BASIC ALGEBRA GLOSSARY
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Title  Description  

Abscissa  The horizontal axis, or the first coordinate in an ordered pair. 

Absolute Maximum  The highest point on a graph, especially over a specified domain. It is the greatest value of f(x) over a defined interval of x, provided y=f(x). 

Absolute Minimum  The lowest point on a graph, especially over a specified domain. It is the least value of f(x) over a defined interval of x, provided y=f(x). 

Absolute Value  The distance on the real number line between a value and zero. It applies best to things for which negative values have no meaning, such as mass or length. 

Accuracy  The quality of approaching an exact value. Distinct from precision, accuracy means to approach correctness, to tend toward an established value. 

Addition  The process of finding a sum or determining a total by joining values together. Values are summed in the process to result in a total. Matrix addition adds elements of matrices of the same order (or dimension). Vector addition results in the diagonal of a parallelogram (if in two dimensions). 

Algebra  The branch of mathematics that allows manipulation of symbols and values to determine quantities that are not always fixed. Variables are essential to algebra. 

Algorithm  A sequence of steps to accomplish a familiar task; a recipe.  
Alpha  The first letter of the Greek alphabet.  
Argument of a Function  The term or expression upon which a function operates. In y=f(x), the argument of the function is x. 

Arithmetic  A branch of mathematics built upon the basic operations of addition, subtraction, division, and multiplication. Powers, roots, and logarithms are often considered arithmetic in nature. 

Arithmetic Mean  What we generally consider to be the average. The sum of a set of values divided by the cardinal number of the set of values. 

Arithmetic Progression  Also Arithmetic Sequence. A series of terms where successive terms are obtained by addition of a constant. 

Arithmetic Sequence  Also Arithmetic Sequence. A series of terms where successive terms are obtained by addition of a constant. 

Arithmetic Series  Akin to Arithmetic Progressions and Arithmetic Sequences, the series typically reflects an addition operator between terms, as a sum.  
Associative Law of Addition  Provides that addition of groups of terms or values is indifferent to the order of grouping. We may add terms in any order, or group them in any order. 

Associative Law of Multiplication  Provides that multiplication of groups of terms or factors is indifferent to the order of grouping. We may multiply factors in any order, or group them in any order. 

Average  Most commonly, average means the arithmetic mean; we sum the values and divide that sum by the number of numbers. The average between two real values is the midpoint between those values. 

Average Rate of Change  The change in value divided by elapsed time.  
Axes  Most simply, the plural of axis. More generally, the horizontal xaxis and the vertical yaxis that comprise the skeleton of Cartesian Coordinates. 

Axiom  Accepted without proof (unlike a theorem), an axiom is readily understood and regarded as fact.  
Axis  In physics, a line about which a body rotates. In mathematics, a line that divides a plane or space into two equal halves, typically demarcated in units. 

Base (Exponential)  Any value that is raised to a power is termed a base value. That power is typically expressed as an exponent, and that exponent could be an integer, a decimal value, or a fraction. The base is the number or expression being raised to the power of the exponent. 

Beta  Beta is the second letter of the Greek alphabet.  
Biconditional  A biconditional statement has literally two conditions. The classic IfThen statement is the biconditional with a hypothesis and conclusion. 

Binomial  A binomial has two terms. Terms are usually separated by plus signs or minus signs. 

Binomial Coefficients  Binomial coefficients are found in Pascal's Triangle. We use these coefficients to raise binomials to successive powers as well as to determine the number of combinations or ways we can take a number of objects from a set of objects. 

BoxandWhisker Plot  In statistical data, a boxandwhisker plot is sometimes used to graphically represent quartiles. Quartiles are the extremes of the body of data, as well as the 25th, 50th and 75 percentiles. 

Braces  Braces act just like parentheses. Always (almost) used in pairs, braces look like this: { }. 

Brackets  Brackets act just like parentheses, coming in pairs to group data or terms.  
Cardinal Number  The number of objects or elements within a set is the Cardinal Number of the set.  
Cartesian Coordinates  The familiar xy coordinate plane is called the plane of Cartesian Coordinates; it is named for Rene Descartes. 

Cartesian Plane  The Cartesian Plane contains the familiar xaxis and yaxis in which we plot ordered pairs. It is the familiar Rectangular Coordinate system. 

ChangeofBase Formula  There is an easy way to change the bases between logarithms. A simple formula, the ChangeofBase formula is an acquired taste. 

Chi  The twentysecond letter of the Greek alphabet.  
Closed Interval  A segment of the real number line including the endpoints.  
Coefficient  A number that indicates the multiple of an algebraic term. In a polynomial, a coefficient is the numeric value preceding the variable(s) that is to be multiplied times the variable(s). 

Cofactor  Typically the result of taking a determinant, it is a number associated with an element in a matrix.  
Common Logarithm  The baseten logarithm is often called the Common Logarithm.  
Common Ratio  In a geometric progression, subsequent terms are obtained by multiplication of terms by a constant called the Common Ratio.  
Composite Number  Composite Numbers relate to positive integers that are not prime. If a positive integer has factors other than itself and one, it is a Composite Number. 

Compound Interest  When the Time Value of Money generates interest and that interest is added to the principal to increase the amount of money to which subsequent interest is added, this is Compound Interest.  
Computation  Computation is the act of taking values and logical mathematical steps to make a calculation.  
Conclusion  When mathematical conclusions are valid the laws of math and science have been adhered to, and a logical approach has been taken. Sometimes conclusions are invalid because scientific or mathematic rigor has not been adhered to. Reason and judgment are often important to reaching sound or valid conclusions. 

