP

want to prove.

WTS

want to show.

ZF

Zermelo–Fraenkel axioms of set theory.

ZFC

Zermelo–Fraenkel axioms (with the Axiom of Choice) of set theory

A

Abscissa

x−coordinate. The abscissa of the point (a, b) is a.

Absolute value

The distance of a number from zero. The positive value.

Acceleration

The rate of change of velocity.

Acute angle

A positive angle that measures less than 90°.

Acute triangle

A triangle each of whose angles measures less than 90°.

Additive identity

A set which is equipped with the operation of addition is an element which when added to any element x in the set yields x.

Adjacent angles

Two angles that share both, a side and a vertex.

Algebra

The mathematics of working with variables.

Algorithm

A set of instructions used to solve a problem or obtain a desired result.

Altitude

The perpendicular distance from the base of a figure to the highest point of the figure.

Amplitude

Half the difference between the largest and the smallest function value of a periodic function.

Angle

The union of two rays with a common endpoint.

Antecedent

The hypothesis of conditional statement.

Antiderivative

The antiderivative of a function f(x), is a function F(x), whose derivative is f(x). Also called the indefinite integral.

Apothem

The perpendicular distance from the center to a side of a regular polygon.

Arc

The set of points on a circle that lie in the interior of a central angle.

Arccos

If x = cos y, then y = arccos x. The inverse of the cosine function.

Arccosec

If x = cosec y, then y = arccosec x. The inverse of the cosecant function.

Arccot

If x = cot y, then y = arccot x. The inverse of the cotangent function.

Arcsec

If x = sec y, then y = arcsec x. The inverse of the secant function.

Arcsin

If x = sin y, then y = arcsin x. The inverse of the sine function.

Arctan

If x = tan y, then y = arctan x. The inverse of the tangent function.

Area

Area of a circle = r²;
Area of a rectangle = height x width;
Area of a triangle = half base x height

Argument

The independent variable in a function.

Arithmetic

Calculations involving the basic operations like addition, subtraction, multiplication, division and exponents of numbers.

Arithmetic mean

The sum of a set of numbers divided by the number of numbers. Also called the average.

Arithmetic sequence

A sequence of numbers of the form a, a + b, a + 2b, a + 3b, ... , a + (n − 1)b.

Arithmetic series

The sum of an arithmetic sequence.

Associative property of addition

(a + b) + c = a + (b + c)

Associative property of multiplication

(a * b) * c = a * (b * c)

Asymptote

A straight line that is a close approximation to a curve as the curve goes off to infinity.

Average

The sum of a set of numbers divided by the number of numbers.

Axiom

A statement that is assumed to be true without proof. Also called as Postulate.

Axis of symmetry

A line that passes through a figure in such a way that the part of the figure on one side of the line is a mirror reflection of the part of the figure on the other side of the line.

B

Bar Graph

A graph that uses horizontal or vertical bars to display data.

Base of a Triangle

The side of a triangle which is perpendicular to the altitude.

Before

In front of, earlier than, at an earlier time.

Between

Point B is between points A and C if AB + BC = AC.

Biconditional statement

A compound statement, that says one sentence is true if and only if the other sentence is true.

Binary number system

The number system used by computers; it has only two numbers, 0 and 1, called binary digits.

Binomial

An algebraic expression that is the sum of two terms.

Binomial distribution

a theoretical distribution of the number of successes in a finite set of independent trials with a constant probability of success. Also called as Bernoulli distribution.

Binomial Expression

It is an expression that uses two terms.

Binomial theorem

The theorem that tells how to expand the expression (a + b)n.

Bisect

1) To cut something in half.
2) To divide a geometric figure into two congruent parts.

C

Calculus

The branch of mathematics dealing with limits, derivatives, definite integrals, indefinite integrals, and power series.

Cardinal Numbers

The numbers 1, 2, 3, . . . as well as some types of infinity, used to describe the number of elements in either finite or infinite sets.

Cartesian coordinates

A system whereby points on a plane are identified by an ordered pair of numbers, representing the distances to two or three perpendicular axes.

Cartesian Plane

The coordinate plane that is formed by a horizontal and vertical axis. They are often labeled the x−axis and y−axis respectively.
1) The point that is the same distance from all the points on a circle.
2) The point that is the same distance from all the points on a sphere.
3) The point inside an ellipse where the major and the minor axes intersect.
4) The center of a circle that can be inscribed in a regular polygon.

Center of mass

The centroid of an object of uniform density.

Central angle

An angle that has its vertex at the center of a circle.

Central Tendencies

A number which in some way conveys the ′center′ or ′middle′ of a set of data. The most frequently used measures are the mean and the median.

