ADVANCED ALGEBRA GLOSSARY

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Additive Inverse for Matrices Mr. X takes the mystery out of Additive Inverse for Matrices, a matrix when added to another equals the Zero Matrix.
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Alternating Series A series in which successive terms have opposite signs.
Every other term is positive; every other term is negative.
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Argument of a Function The term or expression upon which a function operates.
In y=f(x), the argument of the function is x.
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Argument of a Vector The angle at which a vector is directed.
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Arithmetic Progression Also Arithmetic Sequence.
A series of terms where successive terms are obtained by addition of a constant.
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Arithmetic Sequence Also Arithmetic Sequence.
A series of terms where successive terms are obtained by addition of a constant.
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Asymptote A line (or curve) that a function approaches without actually reaching the line as the domain either grows unbounded or approaches a limit. Play_video
Augmented Matrix A matrix form for a linear system of equations where the number of columns is one greater than the number of rows, the final column typically coming from the constants in the linear equations.
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Base, Exponential The value being raised by powers as exponents; the number being raised to the power. Play_video
Beta Beta is the second letter of the Greek alphabet. Play_video
Biconditional A biconditional statement has literally two conditions.
The classic If-Then statement is the biconditional with a hypothesis and conclusion.
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Binomial A binomial has two terms.
Terms are usually separated by plus signs or minus signs.
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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.
Statistics and probability calculations make significant use of binomial coefficients.
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Binomial Probability When outcomes are of a binary nature, the logic of two states (high or low, true or false, or the ones and zeroes of computer data streams) we can employ techniques of binomial probability, with coefficients from Pascal's Triangle, to determine the likelihood of potential events or outcomes. Play_video
Binomial Theorem The Binomial Theorem affords the use of coefficients to calculate probabilities that are determined with the logic of two states.
In situations where outcomes are either true or false, high or low, or the 1 or 0 of binary data streams, the Binomial Theorem gives us efficient calculations for likelihoods of events.
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Boundary Some functions are bounded, some are not.
Some regions are bounded, some are not.
To be bounded means to have a limit; its extent only goes so far, and then it stops or ends.
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Bounded Function A bounded function approaches or reaches a limit.
If a function goes toward infinity it is generally considered unbounded.
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Change-of-Base Formula There is an easy way to change the bases between logarithms.
A simple formula, the Change-of-Base formula is an acquired taste.
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Coefficient Matrix A matrix comprised of coefficients which can be used to solve a system of equations. Play_video
Column, Matrix Strictly speaking, a Column Matrix is often a single column.
More generally, a column is a vertical array of elements within a matrix.
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Combinations Combinations are calculated to be the number of ways that a number of objects may be selected from a group of objects. Play_video
Combinatorics The branch of math that provides calculations for the selection of a number of elements from a set is called Combinatorics. Play_video
Common Logarithm The base-ten logarithm is often called the Common Logarithm. Play_video
Common Ratio In a geometric progression, subsequent terms are obtained by multiplication of terms by a constant called the Common Ratio. Play_video
Complement of an Event The complement of an event pertains to probability.
If the probability of an event is x, then the probability of the complement of that event is 100 percent minus x.
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Complex Conjugate The Complex Conjugate of (a + bi) is (a - bi).
The Complex Conjugate of (c - di) is (c + di).
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Complex Number All numbers, as it turns out, are complex.
When the "imaginary part" has a zero coefficient, the number is purely real.
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Complex Plane The complex number plane is required to map or plot complex numbers because the complex numbers themselves have two components. Play_video
Conic Section Any of the various geometric entities that are formed by slicing a cone (or double cone) are termed Conic Sections.
The list includes: circles, ellipses, parabolas, and hyperbolas.
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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. Play_video
Continuous Compounding When an entity experiences Continuous Compounding it grows unceasingly and constantly, that is, the addition of some portion of its size to its size happens all of the time.
Bacterial growth and population growth are often considered to be functions of Continuous Compounding.
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Continuous Function When the graph of a function has no holes, no gaps, no steps, or no discontinuities, then it is considered Continuous.
It may have cusps.