Conjugates  Conjugates multiply to simpler entities based on changing the operator between terms of each conjugate from positive to negative, or vice versa.  
Consistent System of Equations  When a system of equations has at least one solution (and most often a unique solution) the equations are said to be Consistent.  
Constant  A mathematical value that never changes is said to be constant. Real numbers are constants because their value never changes. In a polynomial, a term with a variable (or variables) raised to the zero power is constant. 

Continuous  A function is considered Continuous if its graph has no gaps, no holes, no steps, and no cusps or discontinuities.  
Coordinate  A value associated with the location of a point is a Coordinate. In one dimension a Coordinate is a single value. In two dimensions, a point is defined by two Coordinates as an ordered pair. 

Coordinate Plane  Twodimensional entities are graphed or plotted in a plane, such as the rectangular plane or Cartesian Plane. Twodimensional polar coordinates are also plotted in a plane. It requires an ordered pair to specify a location in a plane. 

Correlation  When two variables have a strong linear relationship, either increasing proportionally or one variable decreasing as the other increases, we say there is (strong) Correlation between the variables.  
Countable  In common language, countable just means reasonably enumerated or countable, as in there are not too many objects to physically count. In human terms, the grains of sand in the Sahara Desert are not countable. But mathematically they actually are. So Countable means something a little different to the mathematicians. 

Cube Root  Given a real value, the Cube Root is the number or value that, when raised to the third power, equals the given real value. We multiply the cube root of a value times itself and times itself again to obtain the given value. 

Cubic  A Cubic is a thirdorder polynomial.  
Decimal  Digits to the left of the decimal point represent Integer Values. Digits to the right of the decimal point represent Decimal Fractions. All place values whether to the left or the right of the decimal point are successive powers of 10. The term decimal comes from the latin decimus which means tenth. In common language, base 10 numbers with digits to the right of the decimal point are considered decimal values. 

Decimal Fraction  Most simply, decimal fractions are the digits to the right of the decimal point.  
Decreasing  Decreasing means to lessen in extent or scope, to be reduced. A function is considered to be Decreasing if the values in the range decrease as the values from the domain increase. 

Degree (Polynomial)  The Degree of a polynomial is the order, or highest power (term) of the polynomial.  
Delta  Delta is the fourth letter of the Greek alphabet. Uppercase Delta looks like a triangle and is used to mean "the change in..." 

Denominator  The Denominator of a fraction is the number on the bottom; it is the divisor of the numerator.  
Dependent Variable  If y = f(x), then y is a function of x and y is the Dependent Variable. Think of it this way: whatever we get for output "y" depends on the input "x" we grab from the domain of the function. 

Direct Proportion  When variables are in Direct Proportion to one another they have the relation that as one variable grows the other either increases or decreases by a constant multiplication factor. When y = kx, we say the variables are in Direct Proportion. 

Direct Variation  Also direct proportion, Direct Variation describes the relation y = kx.  
Discriminant  In the Quadratic Formula, the radicand (the business inside the squareroot sign) is the Discriminant. In general, a Discriminant provides algebraic information about the roots of polynomials. 

Distance  A length from one point to another is considered a Distance. Any measurement in one dimension confers a length, which is Distance. 

Distance Formula  The familiar Distance Formula in Cartesian (rectangular) coordinates is a version of the Pythagorean Theorem, where the sum of the squares of the legs of a right triangle is equal to the square of the hypotenuse.  
Distributive Property  Given a sum to be multiplied by an outside factor, we may distribute the multiplicative factor over the addends of the sum. The result is that each addend of the sum is multiplied by the outside factor; we then sum the individual products. Example: 3 x (4z + 5) = 12Z + 15. More simply: 5 x (7 + 2) = 5 x 7 + 5 x 2, also written 35 + 10, which is 45. Of course, the original 5 x (9) is 45. So, relax. It's so, so easy. 

Division  The process of finding a quotient or a ratio. One of the four basic operations of arithmetic, division begins with a dividend that is to be divided by, or segmented into parts, by a divisor. The result of dividing the dividend by the divisor is called the quotient. 

Domain  The values that are "legal" and "legitimate" to put into a function are the elements of the Domain of that function. When y = f(x), the legitimate values of x are the Domain of the function. 

Doubling Time  The time it takes an exponential or geometric growth to double in size (grow by 100 percent of the original value) is its doubling time.  
Equality  A statement where two or more values are deemed to have an equal or identical value is a statement of Equality.  
Equation  A statement of equality, or equal value, is termed an Equation. When we solve an Equation we solve for some entity or value that makes the statement true. 

Evaluate  When we Evaluate an expression we determine its value or the value of some entity within it to (typically) make the statement true.  
Even (Integer)  Even integers end with one of the following five digits: 0, 2, 4, 6, or 8. These digits are considered Even and the integers that end with them are also considered Even. When Even integers are divided by two the quotient is an integer. 

Even Function  Even Functions are symmetrical about the yaxis, provided they are expressed as y = f(x). Even Functions adhere to the following: f(x) = f(x). 

Exact  Precise to the fullest extent possible. Complete and entirely accurate. Right on. 

Explicit  Ideas or notions directly expressed or understandable are considered Explicit.  
Exponent  Usually written as a superscript, an Exponent is a number or entity to which some other value is raised, as a power.  
Expression  A mathematical statement of almost any kind is considered an Expression.  
Factor (noun)  The noun Factor is a value that is multiplied with another Factor (or factors) to result in a product. That product of two or more factors is the result of the operation of multiplication. 

Factor (verb)  The verb Factor is the act of dividing some entity into components or pieces that, when multiplied together, produce the given entity. We "break apart" some real value or quantity into its multiplicative factors when we Factor. 