Centroid

The center of mass of an object. The point where the object would balance if supported by a single support. The point in a triangle where the three medians intersect.

Chain rule

A formula for the derivative of the composite of two functions.

Chord

A line segment that connects two points on a curve.

Circle

The set of points in a plane that are a fixed distance from a given point.

Circumcenter

The point in a triangle that is the center of the circle that can be circumscribed about the triangle. The intersection of the perpendicular bisectors of the triangle.

Circumference

The distance around a closed curve.

Circumscribed circle

A circle that passes through all of the vertices of a regular polygon.

Closed figure

A figure that starts and ends at the same point.

Closed interval

An interval that contains its endpoints.

Coefficient

A constant that multiplies a variable.

Cofunction

A function f is cofunction of a function g if f(A) = g(B) whenever A and B are complementary angles. It helps solve trigonometric equations. A simple example is the equation sinA = cosB.

Collinear

Points are collinear if they lie on the same line.

Combination

A subset from a larger set that is considered without regard to the order of the items chosen.

Common Denominator

A whole number greater than zero that is a common multiple of each denominator in two or more fractions.

Common Factor

A number, polynomial or quantity that evenly divides into two or more numbers or algebraic expressions.

Common Multiple

A whole number that is a multiple of two or more given numbers.

Commutative Property of Addition

A property of real numbers that states that the sum of two terms is unaffected by the order in which the terms are added; i.e. the sum remains the same. a + b = b + a.

Commutative Property of Multiplication

A property of real numbers that states that the product of two factors is unaffected by the order in which they are multiplied; i.e. the product remains the same. a*b = b*a.

Complementary angles

Two angles are complementary if their sum is 90°.

Completing the square

The method of adding an expression to both sides of an equation so that one side becomes a perfect square trinomial.

Complex Fraction

A fraction which has, as part of its numerator and/or denominator, at least one other fraction.

Complex fraction

A fraction that contains a fraction in its numerator and or denominator.

Complex number

The sum of an imaginary number and a real number.

Component

The components in the vector (a, b, c) are a, b and c.

Composite function

A function that consists of two functions arranged in such a way that the output of one function becomes the input of the other function.

Composite number

A natural number that is not prime.

Compound Interest

A method of computing interest in which interest is earned on the interest and not just on original balance.

Concave

A figure is concave if a line segment can be drawn so that it goes in, out, then back into the figure.

Concave Polygon

A polygon with one or more diagonals that have points outside the polygon.

Concentric

Two shapes that have the same center point.

Conclusion

An answer or solution arrived at through logical or mathematical reasoning.

Cone

The union of all line segments that connects a point and a closed curve in a different plane from the point.

Congruence

The relationship between two objects that have exactly the same size and shape.

Congruent

Geometric figures that have the same size and shape.

Conic section

Figures formed by the intersection of a plane with a right circular cone. Parabola, hyperbola, ellipse, circle.

Conjecture

A statement that seems to be true, but has not yet been proven.

Conjugate

The conjugate of a complex number is formed by reversing the sign on the imaginary part of the number.

Conjunction

A statement that is really two statements joined by the word AND. Both parts must be true for the statement to be considered true.

Consequent

The part of an ′if − then′ statement that follows the ′then′. Conclusion.

Constant

A value that does not change.

Construction

A precise way of drawing that allows only two tools: the straightedge and compass where the straightedge establishes collinearity and the compass establishes equidistance.

Continuous

A function is continuous if drawn without lifting the pencil off the paper.

Contrapositive

The contrapositive of A→ B is Not B → A.

Convergent series

An infinite series that has a finite sum.

Converse

The statement made by interchanging the hypothesis and the conclusion of a statement.

Convex

A set of points such that for any two points in the set, the line segment that connects them is also in the set.

Convex Polygon

A polygon with all interior angles measuring less than 180. All diagonals of a convex polygon are inside the figure.

Coordinate Axes

The two intersecting perpendicular lines in a plane that form the four quadrants for locating points, given the ordered pair of the points; the axes are referred to as the x−axis and the y−axis.

Coordinate Geometry

The study of geometry using a coordinate plane.

Coordinate Grid

A two−dimensional system in which the coordinates of a point are its distances from two intersecting, usually perpendicular, straight lines called axes.

Coordinate Plane

A plane containing a set of coordinate axes in which each point is located by a set of coordinates.

Coordinate System

A method of representing points in the plane or in space by means of numbers.

Coordinates

A set of numbers that identifies the location of a point.

Coordinates

Numbers that represent a point on a graph.

Coplanar

Points that lie within the same plane.

Corollary

A statement that can be easily proven once a theorem is proved.

Correlation

The amount of positive or negative relationship existing between two measures.