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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. Play_video
Correlation Coefficient We typically use "r" for the Correlation Coefficient.
When two variables are strongly correlated, that is, have a strong linear relationship, r will have a value that approaches either 1 or -1, depending on whether the variables increase with respect to each other.
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Cramer's Rule Cramer's Rule provides a matrix manipulation to solve simultaneous equations. Play_video
Cross Product A product of vectors that generates another vector is often a Cross Product. Play_video
Cubic A Cubic is a third-order polynomial. Play_video
Deductive Logic Deductive Logic is employed before events have transpired, before the fact. Play_video
Degree, Polynomial The Degree of a polynomial is the order, or highest power (term) of the polynomial. Play_video
Determinant A Determinant is a number associated with a square matrix.
It may also be a cofactor, a number associated with a square array from a larger matrix.
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Diagonal Matrix A square matrix with zero values everywhere except on the main diagonal (upper left to lower right) is termed a Diagonal Matrix. Play_video
Dimension, Matrix The Dimension of a matrix is its order, or size.
We label the order of a matrix by its number of rows then its number of columns.
A 4x3 matrix is read as "a four by three matrix" and has four rows and three columns.
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Discontinuity When a function is literally not continuous because of a gap, a step, a hole, or any kind of "break" it is considered discontinuous. Play_video
Discrete Function When the inputs from the domain of the function are not smooth and continuous but rather incremental, the function is considered to be a Discrete Function. Play_video
Discriminant In the Quadratic Formula, the radicand (the business inside the square-root sign) is the Discriminant.
In general, a Discriminant provides algebraic information about the roots of polynomials.
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Disjoint Disjoint sets have no common elements. Play_video
Divergent Geometric Progression An infinite geometric progression (or a significant portion of one) is termed Divergent when its common ratio has an absolute value less than or equal to -1, or greater than or equal to 1. Play_video
Dot Product A product of vector multiplication, the Dot Product is a scalar, which means it has magnitude only and not an associated direction.
The Dot Product does not result in another vector.
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e, Base of Natural Logarithm A very important number, e is approximately 2.718281828459045. Play_video
Eccentricity A parameter of conic sections.
Eccentricity is itself rather eccentric, or out of the ordinary.
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Element Element has a lot of meanings.
Each entry in a matrix is an Element.
Each object in a set can be termed an Element.
A constituent or piece of something bigger is also called an Element.
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Ellipse One of the conic sections, an Ellipse is a plane figure with well-defined properties that often include vertices and a major axis and a minor axis. Play_video
Empty Set The Empty Set is also called the Null Set.
It is the set with nothing in it, and there is but one Null Set (or Empty Set).
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Epsilon The fifth letter of the Greek alphabet is Epsilon. Play_video
Equivalence When we establish Equivalence we set forth two or more equivalent or equal entities. Play_video
Eta Eta is the seventh letter of the Greek alphabet. Play_video
Exclusion Exclusion means to leave out or to not include some value, either from a set or for consideration into a set of values. Play_video
Expansion By Cofactors Expansion By Cofactors is a process to evaluate matrix values such as determinants by taking a sum of values generated by the sum of cofactor products. Play_video
Expected Value The Expected Value is, statistically, the real number or value that is most likely to occur for some event when examined as an average value.
The Expected Value may not actually be an obtainable value; it is an average value.
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Exponential Decay When an established quantity loses value and decreases by some constant percentage over some constant period of time it is considered to experience Exponential Decay. Play_video
Exponential Function An Exponential Function employs the independent variable as an exponent on a constant.
If expressed as y = f(x), the Exponential Function will pass through (0,1).
Such a function is the inverse to a logarithmic function.
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Exponential Growth When an established quantity gains value and increases by some constant percentage over some constant period of time it is considered to experience Exponential Growth. Play_video
Extraneous Solution Sometimes we perform mathematical manipulations and obtain solutions that do not make sense but nevertheless are obtained by following the rules of, say, algebra.
Such solutions are termed Extraneous.
Often they do not strictly satisfy the original conditions of the problem that was solved.