Factor Tree  A Factor Tree is a written mechanism to see the factors or prime factors of some value (usually an integer, but not necessarily).  
Factorial  A Factorial results from the multiplication of successive positive integers. The term Factorial is either a function or a number, depending on its specific use. 

Fibonacci Numbers  This set of numbers itself grows without bound, but the ratio of successive terms in the series converges to the golden ratio.  
First Order Polynomial  This type of equation has no variables raised to integer powers greater than one.  
Fixed  Fixed terms or values are constant, never changing value.  
FOIL (FIOL)  A mnemonic for remembering "firstoutsideinsidelast" for multiplication of two binomials. It is equivalent to FIOL, as we take the sum of products. 

Formula  A recipe or algorithm for calculation, evaluation, simplification, or just about anything we do in mathematics can be called a Formula.  
Fraction  Fractions are many, many things. But always, without fail, fractions are the result of dividing the top value (numerator) by the bottom value (denominator). 

Fractional Exponents  Real values can be raised to powers that are integers, decimals, or fractions. Fractional Exponents can be thought of as having a denominator that is the root of the value being raised to the power, with a numerator akin to an integer power. 

Function  Function takes on several meanings in the language of mathematics. A typical connotation is a relation between variables where for any input (an independent variable or element from the domain) we have a unique output (element in the range, or dependent variable result). 

Gamma  Gamma is the third letter of the Greek alphabet. 

General Form for Equation of a Line  Such a form has integer coefficients for both x and y when describing a line in Cartesian (rectangular) coordinates. 

Geometric Mean  The Geometric Mean of two real values is the square root of the product of the two values. More generally, the Geometric Mean of n values is the nth root of the product of the n values. 

Geometric Progression  This term is used for geometric series, geometric sums, or geometric sequences when subsequent terms result from multiplication by a constant that is most often called the common ratio. 

Geometric Series  A Geometric Series is a form of geometric progression. 

Googol  Ten raised to the power of one hundred equals one Googol. 

Googolplex  Ten raised to the power of a googol is a Googolplex; it is a huge number. 

Greatest Common Factor  The GCF of two integers (usually) is the largest integer that divides evenly into both integers. We sometimes use GCF for nonintegral values. 

Greek  Anyone interested in learning mathematics should embrace the Greek alphabet with 24 letters from alpha to omega. 

HalfLife  When some entity experiences exponential decay (reduction or diminution) the times it takes to lose half of its size (or strength) is its HalfLife. 

Height  Altitude. How tall something is, measured in some perpendicular fashion to the "bottom" is its height. 

Hexahedron  A sixfaced polyhedron is termed a Hexahedron. 

High Quartile  The 75th percentile. Also upper quartile. 

High Quintile  The 80th percentile; upper quintile. 

Horizontal  Horizontal comes from orientation like the horizon; parallel to the "flat" surface of the earth; perpendicular to vertical. 

Hypotenuse  The longest side of a right triangle is the Hypotenuse; it is always opposite the 90degree angle (or right vertex). 

Hypothesis  In a biconditional statement the hypothesis is followed by a conclusion. In the scientific method, the hypothesis is the conjecture to be proved or disproved. 

i, Square Root of 1  The smallcase i is reserved for the squareroot of a negative one; the square of i is 1. 

Identity  As opposed to a conditional statement that is sometimes true, an Identity will always be true. The multiplicative identity is 1; the additive identity is zero. 

Identity Property of Addition  The Identity Property of Addition says that adding zero to (or subtracting zero from) any real value will not change the value. 

Identity Property of Multiplication  The Identity Property of Multiplication says that multiplication of a real value by one (or division by one) will not change the value. 

IfandOnlyIf (Iff)  A statement that shows a condition both necessary and sufficient for the assertion. 

IfThen Statement  The classic biconditional statement is often phrased as an IfThen proposition. 

Impossibility  Despite what some "possibility thinkers" espouse, some things are mathematically impossible. For example, an exact real number cannot be simultaneously irrational and rational. 

Incircle  A circle inscribed within a regular polygon (or any triangle) is an Incircle. In a regular polygon, the radius of the Incircle is the apothem. 

Inconsistent  Inconsistent equations have no simultaneous solution. 

Increasing  If the values in the range of a function increase as the values of the domain increase, the function is said to be Increasing. 

Independent Variable  The set of values from the domain of a function comprise the values for the Independent Variable, the input variable into the function. 

Inductive Logic  Inductive Logic is the logic of afterthefact, or a posteriori. It results from observation of transpired events. 

Inequality  Real numbers can be compared using one of the following four forms: less than (<), lessthanorequalto (≤), greater than (>), or greaterthanorequalto (≥). Statements that use these comparisons are inequalities. If two real numbers are not equal, one has to be greater than the other. 

Infinite  In common language, not countable in any practical manner. In math, having no bounds or boundary. 

Infinite Geometric Progression  When a geometric progression has a common ratio less than one (technically, a common ratio whose absolute value is less than one), then the Infinite Geometric Progression will converge to a limit. 

Infinitesimal  Infinitely small is Infinitesimal, so tiny that it occupies no space. While in human terms anything really small (a molecule) is Infinitesimal, in math the term means approaching zero in size. 

Infinity  That without bound; limitless. 

Inscribed Circle  This term is the same as Incircle, a circle inscribed within a polygon. 

Integer  An Integer is a whole number or its negative. When expressed as a decimal, an Integer has nothing to the right of the decimal point (in American style). 

Interest  Given the timevalueofmoney, Interest is generated on a sum of capital as time passes. 