Corresponding Angles

Any pair of angles on the same side of the transversal, one interior and one exterior, formed when two parallel lines are intersected by a transversal.

Corresponding Sides

Sides in the same relative position on two congruent or similar figures. The corresponding sides of congruent figures are equal and the corresponding sides of similar figures are proportional.

Cosecant

1) In a right triangle, the reciprocal of the sine of an angle.
2) Ratio of the hypotenuse to the opposite side of a right−angled triangle.

Cosine

Ratio of the adjacent side to the hypotenuse of a right−angled triangle.

Cotangent

Ratio of the adjacent to the opposite side of a right−angled triangle.

Critical point

The point on a curve where the first derivative equals zero.

Cubic

A polynomial of degree 3.

Cylinder

The union of all line segments that connect corresponding points on congruent circles in parallel planes.

D

Data

Information collected and used to analyze a particular concept or situation.

Decagon

A polygon with ten sides.

Decimal Fraction

A fraction using a decimal point to represent the denominator of 10 or power of 10.

Decimal numbers

The numbers in the base 10 number system.

Decimal Point

A period or dot separating the ones place from the tenths place in decimal numbers.

Deduction

A conclusion arrived at by reasoning.

Definite integral

The integral of a function over a definite interval.

Degree

Unit of measure of an angle.

Degree of a Monomial

The sum of the exponents on the variables contained in a term.

Degree of a Polynomial

The largest degree among all its terms.

Denominator

The bottom part of a fraction.

Dependent variable

The output of a function.

Derivative

The rate of change of a function.

Determinant

A square matrix used to solve simultaneous equations.

Diagonal

The line segment connecting two non adjacent vertices in a polygon.

Diameter

The line segment joining two points on a circle and passing through the center.

Difference

The result of subtracting two numbers.

Differentiation

The process of finding a derivative.

Digit

The ten symbols, 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9 are digits.

Dimension

The dimension of a space is the number of coordinates needed to identify a location in that space.

Directly proportional

A relationship in which one variable goes up if the other goes up and down if the other goes down.

Discriminant

An expression used to distinguish or separate other expressions in a quantity or equation.

Disjoint

Having no elements in common.

Disjunction

A logical operator that results in true whenever one or more of its operands are true.

Dispersion

The scattering of the values of a frequency distribution of data from an average.

Distance

The length of the line segment joining two points.

Distributive property

A property of real numbers that states that the product of the sum or difference of two numbers is the same as the sum or difference of their products. a(b + c) = ab + ac

Divergent series

A series whose sum is infinite.

Dividend

A number that is divided by another number.

Division

A mathematical operation involving two numbers that tells how many groups there are or how many are in each group.

Divisor

The number by which the dividend is divided.

Dodecahedron

A polyhedron with twelve faces.

Domain

The set of all possible values of the argument of a function.

E

Eccentricity

A number that indicates the shape of a conic section.

Edge

A line segment where two faces of a three−dimensional figure meet.

Elapsed Time

The difference between two times.

Element

A member of a set.

Ellipse

The set of all points in a plane such that the sum of the distances to two fixed points is a constant.

Ellipsoid

A solid of revolution formed by rotating an ellipse about one of its axes.

Empty set

A set that contains no elements.

Endpoint

A point at either end of a line segment, arc or the beginning point of a ray.

Equal To

A symbol that means two things have the same amount, size, number, or value.

Equation

A mathematical statement that says that two expressions have the same value.

Equidistant

Having equal distances.

Equilateral

Having equal sides.

Equilateral triangle

A triangle that has three equal sides.

Equivalent equations

Two equations whose solutions are the same.

Even function

A function that satisfies the property that f(x) = f(−x).

Even number

A natural number that is divisible by 2.

Event

In probability, a set of outcomes.

Exponent

A number that indicates the operation of repeated multiplication.

Exponential function

A function in which an independent variable appears as an exponent.

Exponential Notation

A symbolic way of showing how many times a number or variable is used as a factor.

Expression

A variable or combination of variables, numbers, and operation symbols that represents a mathematical relationship.

Exterior Angle of a Polygon

An angle formed by one side of a polygon and the extension of the adjacent side.

Extremum

A point where a function reaches a maximum or a minimum.

F

Factor

One of two or more expressions that are multiplied together.

Factorial

The product of all the integers from 1 up to the integer in question.The (!) exclaimation point is used to mean factorial.

Fibonacci Sequence

The sequence in which every number is the sum of the two preceding numbers.

Formula

A simple way to display mathematical actions.

Fraction

A small part or item forming a piece of a whole.

Frequency

The number of times an event occurs.