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Extremum The highest and lowest values for the output of a function are called Extremum, the singular form of plural extrema. Play_video
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.
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Fibonacci Numbers This set of numbers itself grows without bound, but the ratio of successive terms in the series converges to the golden ratio. Play_video
Finite The common meaning of Finite and its meaning to mathematicians are not quite the same.
In everyday language, Finite means countable within a reasonable time.
To math people, Finite means not infinite; it means, simply, having a bound.
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First Quartile In certain sets of data it is appropriate to divide the values into fourths by frequency of occurrence.
The First Quartile is the 25th percentile, or the high-end value of the low-end quarter of data values.
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First Quintile In certain sets of data it is appropriate to divide the values into fifths by frequency of occurrence.
The First Quintile is the 20th percentile, or the high-end value of the lowest 20 percent (fifth) of data values.
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Formula A recipe or algorithm for calculation, evaluation, simplification, or just about anything we do in mathematics can be called a Formula. Play_video
Fourth Quintile When data is appropriately characterized by percentiles, the Fourth Quintile is the 80th percentile, with only 20 percent of the data values greater than this; it is the bottom of the highest fifth. Play_video
Frequency How often (or frequently) does something occur? That is its Frequency.
The Frequency of a waveform is inversely proportional to its wavelength.
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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).
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Fundamental Theorem of Algebra Single-variable polynomials with complex coefficients have at least one complex root.
The field of complex numbers is closed.
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Fundamental Theorem of Arithmetic A theorem that all integers can be written as the product of prime numbers is often called the Fundamental Theorem of Arithmetic. Play_video
Gamma Gamma is the third letter of the Greek alphabet.
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Gauss-Jordan Elimination Gauss Jordan Elimination is a traditional matrix row manipulation used to find inverse matrices.
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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.
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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.
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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.
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Geometric Series A Geometric Series is a form of geometric progression.
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Googol Ten raised to the power of one hundred equals one Googol.
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Googolplex Ten raised to the power of a googol is a Googolplex; it is a huge number.
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Greek Anyone interested in learning mathematics should embrace the Greek alphabet with 24 letters from alpha to omega.
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Half-Life When some entity experiences exponential decay (reduction or diminution) the times it takes to lose half of its size (or strength) is its Half-Life.
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Harmonic A small integral multiple (or divisor) of a waveform is a harmonic.
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Helix A straight line wrapped around a circular cylinder at some angle not perpendicular to the base of the cylinder results in a Helix.
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Heron's Formula A wonderful little recipe (algorithm) for finding the area of a triangle when sides are known and the altitude is not known, the formula is best expressed with a semiperimeter.
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Hexahedron A six-faced polyhedron is termed a Hexahedron.
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High Quartile The 75th percentile.
Also upper quartile.
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High Quintile The 80th percentile; upper quintile.
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Hole A missing element (typically a point) from an otherwise continuous function is called a Hole.
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Homogeneous Equations Homogeneous Equations have terms of like power or order.
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Horizontal Horizontal comes from orientation like the horizon; parallel to the "flat" surface of the earth; perpendicular to vertical.
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Hyperbola A conic section of specific mathematical relation to foci; its shape is the intersection of a double cone with a plane.
The difference between distances from a locus on the Hyperbola to the two foci is a constant.
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Hyperbolic Geometry Hyperbolic Geometry is non-Euclidean geometry; within it the Parallel Postulate does not hold.
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Hypotenuse The longest side of a right triangle is the Hypotenuse; it is always opposite the 90-degree angle (or right vertex).
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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.
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i, Square Root of -1 The small-case i is reserved for the square-root of a negative one; the square of i is -1.
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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.
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Identity Matrix The Identity Matrix is a square matrix with zeros everywhere except on the main diagonal, which has all elements equal to one.
It is the product of a matrix and its inverse.
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If-and-Only-If (Iff) A statement that shows a condition both necessary and sufficient for the assertion.
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If-Then Statement The classic biconditional statement is often phrased as an If-Then proposition.
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Imaginary Number Imaginary Numbers exist, but we do not call them "real." Play_video
Implicit Implied as opposed to absolutely expressed, Implicit functions typically have two (or more) variables on one side of the equation.