Interior  Interior means within or "inbetween."  
Interquartile Range  The Interquartile Range is the half of overall data between the 25th and 75th percentiles. 

Intersection  Where geometric entities cross, or where sets have common elements, is termed an Intersection. 

Interval  The space or region between two defined values is an Interval. 

Interval Notation  With brackets or parentheses, depending on whether endpoints are included in the set, Interval Notation expresses the solution set for an inequality. 

Invariant  Constant. Not changing. Static. That which does not vary. 

Inverse  Inverse carries a lot of meanings within the language of mathematics. 

Inverse Variation  Variables or factors that multiply to a constant value. The relation between two variables, when their product is constant, are said to be in a relation of Inverse Variation. 

Inverse, Conditional  Given an initial ifthen statement, the negative of both the hypothesis and conclusion provides the Inverse to the original statement. 

Inversely Proportional  The relationship between two variables when the product of two variables is a constant. Two variables in a relation of Inverse Variation are said to be Inversely Proportional. 

Iota  The ninth letter of the Greek alphabet, Iota means a very small amount. 

Irrational Number  A real number that cannot be expressed exactly as the ratio of two integers. Irrational Numbers, when expressed as decimals, never repeat or terminate. 

Iteration  A procedure that repeats, typically by adding some value to a variable in the process with each new calculation is called an iterative process, and each cycle of the calculation is an Iteration. A computational procedure in which a cycle of operations is repeated, often to approximate the solution to a problem. 

Joint Variation  Joint Variation is identical to direct variation; as one variable increases so, too, does the other variable increase proportionally. 

Jump  A step within a function is sometimes termed a Jump. 

Lambda  Lambda is the eleventh letter of the Greek alphabet and is used for wavelength in physics. 

Leading Coefficient  We usually write polynomials with the first term having the highest order, or power. The coefficient of this leading term is literally the Leading Coefficient. 

Leading Term  The first term in a polynomial, most typically the highestorder term, is the Leading Term of the polynomial.  
Least Common Denominator  When two or more fractions are being summed we want the LCD to facilitate the operation of addition. 

Least Common Multiple  The LCM is most typically applied to integers. It is the smallest value evenly divisible by each number for which we seek the LCM. 

Leg, Triangle  Most generally the legs of a triangle refer to the perpendicular sides of a right triangle only. 

Like Terms  Like Terms have the same variables raised to identical powers. 

Line  A collection of points that comprise the shortest path between two points in Euclidean geometry is a Line; all points in a Line are collinear and, of course, coplanar. 

Line Segment  A section of a line, with endpoints on both ends, is a Line Segment. 

Linear  As the first four letters imply, Linear means "of a line" or "lined up" in a collinear fashion. 

Local Maximum  A Local Maximum is a high spot on the graph of a function. Also termed a relative maximum, it is the greatest value within a defined neighborhood. 

Local Minimum  A Local Minimum is a low spot on the graph of a function. Also termed a relative minimum, it is the least value within a defined neighborhood. 

Loci  The points that comprise a function (or graph thereof) are its Loci. 

Locus  A single point on a function or on its graph is a Locus. 

Logarithm  A Logarithm is a number associated with a power and a base; the function is the inverse of an exponential function. 

Logic  Logic takes many forms and is instrumental in understanding the language of mathematics. 

Lower Quartile  Also first quartile, it is the 25th percentile, where 75 percent of the data is greater than this value. 

Lower Quintile  The 20th percentile; also first quintile. 

Magnitude (Powers of Ten)  When we multiply a real number times ten, we increase its magnitude by one. When we divide a real number by ten, we decrease its magnitude by one. Very much like place value, "orders of magnitude" refer to powers of ten, where greater place values indicate a greater magnitude. Conversely, lesser place values indicate a decrease in magnitude. 

Matrix  A rectangular array of numbers is often called a Matrix. 

Matrix Addition  Matrix Addition applies to matrices of like order, the same size. 

Maxima  The plural of maximum. Maxima are "high spots" on the graph of a function. 

Maximize  A process to establish the greatest extent, value, or size possible. 

Maximum  A highest value. A local Maximum is the highest value of a function within some defined neighborhood. 

Measure  A noun or verb, Measure implies comparison to an established standard. 

Measurement  The result from comparison to an established standard, Measurement may be exact only to an agreedto precision. 

Median, Data  The Median of a set of data is the value in the middle of an ordered or sorted list, with just as many values higher than the Median as lower than the Median. 

Midpoint  Every line segment (or side of a polygon) contains a point equidistant from the endpoints (or vertices), the Midpoint. 

Midpoint Formula  A simple recipe for finding the Midpoint of a line segment in Cartesian or rectangular coordinates. Add the xcoordinates of the endpoints of the line segment and divide by two for the xcoordinate of the midpoint. The yvalue follows similarly. 

Minima  The plural of minimum. Minima are low points on the graph of a function. 

Minimize  A process to establish the least extent, value, or size possible. 

Minimum  A low point or least value in the neighborhood of the graph of a function is a Minimum, the singular of minima. 

Minute, Time  Onesixtieth of an hour comprises one Minute of time. 

Mixed Number  We may write an "improper" fraction as a whole number followed immediately with a "proper" fraction. Such a form is termed a Mixed Fraction. 

Mode  While Mode can take on several meanings in mathematics, it generally is used for the value of data with the greatest frequency of occurrence in a list of values. 

Monomial  A single term. Casually, "term" and "monomial" are synonymous; strictly, a term is a monomial without a coefficient. 

Mu  The twelfth letter of the Greek alphabet, Mu is used for both the mean and median in a normal distribution. 