Frequency Distribution

An organized display of a set of data that shows how often each different piece of data occurs.

Frequency Table

A table that shows how often each item, number or range of numbers occurs in a set of data.

Function

A mathematical relationship between two variables, sets of numbers, or an independent variable and a dependent variable.

Function Notation

A notation in which a function is named with a letter and the input is shown in parentheses after the function name.

Fundamental Counting Principle

The principle that states that all possible outcomes in a sample space can be found by multiplying the number of ways each event can occur.

G

Geometric mean

The geometric mean of two numbers is the square root of the product of the numbers.

Geometric series

A series with a constant ratio between successive terms.

Geometry

The branch of mathematics that deals with the measurement, properties and relationships of points, lines, angles, planes, and two and three−dimensional figures.

Googol

A really cool number that is a one with 100 zeros after it. The correct way to write it out is 1100.

Graph

The graph of an equation is the set of points that make the equation true.

Great circle

The circle formed by the intersection of a plane passing through the center of a sphere.

Greatest Common Factor (GCD)

The greatest common factor of two numbers is the largestnumber that divides both numbers evenly.

Group

A number of individuals or objects that are assembled together or that have some unifying relationship.

H

Half plane

The set of all points in a plane that lie on one side of a line in the plane.

Harmonic sequence

A sequence is a harmonic sequence if the reciprocals of the numbers inthe sequence form an arithmetic sequence.

Height

The perpendicular distance from a vertex to the line containing the opposite side of a plane figure.

Heptagon

A polygon with seven sides.

Hexadecimal number

A number written in base sixteen.

Hexagon

A polygon with six sides.

Hexahedron

A polyhedron with six faces.

Histogram

A special kind of vertical bar graph that displays the frequency of data that has been organized into equal intervals.

Horizontal Line

A line that is parallel to the horizon. A horizontal line is straight across.

Hyperbola

The set of all points in a plane such that the difference of the distances to two fixed points is a constant.

Hypotenuse

The longest side of a right triangle.

Hypothesis

A proposition that is being investigated, which is yet to be proven.

I

Identity

An equation that is true for all values of the variable.

Identity matrix

A square matrix with ones along the diagonal and zeros everywhere else.

Imaginary number

A number of the form ni, where n is a real number, and i2 = −1.

Implication

A conditional statement.

Improper fraction

A fraction with a numerator that is greater than the denominator.

Incenter

The center of a circle that is inscribed in a triangle.

Incircle

The circle that can be inscribed in a triangle.

Increment

A small change, usually indicated by the greek letter delta (?).

Indefinite integral

The sum of the antiderivative of a function and an arbitrary constant.

Independent events

Two or more events in which the outcome of one event has no effect on the outcome of the other event or events.

Independent variable

The input number to a function.

Inductive Reasoning

Making a generalization from specific cases; used to formulate a general rule after examining a pattern.

Inequality

A relationship between two quantities indicating that one is strictly less than or less than or equal to the other.

Infinity

A limitless quantity.

Inflection point

A point on a curve such that the curve is concave up on one side of the point,and concave down on the other side of the point.

Inscribed polygon

A polygon placed inside a circle so that each vertex of the polygon touchesthe circle.

Integers

The set of numbers containing zero, the natural numbers, and all the negatives of thenatural numbers.

Integral

Refers to an integer; an integral solution to a problem cannot be a decimal or fraction.

Integral Exponent

An exponent that is an integer.

Integrand

A function that is to be integrated.

Integration

The process of finding an integral.

Intercept

The x−intercept of a curve is the point where the curve crosses the x − axis and they − intercept of a curve is the point where the curve crosses the y − axis.

Interest

The amount of money charged for borrowing money or the profit that is made on invested capital.

Interest Rate

The percent of interest charged on money borrowed or earned on money invested.

Interior Angle

An angle on the inside of a polygon formed by two adjacent sides of the polygon.

Intersect

To meet or cross.

Intersecting Lines

Lines that share a common point.

Intersection of Sets

The set of elements that belong to each of two or more sets.

Interval

A set containing all numbers between two given numbers.

Inverse

Something that is opposite or the reverse as in sequence or character.

Inverse Operation

An operation that is the opposite of another operation.

Inverse Property

A property of real numbers that states that the result of two real numbers that when combined will result in the identity element.

Inversely proportional

Two quantities are said to be proportional if they vary in such a way that one of the quantities is a constant multiple of the other.

Irrational number

A number that cannot be expressed as the ratio of two integers.

Irregular Polygon

A polygon whose sides and angles are not all congruent.

Isometry

A transformation of a figure that does not change the distances of any two pointsin the figure.

Isosceles Trapezoid

A trapezoid in which the two nonparallel sides are congruent.