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Impossibility Despite what some "possibility thinkers" espouse, some things are mathematically impossible.
For example, an exact real number cannot be simultaneously irrational and rational.
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Inconsistent Inconsistent equations have no simultaneous solution.
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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.
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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.
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Indeterminate Often a resultant fraction like 0/0 is an Indeterminate form that requires more analysis to determine its true nature, depending on the functions involved.
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Inductive Logic Inductive Logic is the logic of after-the-fact, or a posteriori.
It results from observation of transpired events.
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Infinite In common language, not countable in any practical manner.
In math, having no bounds or boundary.
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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.
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Infinite Series Any series of terms whose progression has an unlimited (limitless) number of terms is an Infinite Series.
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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.
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Infinity That without bound; limitless.
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Inflection On the graph of a function, a point of Inflection is where the curve begins to "bend the other way." Play_video
Inner Product With vectors, the dot product is considered an Inner Product.
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Inscribed Circle This term is the same as Incircle, a circle inscribed within a polygon.
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Instantaneous Velocity The reading at any instant on a speedometer gives an Instantaneous Velocity.
To be precise, the speedometer gives an instant snapshot of speed (only) with no direction; physical velocity has both magnitude and direction, as a vector.
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Interest Given the time-value-of-money, Interest is generated on a sum of capital as time passes.
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Intermediate Value Theorem The IVT basically says that between two different values is an intermediate value somewhere between the extremes.
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Interquartile Range The Interquartile Range is the half of overall data between the 25th and 75th percentiles.
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Intersection Where geometric entities cross, or where sets have common elements, is termed an Intersection.
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Interval The space or region between two defined values is an Interval.
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Interval Notation With brackets or parentheses, depending on whether endpoints are included in the set, Interval Notation expresses the solution set for an inequality.
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Invariant Constant.
Not changing.
Static.
That which does not vary.
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Inverse Inverse carries a lot of meanings within the language of mathematics.
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Inverse Cosecant Given a number, this function returns the angle whose cosecant is the given number.
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Inverse Cosine Given a number, this function returns the angle whose cosine is the given number.
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Inverse Cotangent Given a number, this function returns the angle whose cotangent is the given number.
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Inverse Function For most functions in Cartesian coordinates, the inverse function is the mirror image around the x=y line.
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Inverse Secant Given a number, this function returns the angle whose secant is the given number.
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Inverse Sine Given a number, this function returns the angle whose sine is the given number.
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Inverse Tangent Given a number, this function returns the angle whose tangent is the given number.
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Inverse Trigonometric Function Given a number, this function returns the angle whose trig function is the given number.
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Inverse Variation Variables or factors that multiply to a constant value are said to be in a relation of Inverse Variation.
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Inverse, Conditional Given an initial if-then statement, the negative of both the hypothesis and conclusion provides the Inverse to the original statement.
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Inverse, Matrix When two matrices multiply to produce the identity matrix, each is said to be the Inverse Matrix of the other.
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Inversely Proportional When the product of two variables is a constant the variables are said to be Inversely Proportional to one another.
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Iota The ninth letter of the Greek alphabet, Iota means a very small amount.
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Irrational Number An Irrational Number cannot be expressed exactly as the ratio of two integers.
Irrational Numbers, when expressed as decimals, never repeat or terminate.
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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.
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Joint Variation Joint Variation is identical to direct variation; as one variable increases so, too, does the other variable increase proportionally.
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Jump A step within a function is sometimes termed a Jump.
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Kappa The tenth letter of the Greek alphabet is Kappa, popular on college campuses with sororities and fraternities.
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Lambda Lambda is the eleventh letter of the Greek alphabet and is used for wavelength in physics.
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Leading Coefficient Most typically we write polynomials with the first term having the highest order, or power.
The coefficient of this leading term is literally the Leading Coefficient.
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Leading Term The first term in a polynomial, most typically the highest-order term, is the Leading Term of the polynomial.
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Least Upper Bound As the name implies, a function often has a highest value or a limit beyond which it may not realize.