Multiplication  You know, times. The operation to simplify addition of identical values. You should learn your Times Tables, the basic facts of Multiplication. 

Multiplicative Inverse  Another name for Multiplicative Inverse is reciprocal. Reciprocals multiply to one. 

Natural  The set of Natural Numbers is also the set of counting numbers, the same numbers we learn to count when we're little kids: 1, 2, 3, 4.... Precisely in the language of math these are the positive integers. 

Natural Logarithm  The base of the Natural Logarithms is e, approximately 2.718. At 100 percent annual interest with continuous compounding over a year, the multiplication factor of principal is precisely e. 

Natural Numbers  The set of Natural Numbers is also the set of counting numbers, the same numbers we learn to count when we're little kids: 1, 2, 3, 4.... More precisely in the language of math these are the positive integers. 

Negative  Real values less than zero are Negative. We also consider the Negative of a real value to have the opposite sign, as the opposite (or Negative) of a Negative value is Positive. 

Negative Number  A real value less than zero is a Negative Number. 

Negative Reciprocal  The product of two Negative Reciprocals is 1. When lines in Cartesian or rectangular coordinates meet at right angles they have Negative Reciprocal slopes, unless they are precisely horizontal and vertical. 

Noncollinear  Not linear, not aligned, not part of the same line. Not collinear. 

Nonagon  A ninesided polygon. 

Nonnegative  We have occasions to refer to all positive values as well as to zero. These are all the real values that are Nonnegative. Literally, not negative. 

Nonzero  Literally, not zero. Typically used to mean either positive or negative values. 

Nth Degree  Simply raised to the degree of integer (usually) n, or N. In common, everyday language, to pursue something excessively, as parents giving the suitor of their teenage daughter an interrogation "to the nth degree." 

Nth Root  Given some integer N and a real value, the Nth Root of the real value is the number that when raised to the N power returns the real value.  
Nu  Nu is the 13th letter of the Greek alphabet. 

Null Set  The Null Set is the empty set. Mathematically there is but one empty set, the unique Null Set, the set with nothing in it. 

Number Line  The real Number Line is a depiction of the set of all real numbers from negative infinity to positive infinity. All real numbers lie on the Real Number Line. 

Numerator  The top number in a fraction, above the fraction bar, is the Numerator. It is the dividend to be divided by the divisor, which is the denominator. 

Octagon  An eightsided polygon. 

Octant  As we have four quadrants in the rectangular plane, we have eight Octants in rectangular space. In three dimensions the three axes divide space into eight sections, each termed an Octant. 

Odd  In common language: strange or unusual. For integers, numbers ending with any of these digits: 1, 3, 5, 7, or 9. 

Odds  The likelihood or probability of an event or specific outcome is termed the Odds of the event occurring. Odds, or probabilities, are always represented with values between 0 and 1, or between zero and 100 percent (inclusively). 

Omega  The last, or 24th, letter of the Greek alphabet is Omega. Uppercase Omega is used for ohms, a unit of electrical resistance. Lowercase Omega is used for angular velocity, a speed of rotation. 

Omicron  The 15th letter of the Greek alphabet. We don't use it in math because it looks just like an "o" or a zero. 

OneDimensional  Linear, or along one line of direction. Informally, constrained to stay along a narrow line. 

Open Interval  A section of a line whose set does not include the endpoints is considered an Open Interval. 

Operation  The processes of addition, subtraction, multiplication, and division are each termed an Operation. So, too, is raising a value to a exponent. 

Opposite  Many meanings are found for Opposite, including having direction 180 degrees from an original direction, or having the negative sign of a previous sign. Opposite real values have identical absolute values. 

Order (Polynomial)  The Order of a Polynomial relates to the highest power of variables in a term, typically the Order of the leading term of the Polynomial.  
Order of Operations  We have a hierarchy of Order to Operations in the language of mathematics. We do multiplication before we do addition, and we also work lefttoright. We work first inside of expressions within parentheses, then outward. 

Order, Polynomial  The Order of a Polynomial relates to the highest power of variables in a term, typically the Order of the leading term of the Polynomial. 

Ordered Pair  Two coordinates are required to label a point in a plane, typically (x, y). 

Ordered Triple  Three coordinates are required to label a point in space, typically (x, y, z). 

Ordinal Number  Ordinal Numbers are ordinary numbers, or the sequential references of order as first, second, third, and so on. 

Ordinate  In Cartesian or rectangular coordinates, the yaxis, or the coordinate from the yaxis; the second coordinate in an ordered pair. 

Origin  In one dimension: (0). In two dimensions: (0,0). In three dimensions: (0, 0, 0). 

Orthogonal  Most generally Orthogonal means perpendicular to a plane. 

Outcome  A specific event is often termed an Outcome. 

Outlier  When plotting data points, as in a scatterplot, if a single data point is far removed from the neighborhood of the other data points, such a farremoved data point is called an Outlier. 

Parabola  The graph of a quadratic function is a Parabola, a conic section. 

Parallel Lines  Coplanar Lines that never meet or cross are Parallel. If lines simply never cross, they may be skew (noncoplanar). 

Parametric Equation  In a general sense, we have a Parametric Equation when we define something in specific terms of something else. 

Parentheses  Symbols ( ) serve to isolate or group written entities. 

Parenthesis  Symbols ( ) serve to isolate or group written entities. 

Pascal's Triangle  Pascal's Triangle is an important device for understanding binomial expansion and combinatorics. 

Pentagon  A fivesided polygon. 

Percent  Literally, per hundred. Percents are equivalent to Fractions where the numerator reads as the percent and the denominator is 100. 

Percentage  Any reference to percent is a Percentage; the fraction of 100 a value represents. 