Isosceles Triangle

A triangle that has exactly two sides of equal length.

J

Joint probability function

A function that gives the probability that each of two or more random variables takes at a particular value.

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 whose elements above the principal diagonal are equal to 1, but all other elements are 0.

K

Key

A table for decoding or interpreting.

Kilogram

A metric unit to measure mass. The abbreviation for kilogram is ′kg′.

Kilometer

A metric unit of length roughly equivalent to 6/10 of a mile. The abbreviation for kilogram is ′km′.

L

Lattice point

A point with integer coordinates.

Latus rectum

The chord through the focus of a parabola parallel to the directrix. The chord through a focus of an ellipse perpendicular to the major axis.

Least common denominator

The smallest number that two different denominators can divide into evenly.

Least common multiple

The smallest multiple that is exactly divisible by every member of a set of numbers.

Lemma

A theorem that is proved mainly as an aid in proving another theorem.

Length

A value of distance.

Like terms

Two terms each of whose parts, with the exception of their coefficients, is the same.

Line

A straight set of points that extends off into infinity in both directions.

Line Graph

A graph that uses line segments to show changes in data.

Line segment

Two points on a line, and all the points between those two points.

Linear Equation

An equation of the first degree that contains one or more variables.

Linear Inequalities

An inequality of the first degree that contains one or more variables.

Linear Pair of Angles

A pair of adjacent angles formed by intersecting lines. Linear pairs of angles are supplementary.

Logarithm

A mathematical term for the ratio of values expressed by the base 10 or e. If the base is 10, the logarithm is called common. If the base is e, the logarithm is called natural.

Logic

The study of sound reasoning.

Logical Reasoning

The process of using a rational, systematic series of steps based on sound mathematical procedures to arrive at a conclusion.

M

Magnitude

The magnitude of a vector is its length.

Major arc

An arc of measure greater than 180°.

Major axis

The line segment connecting the two vertices that are farthest apart in an ellipse.

Mass

The amount of matter or substance in an object.

Mathematical Argument

A chain of mathematical reasoning intended to convince the audience of the truth of a statement.

Mathematical Reasoning

Applying mathematical techniques, concepts, and processes.

Mathematical Relationship

The connection between two quantities, properties, or concepts.

Mathematical Solution

The statements or values that correctly answers a mathematical question or completes an open mathematical sentence.

Mathematical Statement

A mathematical sentence whose truth−value can be determined to be either true or false.

Mathematical Symbol

A character that is used to indicate a mathematical relation or operation; it has a precise mathematical meaning.

Mathematics

This field studies values, numbers, and quantities. Also known as math.

Matrix

A table of numbers arranged in rows and columns.

Maxima

The points on a curve where the value is greater than that of the surrounding points.

Maximum / Minimum Point

The highest / lowest point on a graph.

Mean

The average of a numerical set.

Measure

To find the dimensions or quantity of an object or figure.

Measure of an Angle

The number of degrees or radians contained in the angle.

Median

The value of a numerical set that equally divides the number of values that are larger and smaller.

Mental Math

Mental calculation comprises mathematical calculations using only the human brain.

Metric

A system of related measures that facilitates the quantification of some particular units such as meter or mile for length, or gram or ton for weight.

Metric System

A system of measurement based on tens.

Midpoint

A point equidistant from the ends of a line.

Minima

The points on a curve where the value is less than that of the surrounding points.

Minor arc

An arc on a circle that is less than 180°.

Minor axis

The shortest distance across an ellipse through the center.

Missing Value

A value omitted from an equation that is needed to make the equation true.

Mixed Number

A number composed of an integer and a proper fraction.

Mode

The number that occurs most frequently in a set of data.

Modulus

The absolute value of a complex number.

Monomial

An algebraic expression that does not involve any additions or subtractions.

Multiple

The product of a given whole number and any other whole number.

Multiplicand

The number that is multiplied by the multiplier.

Multiplication

The mathematical operation of scaling one number by another.

Multiplicative inverse

The reciprocal of the number, which when multiplied by a given number, produces the multiplicative identity 1.

Multiplier

The number by which a multiplicand is multiplied.

N

Natural logarithm

The logarithm with the base of e.

Natural numbers

Non−negative whole numbers.

Negative number

A real number less than zero.

Nonadjacent Side of an Angle

Theside of the triangle that does not make up either side ofthe angle.

Nonagon

A polygon with nine sides and nine angles.

Noncollinear

Not lying on the same straight line.

Nonlinear Equation

An equation or inequality that, when represented graphically, results in a graph that is not a straight line.

Nonrepeating Decimal

A decimal that does not repeat; it either terminates or continues in no discernible pattern.