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Leg, Trapezoid The Leg of a Trapezoid is one of the non-parallel sides.
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Leg, Triangle Most generally the legs of a triangle refer to the perpendicular sides of a right triangle only.
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Lemma A little, inconsequential theorem is sometimes called a Lemma.
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Limit Some functions have a Limit, a bound beyond which they may not realize.
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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.
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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.
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Loci The points that comprise a function (or graph thereof) are its Loci.
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Locus A single point on a function or on its graph is a Locus.
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Logarithm A Logarithm is a number associated with a power and a base; the function is the inverse of an exponential function.
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Logic Logic takes many forms and is instrumental in understanding the language of mathematics.
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Lower Bound As the name suggests, some functions are limited on the low side.
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Lower Quartile Also first quartile, it is the 25th percentile, where 75 percent of the data is greater than this value.
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Lower Quintile The 20th percentile; also first quintile.
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Magnitude, Powers of Ten Often when we compare the multiplication by various powers of ten we speak of the magnitude of the effect of the multiplication.
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Magnitude, Vectors The Magnitude of a vector is the length of the vector.
We may apply a Pythagorean relation to the perpendicular components of the vector to find the length.
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Major Axis Certain conic sections have a Major Axis, a line (segment) between vertices.
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Matrix A rectangular array of numbers is often called a Matrix.
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Matrix Addition Matrix Addition applies to matrices of like order, the same size.
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Matrix Element One of the numbers or terms within the rectangular array of terms in a matrix is an Element of the Matrix.
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Matrix Multiplication To multiply two matrices: the number of columns in the first matrix must match the number of rows in the second matrix.
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Maxima The plural of maximum.
Maxima are "high spots" on the graph of a function.
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Maximize A process to establish the greatest extent, value, or size possible.
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Maximum A highest value.
A local Maximum is the highest value of a function within some defined neighborhood.
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Mean Value Theorem Essentially, between any two extremes is an average value.
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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.
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Median, Trapezoid The average of the lengths of the bases of a trapezoid.
The Median is a line segment parallel to and equidistant from the bases.
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Minima The plural of minimum.
Minima are low points on the graph of a function.
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Minimize A process to establish the least extent, value, or size possible.
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Minimum A low point or least value in the neighborhood of the graph of a function is a Minimum, the singular of minima.
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Minor Axis A line or line segment specific to certain conic sections.
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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.
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Modulo N Often written as "mod n," it is the remainder after division, and it makes sense in the realm of integers (only).
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Modulus Most typically it is the length of a vector.
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Modus Ponens We have "If A, then B." Modus Ponens is a piece of logic that goes like this: if we know A to be true, then we know that B must be true, too.
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Modus Tollens Begin with "If A, then B." That's a given.
We (somehow) know that B is false.
We then may infer (but not conclude) that A is false.
Modus Tollens is not particularly robust; it is not entirely dependable.
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Moment Moment takes on many meanings in statistics and physics.
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Moment of Inertia Each shape or body has an associated Moment of Inertia related to mass distribution and the choice of the axis around which the body is rotated.
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Mu The twelfth letter of the Greek alphabet, Mu is used for both the mean and median in a normal distribution.
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Multiplicative Inverse Another name for Multiplicative Inverse is reciprocal.
Reciprocals multiply to one.
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Multiplicative Inverse, Matrix The Multiplicative Inverse of a Matrix is the matrix for whom the operation of matrix multiplication on another matrix produces the identity matrix.
More commonly it is termed simply the Inverse Matrix.
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Multivariable Having more than one variable.
Also multivariate.
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Multivariate Having more than one variable.
Also multivariable.
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N-gon When a polynomial has so many sides that we cannot easily remember its name, we just take the number of sides (n) and add "gon" to our characterization, as a 16-sided polygon would be called a "16-gon." Play_video
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.
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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.
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Newton's Method An iterative method for finding roots of polynomials.
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Non-collinear Not linear, not aligned, not part of the same line.
Not collinear.
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Non-Euclidean A geometry in which the Parallel Postulate does not hold may be termed a Non-Euclidean geometry.