Percentile  Certain types of data lend themselves to description by what percent of the values exceed (or fall below) a specific data value. A Percentile states what percent of the data is less than the specific data value. 

Perfect Square  A Perfect Square is simply a number, value, or mathematical expression that results from any of these entities multiplied by itself. Most generally a Perfect Square is an integer that is the product of another integer times itself. 

Perimeter  The distance around the outside of a planar object or a plane figure is its perimeter. 

Permutation  A specific order to the grouping of objects in a combination is termed a Permutation. 

Perpendicular  At right angles. 

Phi  The twentyfirst letter of the Greek alphabet. 

Pi  The constant ratio of circumference to diameter is represented by the 16th letter of the Greek alphabet; it is approximately 3.14159. 

Plane  An infinite expanse of points in two dimensions. 

Plus  A symbol for addition, or the operation itself. 

Point  A location of infinitesimal size, that is, no size. A mathematical idea. 

PointSlope Equation  A handy algebraic relation to obtain an equation of a line from a given point and slope. 

Polygon  A closed plane figure with straight sides. 

Polynomial  A series of terms (or a single term, a monomial), usually with at least one variable; terms are separated by plus signs or minus signs.  
Population  Statistically when we sample a Population we generally seek a representative sample. A Population is the group from which we take a sample. 

Positive  Real values are Positive when they are greater than zero. 

Postulate  A farreaching conjecture or sense of reasoning for which an obvious and substantive base appears most reasonable. 

Power  Power most often means the value of an exponent. In advanced mathematics, a type of series where an infinite number of terms are raised to successive integer powers. 

Precision  The quality of finer measurement or estimation is termed Precision.  
Prime Factorization  The process of finding the prime factors of a composite number is called Prime Factorization. 

Prime Number  A positive integer evenly divisible by itself and one but no other integers is considered a Prime Number. 

Principal  An amount, typically money, upon which the time value of money (accumulation of an added percentage over a defined time) generates interest is termed Principal. 

Probability  The likelihood of an event or particular outcome is its Probability. All Probabilities are between 0 and 1 (between zero percent and 100 percent). 

Product  The result of the operation of multiplication is called a Product. 

Proper Subset  A set that is a subset of a given set and not identical to the given set is a Proper Subset of the given set. 

Proportional  In a (constant) ratio. 

Psi  The 23rd letter (nexttolast) of the Greek alphabet. 

Pyramid  A geometric solid with a base of a polygon and planar lateral sides that meet at a point called an apex is termed a Pyramid. 

Pythagorean Triple  A series of three integers for whom the Pythagorean relation holds, as 345 or 51213, because 3Â² + 4Â² = 5Â² and 5Â² + 12Â² = 13Â². 

Quadrangle  Another name for a quadrilateral, a foursided polygon. 

Quadrant  One of the four areas of the rectangular or Cartesian plane that is divided into fourths by the two axes. 

Quadratic  A secondorder polynomial of the form ax² + bx + c = 0 is considered a Quadratic; it graphs to a parabola.  
Quadratic Equation  Any secondorder polynomial in one variable set equal to a constant is termed a Quadratic Equation. 

Quadruple  A verb or noun; to multiply by four or the fourth integral multiple, respectively. 

Quartiles  Most generally, the 25th and 75th percentiles are termed the Low Quartile and High Quartile, respectively. 

Quintiles  Most generally, the 20th and 80th percentiles are termed the Low Quintile and High Quintile, respectively. 

Quintuple  A verb or noun; to multiply by five or the fifth integral multiple, respectively. 

Quotient  The result of the operation of division, the Quotient results from dividing a dividend by a divisor; also the value of a fraction that is always numerator divided by denominator. 

Radical  A root symbol. Strictly, the radical is the type of root, with the number of the root expressed as an index and an absence of an index indicating a square root; the radicand is the number expressed within the radical. Informally, simply a square root. 

Radicand  A number taken to a root is a Radicand; the number under a root sign or written inside a Radical.  
Radius  Onehalf the diameter of a circle is the Radius. It is the distance from the center of a circle to any point on the circle. 

Range  We may speak of a Range of values as simply the difference between high and low values of a data set. More specifically, the values generated by the input of domain values into a function map into the Range of values of the function. 

Ratio  Sometimes Ratio is meant to state a constant proportion. More generally, the Ratio of two real values is the quotient that results from dividing one number by the other. 

Rational  A Rational number can be expressed as the ratio of two integers. When expressed as a decimal, a Rational number will either repeat or terminate (with repeating zeros). 

Rational Expression  Mathematical statements written as fractions with a numerator and a denominator are often termed Rational Expressions. 

Ray  A set of collinear points, a Ray has an endpoint and proceeds infinitely far in a single direction. 

Real Number  Situated on the Real Number line, a real value is either less than, equal to, or greater than every other real value. 

Reciprocal  Every nonzero real value has a Reciprocal. A number and its Reciprocal multiply to one. We may find a Reciprocal of a number by dividing it into 1. 

Rectangle  A quadrilateral with many special properties, including all those of a parallelogram, and then some. 

Rectangular Coordinates  The familiar xy coordinate plane; Cartesian Coordinates. 

Reflexive  Literally "in relation to itself." When we say A = A, we employ a Reflexive property. 

Regular Polygon  A Regular Polygon is both equilateral (all sides congruent) and equiangular (all angles congruent). 

Regular Prism  A Prism with bases of Regular polygons. 

Regular Pyramid  A Pyramid with a base of a Regular polygon. 

Relative Maximum  Also a local Maximum, a high spot on the graph of a function. It is the greatest value within a defined neighborhood. 