Nonstandard Measurement

The use of items as measurement tools that are not uniform in size.

Null set

A set with no elements. Also called empty set.

Number

The concept of an amount, quantity in a collection.

Number Line

A line on which each point represents a real number.

Number Sense

Having a good conceptual understanding of numbers and number concepts.

Number Sentence

A mathematical statement that has numbers, at least one operation sign and an equal or inequality sign.

Number System

A system used to represent numbers.

Numeral

A symbol that represents a number.

Numeral

A symbol that stands for a number.

Numeration

The act or process of counting or numbering.

Numerator

The top number of a fraction.

Numerator

The top of a fraction.

Numeric Expression

Any combination of words, variables, constants, and/or operators that result in a number; also known as an arithmetic expression.

Numeric Pattern

An arrangement of numbers that repeat or that follow a specified rule.

Numerically

Expressed in or involving numbers or a number system.

O

Obtuse angle

An angle whose measure is greater than 90°.

Obtuse triangle

A triangle with an angle greater than 90°.

Octagon

A polygon with 8 sides.

Octahedron

A polyhedron with 8 faces.

Octal number

A number in base 8.

Odd function

A function that satisfies the property that f(−x) = −f(x). This means that when −x is substituted into f for x the sign of the function changes.

Odd number

A whole number that is not divisible by 2.

One-Digit Number

A number consisting of just one digit.

Open Figure

A figure that is not closed; i.e. it does not start and end at the same point.

Open interval

An interval that does not contain both its endpoints.

Open Sentence

A statement that contains at least one unknown.

Operation

Procedures used to combine numbers, expressions, or polynomials into a single result.

Order

To place numbers or objects in a sequential arrangement.

Order of Operations

A specified sequence in which mathematical operations are expected to be performed.

Ordered pair

A set of two numbers in which the order has an agreed upon meaning.

Ordinate

The second coordinate of a cartesian ordered pair.

Origin

The point (0, 0) on a Cartesian Coordinate System.

Orthocenter

The point in a triangle where the three altitudes intersect.

Orthocenter

The point in a triangle where the three altitudes intersect.

Orthogonal

Having a set of mutually perpendicular axes; meeting at right angles.

P

Parabola

The set of all points in a plane that are equally distant from a fixed point called the focus and a fixed line.

Paraboloid

A surface that is formed by rotating a parabola about its axis.

Parallel

Two lines are parallel if they are in the same plane and never intersect.

Parallel Lines

Lines in the same plane that never intersect no matter how far they are extended. They are always equidistant from each other.

Parallelepiped

A solid figure with six faces such that the planes containing two opposite faces are parallel. Each face is a parallelogram.

Parallelogram

A quadrilateral with opposite sides parallel.

Pentagon

A five sided polygon.

Percent

A fraction in which the denominator is assumed to be 100.

Percent Decrease

The magnitude of decrease expressed as a percent of the original quantity.

Percent Increase

The magnitude of increase as a percent of the original quantity.

Percentile

A value on a scale that indicates the percent of a distribution that is equal to it or below it.

Perfect number

A number that is the sum of all its factors except itself.

Perfect Square

A whole number resulting from multiplying an integer by itself.

Perimeter

The sum of the lengths of the sides of a polygon.

Periodic function

A function that keeps repeating the same values.

Permutation

A permutation of the set of numbers is a reordering of the numbers.

Perpendicular

Two lines are perpendicular if the angle between them is 90°

Perpendicular Bisector

A line, segment or ray that is perpendicular to and bisects a line segment.

Pi

The ratio of the circumference of a circle to its diameter.

Pie Chart

A chart in which the data is represented by sectors of a circle.

Plane

A flat surfaces that stretches off into infinity.

Polar coordinates

A coordinate system of ordered pairs in which the first number of the pair represents distance from the origin, and the second number of the pair represents the angle of inclination from the horizontal axis.

Polygon

A solid that is bounded by plane polygons.

Polynomial

A mathematical function that is the sum of a number of terms.

Positive number

A real number greater than zero.

Postulate

A fundamental statement that is assumed to be true without proof.

Power

A number that indicates the operation of repeated multiplication.

Prime number

A number whose only factors are itself and 1.

Product

The result of two numbers being multiplied.

Profit

The amount of money left after expenses have been subtracted from income.

Proof

A valid argument, expressed in written form, justified by axioms, definitions and theorems.

Proper fraction

A fraction whose numerator is less than its denominator.

Properties

Characteristics of a shape or object.

Properties of Real Numbers

Rules that apply to the operations with real numbers.

Proportional Reasoning

Using the concept of proportions when analyzing and solving a mathematical situation.