In such a geometry, the shortest distance between two points may not be a straight line.
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Nonagon A nine-sided polygon.
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Noninvertible Chiefly a term for matrices, literally unable to be inverted.
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Nonzero Literally, not zero.
Typically used to mean either positive or negative values.
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Norm The heavy-set guy from the Boston tavern Cheers.
Actually, its either a kind of average or a length.
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Normal Usually meaning orthogonal (as to a plane), Normal sometimes means also merely perpendicular.
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Normalize We might Normalize data by culling errors.
Or we might Normalize a vector by assigning a unit vector in its direction.
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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."
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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.
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Nu Nu is the 13th letter of the Greek alphabet.
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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.
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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.
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Oblique In one sense, at an angle or not perfectly horizontal or vertical.
An Oblique triangle is any triangle that is not a right triangle.
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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.
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Odd Function An Odd Function adheres to this property: f(-x) = -f(x).
The standard sine function is an odd function.
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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).
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Omega The last, or 24th, letter of the Greek alphabet is Omega.
Upper-case Omega is used for ohms, a unit of electrical resistance.
Lower-case Omega is used for angular velocity, a speed of rotation.
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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.
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Open Interval A section of a line whose set does not include the endpoints is considered an Open Interval.
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Order, Matrix The Order of a Matrix is its size, expressed as "rows by columns." Play_video
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.
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Ordered Pair Two coordinates are required to label a point in a plane, typically (x, y).
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Ordered Triple Three coordinates are required to label a point in space, typically (x, y, z).
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Ordinal Number Ordinal Numbers are ordinary numbers, or the sequential references of order as first, second, third, and so on.
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Orthogonal Most generally Orthogonal means perpendicular to a plane.
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Outcome A specific event is often termed an Outcome.
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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 far-removed data point is called an Outlier.
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Parabola The graph of a quadratic function is a Parabola, a conic section.
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Parallel Lines Coplanar Lines that never meet or cross are Parallel.
If lines simply never cross, they may be skew (non-coplanar).
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Parallel Planes Two distinct planes, collections of flat expansion of points, that never meet are considered Parallel Planes.
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Parallel Postulate Given a line and a specific point not on the line, there is only one line through the specific point parallel to the given line.
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Parallelepiped A shoebox is a Parallelepiped.
Any geometric body with six faces that are each parallelograms that are in planes parallel to the opposite face.
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Parallelogram A quadrilateral with two pairs of parallel sides is a Parallelogram; it has many dependable properties.
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Parametric Equation In a general sense, we have a Parametric Equation when we define something in specific terms of something else.
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Partial Fraction A Fraction built from the decomposition of other terms.
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Partial Sum A Partial Sum occurs when we sum only a finite number of terms from a larger or infinite series of terms.
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Pascal's Triangle Pascal's Triangle is an important device for understanding binomial expansion and combinatorics.
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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.
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Period Measured in time, or angle, or even sometimes distance, the Period of a repetitive function is the time (or angle or distance) it takes to complete a cycle.
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Periodic Functions that repeat a cycle over and over again are considered Periodic.
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Permutation A specific order to the grouping of objects in a combination is termed a Permutation.
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Perpendicular At right angles.
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Perpendicular Bisector A line segment (or side of a polygon) has a unique line through its midpoint perpendicular to the line segment (or side). Play_video
Phase Shift This applies to sinusoids moved left or right by a change to the argument (the angle).
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Phi The twenty-first letter of the Greek alphabet.
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Piecewise Literally taken in sections or pieces.
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Piecewise Continuous Function When a function is defined over an interval of the domain by different relations to the dependent variable we call it a Piecewise Continuous Function.
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Plane An infinite expanse of points in two dimensions.
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Plane Geometry Basic geometry is Plane Geometry.
We hold to the parallel postulate and Euclidean principles.
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Point-Slope Equation A handy algebraic relation to obtain an equation of a line from a given point and slope.
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Polar Complex Number We may express complex numbers in trigonometric form.
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Polar Coordinates In labeling a point in a plane we need two coordinates.
In Polar Coordinates we use a radius and an angle, as (r, theta).