Relative Minimum  Also a local Minimum, a low spot on the graph of a function. It is the least value within a defined neighborhood. 

Relatively Prime  Two integers with no common factors other than one are said to be Relatively Prime. 

Remainder  When a divisor does not divide evenly into the dividend, we have a Remainder. 

Revolutions per Minute  Abbreviated "rpm," it conveys the number of complete circular rotations that occur every 60 seconds at some constant rate of revolution. 

Rho  Lowercase Rho, the 17th letter of the Greek alphabet, is often used for density (mass per unit volume) in physics. 

Right Angle  An angle of 90 degrees or pi/2 radians. Perpendicular lines meet at Right Angles. 

Right Triangle  A triangle with a right angle. 

Root (Number)  The Root of a given Number is the value that raised to the power of the root returns the given number.  
Root Mean Square  Abbreviated RMS it is the square root of the arithmetic mean of the squares of some real values, as from a data set. 

Root, Number  The Root of a given Number is the value that raised to the power of the root returns the given number. 

Rotation  Movement in a circulation or circular fashion, often around a point or an axis, is termed Rotation. 

Rounding  Not exactly truncating, rounding involves reduction in the precision of a value to approximate that value to some exact value with less precision. 

Sample  When we Sample a population we typically seek a representative Sample. 

Sample Space  We often use Sample Space to designate all the possibilities of potential outcomes for an event or process. 

Scalar  A value with unit of size (magnitude) and no direction is termed a Scalar. Contrast with a vector that has both magnitude and direction; a Scalar has magnitude but no direction. 

Scalene  A triangle is considered Scalene if no two sides have the same length. 

Scatterplot  A planar plot of points from two variables with each point representative of a datum from both variables, most often with some relation or correlation. 

Scientific Notation  Scientific Notation is an easy way to represent either very large numbers or very small numbers. Large numbers are expressed with positive powers of ten; small numbers are expressed with negative powers of ten. Such numbers often represent physical quantities or values that would be inconvenient or cumbersome to write with typical decimal representations. 

Second, Degree  While "second degree" applies to a polynomial, a single Second with respect to Degree measure is onesixtieth of one minute, or one sixtieth of one sixtieth of one degree, or 1/1,296,000 of a revolution. 

Second, Time  One sixtieth of a minute, or 1/3600 of an hour, is one Second of Time. 

SecondOrder Polynomial  A polynomial in which the highestorder term is of order two. The highest power in secondorder univariate (one variable) polynomial is two; the degree of such a polynomial is degree two. 

Segment, Circle  A portion of a circle bounded by a chord and the circle itself. 

Segment, Line  A Line Segment is a set of collinear points bounded on both ends with, literally, endpoints. 

Semicircle  Half a circle; the portion of a circle on one side of a diameter. 

Series  Most often a sequence of terms to be summed. Informally, any sequence of terms may be a Series. 

Set  Any collection of objects or values is considered a Set, whose cardinal number is the number of objects in the Set. 

Set Intersection  The Intersection of two (or more) Sets is the subset common to both (or all) Sets. Logically, the Intersection of two Sets A and B is literally the Set of "A and B." 

Set Union  The Union of two (or more) Sets is the Set that contains both (or all) Sets. Logically, the Union of two Sets A and B is the Set of elements contained in either Set A or B, literally "A or B." 

Sigma  The 18th letter of the Greek alphabet, uppercase sigma is used for summation notation, lowercase Sigma often denotes a standard deviation in statistics. 

Significant Digits  Informally, Digits that are not zero. Slightly more formally, nonzero Digits as well as zeros between nonzero Digits. Strictly, the number of Digits required to express a calculated value to within the reasonable tolerance or uncertainty of calculation. 

Simple Closed Curve  A planar figure that neither crosses itself or contains a gap is a Simple Closed Curve; note that a curve can be "straight" according to the mathematicians. 

Simple Harmonic Motion  Periodic Motion with constant length of cycle time (a fixed period) is termed Simple Harmonic Motion. 

Simplify  To express (or rewrite) in more concise terms. To make simpler. 

Simultaneous Equations  Equations with common solutions are Simultaneous Equations. Also, equivalent equalities (statements with equal signs) may be termed Simultaneous Equations. 

Skew  Lines neither intersecting nor parallel (noncoplanar lines) are termed Skew lines. 

Slope  A number associated with a line graphed in a plane, Slope is the ratio of rise over run, an indication of the steepness of the line. We may write a line as y = mx + b and use the value of m for Slope. 

SlopeIntercept Equation of a Line  The familiar y = mx + b, where m represents Slope and b is the yIntercept. 

Solid  A threedimensional geometric figure or body that includes the interior region. 

Solution  Too often in math class, "the answer." More directly, a Solution is a value (or set of values) that makes a mathematical statement true. 

Solution Set  Strictly, any Solution is a Solution Set, the value(s) that make a mathematical statement true. 

Speed  A (typically fixed) ratio of length or distance to a unit of time; Speed is a scalar value, as in miles per hour (mph) or feet per second (fps). 

Sphere  A threedimensional figure comprised of points equidistant from a center point; a Sphere has a fixed radius. 

Square  1 (noun)  the regular quadrilateral that is both equilateral and equiangular. 2 (noun)  the result of multiplying a number times itself. 3 (verb)  the operation of multiplying a number times itself; equivalently raising it to second power, or to the exponent 2. 

Square Matrix  A Square Matrix has the same number of rows as columns. 

Square Root  Given a real value, the number that times itself (squared) produces the given value.  
SSS Congruence  Two triangles whose corresponding sides are congruent are themselves congruent. 