Proportionality

The quality, character or fact of being proportional.

Protractor

A device for measuring angles.

Pyramid

The union of all line segments that connect a given point and the points that lie on a given polygon.

Pythagorean Theorem

The theorem that relates the three sides of a right triangle.

Pythagorean triple

Three natural numbers that satisfy the pythagorean theorem that relates the three sides of a right triangle.

Q

Quadrant

One of the quarters of the plane of the Cartesian coordinate system.

Quadratic

A term that means ′Of the second degree′.

Quadratic equation

An equation involving the second power, but no higher power of an unknown.

Quadratic formula

The formula in the form for finding roots of the quadratic equation.

Quadratic Function

A function given by a polynomial of degree 2. The graph of these functions are parabolas.

Quadrilateral

A polygon with 4 sides.

Quartic

A polynomial of degree 4.

Quartiles

The 25th, 50th and 75th percentile points.

Quintic

A polynomial of degree 5.

Quotient

The answer to a division problem.

R

R

Abbreviation for the real numbers.

Radian

The ratio of an arc of a circle to the radius of the circle.

Radii

Radii is the plural form of radius.

Radius

The distance from the center to a point on a circle. The line segment from the center to a point on a circle.

Random Sample

A sample obtained by a selection from a population, in which element of the population has an equal chance of being selected.

Random Variable

A function on a probability space.

Range

The set of all possible values for the output of a function.

Range of a Data

In statistics, it is the difference between the largest and the smallest values in a set of numbers.

Range of a Function

The set of output values of a function.

Rate

Ratios that compare quantities of different units.

Rate of Change

The amount the function′s output increases or decreases for each unit of change in the input.

Rate of Interest

The percent charged or paid for the use of money.

Ratio

The relationship between two numbers.

Rational number

A number that can be expressed as the ratio of two integers.

Raw Data

Collected information before the application of statistical procedures.

Ray

A part of a line that has one endpoint and goes on forever in one direction.

Real numbers

The union of the set of rational numbers and irrational numbers.

Reasonable Estimate

An approximation of the result of a given problem or calculation using rational, logical procedures.

Reasoning

Engaging in a process that leads to a conclusion or inference using known facts or assumptions.

Reciprocal

Multiplicative inverse.

Rectangle

A quadrilateral with four 90° angles.

Rectangular coordinates

A Cartesian coordinate system which specifies each point uniquely in a plane by a pair of numerical coordinates.

Reflex Angle

An angle that has a value greater than 180° but less that 360°.

Region

A part of a plane.

Regrouping

To pause and get organized before trying again; to group or categorize again.

Regular polygon

A polygon in which all the angles are equal and all of the sides are equal.

Relation

A set of ordered pairs.

Remainder

The part of the dividend that is left over when the dividend is not evenly divisible by the divisor.

Repeating decimal

A decimal in which the digits endlessly repeat a pattern.

Rhombus

A quadrilateral with four equal sides.

Right angle

An angle whose measure is 90°.

Right circular cone

A cone whose base is a circle located so that the line connecting the vertex to the center of the circle is perpendicular to the plane containing the circle.

Right circular cylinder

A cylinder whose bases are circles and whose axis is perpendicular to its bases.

Right triangle

A triangle that contains a right angle.

Root

The root of an equation is the same as the solution to the equation.

S

Sale Price

The price of a product after the discount has been subtracted from the original price.

Sales

The amount of money generated when goods are sold.

Sample

A representative part or a single item from a larger whole or group; a finite part of a statistical population whose properties are studied to gain information about the whole.

Sample Space

A list of all possible outcomes in a given situation.

Sampling

The process of selecting a small group which would be representative of the entire population; used in taking a survey.

Scalar

A quantity that has size but no direction.

Scalar Matrix

A scalar matrix has diagonal elements that are all equal while the nondiagonal elements are all 0.

Scalene triangle

A triangle with three unequal sides.

Secant

A line that intersects a circle or a curve in two places.

Sector

A region bounded by two radii of a circle and the arc whose endpoints lie on those radii.

Sector of a Circle

The region of the circle formed by two radii and their intercepted arc.

Segment

One of several parts or pieces that fit with others to constitute a whole object.

Sequence

A set of numbers arranged in a special order or pattern.

Series

The sum of a sequence.

Set

A well defined group of objects.

Side

A line segment joining two adjacent vertices of a polygon.

Similar

Two polygons are similar if their corresponding sides are proportional.

Similar Figures

Figures that have the same shape, but not necessarily the same size.

Similar Triangles

Triangles that have the same shape but not necessarily the same size; corresponding sides are in proportion and corresponding angles are congruent.

Similarity

Objects that have the same shape, but not the same size.