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Polar-Rectangular Conversion An algorithm for changing (r, theta) to (x, y).
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Polygon A closed plane figure with straight sides.
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Polyhedron A geometric solid with faces that are polygons.
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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.
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Population Statistically when we sample a Population we generally seek a representative sample.
A Population is the group from which we take a sample.
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Postulate A far-reaching conjecture or sense of reasoning for which an obvious and substantive base appears most reasonable.
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Precision The quality of finer measurement or estimation is termed Precision. Play_video
Prime Number A positive integer evenly divisible by itself and one but no other integers is considered a Prime Number.
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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.
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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).
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Projectile Motion Projectile Motion is a parabolic arc caused by gravity.
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Proof An ingredient in pudding.
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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.
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Proportional In a (constant) ratio.
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Psi The 23rd letter (next-to-last) of the Greek alphabet.
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Pure Imaginary Number Given a complex number of the form a + bi, when a = 0 we say that the number is a Pure (or purely) Imaginary Number. Play_video
Quadrant One of the four areas of the rectangular or Cartesian plane that is divided into fourths by the two axes.
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Quadratic A second-order polynomial of the form ax² + bx = c = 0 is considered a Quadratic; it graphs to a parabola.
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Quadratic Equation Any second-order polynomial in one variable set equal to a constant is termed a Quadratic Equation.
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Quartiles Most generally, the 25th and 75th percentiles are termed the Low Quartile and High Quartile, respectively.
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Quintiles Most generally, the 20th and 80th percentiles are termed the Low Quintile and High Quintile, respectively.
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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.
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Radian A Radian is an angle (measure) that subtends an arc length (on a circle) equal to the radius of the circle.
Radians are just as good as degrees for measuring angles, and sometimes better.
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Radian Measure Radian Measure is just as good as degree measure for angles, and sometimes better.
Pi radians are equivalent to 180 degrees.
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Radical A root symbol or the root itself is sometimes termed a Radical.
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Radius One-half the diameter of a circle is the Radius.
It is the distance from the center of a circle to any point on the circle.
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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.
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Ratio Sometimes Ratio is meant to state a constant proportion.
More generally, the Ratio of two real values is the quotient of one number divided by the other.
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Rational Expression Mathematical statements written as fractions with a numerator and a denominator are often termed Rational Expressions.
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Recursive A Recursive formula or series has successive terms defined by operations or permutations on the term.
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Reflexive Literally "in relation to itself." When we say A = A, we employ a Reflexive property.
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Regression A statistical method of evaluating least-squares to find a best-fit line or curve to data.
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Regression Line To find a best-fit linear relation with scatterplot data, we use Linear Regression to find a Regression Line.
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Regular Polygon A Regular Polygon is both equilateral (all sides congruent) and equiangular (all angles congruent).
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Relative Maximum Also a local Maximum, a high spot on the graph of a function.
It is the greatest value within a defined neighborhood.
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Relative Minimum Also a local Minimum, a low spot on the graph of a function.
It is the least value within a defined neighborhood.
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Revolutions Per Minute Abbreviated "rpm" it conveys the number of complete circular rotations that occur every 60 seconds at some constant rate of revolution.
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Rho Lower-case Rho, the 17th letter of the Greek alphabet, is often used for density (mass per unit volume) in physics.
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Right Angle An angle of 90 degrees or pi/2 radians.
Perpendicular lines meet at Right Angles.
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Right Circular Cone A cone with a circular base and an apex directly above the center of the base.
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Right Cone Any Cone, circular or otherwise, with its apex directly above the center of the base.
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Right Triangle A triangle with a right angle.
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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.
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Row Operations Arithmetic Operations on the Rows of a matrix to solve simultaneous equations.
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Row-Echelon Matrix A Matrix upon which Row operations have been performed.
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Sample When we Sample a population we typically seek a representative Sample.
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Sample Space We often use Sample Space to designate all the possibilities of potential outcomes for an event or process.
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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.
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Scalar Product A Product of vector multiplication, such as a dot product, that results in a value that is Scalar with size (magnitude) but no associated direction.
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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.