Standard Equation of a Line  When expressing the Equation of a Line with integral coefficients we may have the Standard Equation of a Line. 

Standard Position  An angle in Standard Position has been rotated counterclockwise (for positive rotation) from an initial ray on the positive xaxis. 

StemandLeaf Plot  A graphical device to group statistical data, typically by leading digits. 

Step Function  A discontinuous Function where the range jumps in increments (usually fixed) may be a Step Function. 

Straight Angle  An angle of 180 degrees or pi radians. 

Strict Inequality  A Strict Inequality is an inequality that does not include an "or equal to...". Strict inequality only apply to unequal values, as one is either greater than (>) or less than (<) the other. 

Subset  Every set is a Subset of itself. A Subset has elements all contained in a "parent" set. 

Subtraction  The operation we begin thinking of as "take away" or "minus" is a way to find the difference between values. 

Sum  The result of addition. 

Symmetry  Having a like but reversed profile or image (a mirror image) about a line is having the quality of Symmetry about the axis (of Symmetry). 

System of Equations  Most generally simultaneous Equations, or a set of Equations with identical variables. 

Tangent Line  A Line is said to be Tangent to a function when it touches the graph of the function at a single point. 

Tau  Tau is the 19th letter of the Greek alphabet. 

Term  In most mathematical expressions a single Term is isolated from other Terms by plus or minus signs. A Term is the same as a Monomial, in casual mathematical language. More strictly, a Term is a Monomial with no coefficient. 

Tessellate  A planar pattern of repeating geometric shapes is a Tessellation; to produce these shapes is to Tessellate. 

Third Quartile  For certain types of data, it is the 75th percentile. Also high quartile or upper quartile. 

Three Dimensions  The Dimensions of space or volume are Three Dimensions, typically labeled with rectangular, spherical, or cylindrical coordinates. 

Transitive Property  The Transitive Property is exhibited when three values are related in the following manner: If A = B and B = C, then A = C. The relation need not be equality. 

Transversal  A line that crosses two or more parallel lines is often termed a Transversal. 

Triangle  A threesided polygon. Triangles are either acute, right, or obtuse. 

Trinomial  A polynomial with three terms.  
Triple  As a verb, Triple means to multiply by three. As a noun, the result from multiplication by three. 

Truncation  Replace the lesser digits of some number with zeros with no regard for rounding; this is Truncation. 

Two Dimensions  A plane has Two Dimensions. Planar figures are Two Dimensional. 

Uncountable  In human terms, Uncountable means too many to practically count or enumerate. In math, an infinite function without a onetoone correspondence to natural numbers. 

Uniform  Constant and unchanging; fixed. 

Union  The Union of two or more sets is the set of elements from all the sets. The Union of sets A and B is literally the set "A and B." 

Upper Quartile  Also the high quartile, the 75th percentile. 

Upper Quintile  Also high quintile, the 80th percentile. 

Upsilon  Upsilon is the 20th letter of the Greek alphabet. 

Variable  A Variable is a symbol, most often a letter, to represent a quantity that may change value, that is literally to vary in its value. 

Velocity  Formally a vector in physics, Velocity has both magnitude (speed) and direction, as in miles per hour (mph) northwest (NW) or feet per second (fps) upward.  
Venn Diagram  Most often graphics of overlapping circles and ovals, a Venn Diagram depicts sets, subsets, and their intersections and unions. 

Verify  To confirm is to Verify. When we Verify, we prove or establish some assertion to a dependable conclusion independent from bias. There is wisdom in these words: "Trust, but Verify." 

Vertex  A "corner" of a polygon is a Vertex; an extremum of a conic section is a Vertex; the endpoint(s) of rays that form an angle is a Vertex. 

Vertical  Straight up, perpendicular to horizontal, is Vertical. Vertical lines have an indeterminate or infinite slope. 

Vertical Angles  When two lines cross (intersect) they form two pairs of Vertical Angles; the Angles within each pair of Vertical Angles are congruent.  
Vertical Line Test  Given a relation between x and y expressed as y = f(x), the relation is a function if the graph passes the Vertical Line Test; no vertical line may cross the graph more than once. No single element from the domain of x may generate more than a single value of y mapped into the range, to be considered a function. 

Volume  The extent to which an object fills units of threedimensional space is its Volume. 

Weighted Average  When several factors comprise a score or calculation and the factors have different amounts of importance to the overall result, a Weighted Average may be calculated by assigning more importance (or "weight") to one factor over another. 

Whole Numbers  Most often, the set of positive integers and zero. 

xIntercept  Where a graph crosses (intersects) the xaxis in rectangular or Cartesian coordinates is termed an XIntercept. 

xy Plane  The familiar coordinate plane. The xaxis is almost universally horizontal; the yaxis is subsequently vertical. Or, the Plane of XY in threedimensional space with ordered triples (x, y, z). 

xz Plane  In three dimensions, the plane orthogonal to the yaxis. 

Xi  The 14th letter of the Greek alphabet. 

yIntercept  The point where a function graph crosses (intersects) the yaxis is termed the YIntercept. In the familiar linear equation form (SlopeIntercept form) of y = mx + b, the value of b is the YIntercept. 

yz Plane  In three dimensions, the plane orthogonal to the xaxis. 

Zero  The only real value that is neither negative nor positive. It is an integer value. 

Zero Slope  When the calculation of Slope is Zero there is a rise of Zero over any value of run. Most generally, a horizontal line has Zero Slope. 

Zero, Function  The Zero of a Function is the x value for which the output, y, of the function is zero; provided, of course, that y = f(x). 

Zeta  The sixth letter of the Greek alphabet. 
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