Simoultaneous equations

A group of equations that are all true at the same time.

Simple Interest

The amount obtained by multiplying the principal by the rate by the time.

Simulation

Simulation is the process of carrying out extensive data collection with a simple, safe, inexpensive, easy−to−duplicate event.

Sine

In a right triangle, the length of a side opposite an angle divided by the length of the hypotenuse of the triangle.

Skew

Two lines that are not in the same plane.

Slide

A transformation that slides a figure a given distance in a given direction.

Slope

The slope of a line is the change in the vertical coordinates or the change in the horizontal coordinates of any two points on the line.

Solid

A three dimensional object that completely encloses a volume of space.

Solution

The value or values that make an equation, inequality or open sentence true.

Solution Set

The set of values that make an equation or statement true.

Sphere

The set of all points in space that are a fixed distance from a given point.

Square

A quadrilateral with four equal sides and four 90° angles.

Square root

A number that when multiplied by itself equals a given number.

Standard Deviation

A statistic that measures the dispersion of a sample.

Standard Form

A number is written in standard form when each digit is in a place value.

Statistics

The collection, organization, presentation, and analysis of data.

Straight Angle

A straight angle has a value of 180°. Two rays in opposite directions from their common endpoint form this angle.

Straight Edge

A tool used to make a straight line.

Subset

A set contained within another set.

Substitute

To replace variables in a given expression or equation with designated values in order to evaluate the expression.

Subtraction

An arithmetic process when one value is taken away from another.

Sum

The result of adding.

Supplementary Angles

Two angles whose measures sum to 180°.

Surface Area

The sum of the areas of the faces or curved surface of a three−dimensional object.

Survey

A process of asking either written or verbal questions for acquiring information/data.

Symbol

A notation used to represent an operation or abstract idea.

Symmetric

Two points are symmetric with respect to a third point if the segments joining them to the third point are equal.

Symmetry

A figure has symmetry if it has parts that correspond with each other in terms of size, form and arrangement.

System of Equations

A set of equations that may share a common solution or common solutions.

System of Linear Equations

Set of equations of the first degree.

T

Table

A systematic or orderly list of values, usually in rows and columns.

Tally Mark

A mark used to keep track of data being counted.

Tangent

A line segment, line or ray that intersects a circle in only one point.

Term

A part of a sum in an algebraic expression.

Terminating decimal

A fraction whose decimal representation contains a finite number of digits.

Tetrahedron

A polyhedron with four faces.

Theorem

A statement that has been proven.

Trajectory

The path that a body makes as it moves through space.

Transitive property

The property that states that if a = b, and b = c, then a = c.

Translation

A shift of the axes of the Cartesian Coordinate System.

Transversal

A line that intersects two other lines.

Trapezoid

A quadrilateral that has exactly two sides parallel.

Triangle

A three sided polygon.

Trinomial

A polynomial with exactly three terms.

U

Union

If two sets are given, a set can be formed by using all the elements of the two sets. Such a collection is said to be the union of the given sets.

Unit Fraction

A fraction with a numerator of 1.

Unit Price

The price of one item or one unit.

Unit vector

A vector of length 1.

Unlikely

In probability, an event that has a very small chance of occurring.

V

Variable

A symbol used to represent a value.

Variance

The value of the standard deviation squared.

Vector

A quantity that has both magnitude and direction.

Velocity

The rate of change of position. The first derivative of the position function.

Venn diagram

A drawing showing relationships among sets.

Verify

To ascertain or confirm that a mathematical property, concept or statement is true.

Vertex

The point on an angle where the two sides intersect.

Vertical

A direction perpendicular to the horizon which is straight up and down.

Vertical Angles

The pair of angles that are directly across from each other when two straight lines intersect. They are always non−adjacent angles.

Vertical Line

A line that is straight up and down and has right angles to the horizon.

Vertices

The points of intersection of lines or the points opposite the base of a figure.

Volume

Measurement of space.

W

Whole numbers

The set of numbers that includes zero and all of the natural numbers.

Width

Width is a distance value that is lateral i.e. side to side.

X

x-axis

The horizontal axis in a Cartesian Coordinate System.

x-intercept

The value of x at the point where a curve crosses the x−axis.

Y

y-axis

The vertical axis in a Cartesian Coordinate System.

y-intercept

The value of y at the point where a curve crosses the y−axis.

Z

Zero

The number which indicates no quantity, size or magnitude; zero is neither negative nor positive; it is the additive identity.

Zero Property of Addition

The property that states that the sum of a number and zero is that same number.

Zero Property of Multiplication

The property that explains how the product of any number and zero is zero.

Zeros of a Function

The points at which the value of a function is zero.