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Second, Degree While "second degree" applies to a polynomial, a single Second with respect to Degree measure is one-sixtieth of one minute, or one sixtieth of one sixtieth of one degree, or 1/1,296,000 of a revolution.
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Second-Order Polynomial A polynomial in which the highest-order term is of order two.
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Sequence Informally, any series is a Sequence.
More formally, any series of terms that adheres or conforms to a pattern.
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Series Most often a sequence of terms to be summed.
Informally, any sequence of terms may be a Series.
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Set Any collection of objects or values is considered a Set, whose cardinal number is the number of objects in the Set.
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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."
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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."
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Sigma The 18th letter of the Greek alphabet, upper-case sigma is used for summation notation, lower-case Sigma often denotes a standard deviation in statistics.
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Sigma Notation Literally summation Notation, Sigma Notation employs an iterative mechanism around an upper-case Sigma to express the sum of a series or sequence of terms.
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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.
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Simple Harmonic Motion Periodic Motion with constant length of cycle time (a fixed period) is termed Simple Harmonic Motion.
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Simultaneous Equations Equations with common solutions are Simultaneous Equations.
Also, equivalent equalities (statements with equal signs) may be termed Simultaneous Equations.
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Singular Matrix A square Matrix with no inverse is termed a Singular Matrix.
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Sinusoid A sine wave is called a Sinusoid; a cosine graph is also a Sinusoid.
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Skew Lines neither intersecting nor parallel (non-coplanar lines) are termed Skew lines.
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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.
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Slope-Intercept Equation of a Line The familiar y = mx + b, where m represents Slope and b is the y-Intercept.
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Solid A three-dimensional geometric figure or body that includes the interior region.
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Solid of Revolution When a function is rotated around an axis (of Revolution) it generates a Solid of Revolution.
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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.
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Solution Set Strictly, any Solution is a Solution Set, the value(s) that make a mathematical statement true.
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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).
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Sphere A three-dimensional figure comprised of points equidistant from a center point; a Sphere has a fixed radius.
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Spherical Geometry Unlike plane Geometry, Spherical Geometry is not based on the parallel postulate.
Many of our accepted geometric theorems, principles, and tenets (from plane Geometry) simply do not hold in Spherical Geometry.
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Spherical Trigonometry Unlike plane Trigonometry, elementary Spherical Trigonometry is three dimensional.
If based in spherical geometry, the math of Spherical Trig gets downright grisly.
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Spheroid An oblate sphere.
Sometimes, an ellipsoid.
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Spiral Sometimes Spiral is used to describe a helix.
A genuine Spiral is a plane figure of changing radius from a (usually fixed) origin.
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Square Matrix A Square Matrix has the same number of rows as columns.
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SSS Congruence Two triangles whose corresponding sides are congruent are themselves congruent.
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SSS Similarity When corresponding sides of two triangles are in a fixed ratio the triangles are similar.
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Standard Equation of a Line When expressing the Equation of a Line with integral coefficients we may have the Standard Equation of a Line.
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Standard Position An angle in Standard Position has been rotated counterclockwise (for positive rotation) from an initial ray on the positive x-axis.
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Step Function A discontinuous Function where the range jumps in increments (usually fixed) may be a Step Function.
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Straight Angle An angle of 180 degrees or pi radians.
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Subset Every set is a Subset of itself.
A Subset has elements all contained in a "parent" set.
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Supplementary Supplementary angles sum to 180 degrees, or pi radians.
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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).
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Synthetic Division Synthetic Division is a technique to simplify the long division of polynomials.
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System of Equations Most generally simultaneous Equations, or a set of Equations with identical variables.
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Tangent A line that touches a function curve at a single point is said to be Tangent to the function.
Tangent is also one of the six basic trigonometric functions; it is the ratio of the opposite side (from a specified angle) of a right triangle to the adjacent side.
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Tangent Line A Line is said to be Tangent to a function when it touches the graph of the function at a single point.
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Tau Tau is the 19th letter of the Greek alphabet.
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Taylor Series Many common functions can be written as an expansion of the function about a point in a form known as a Taylor Series.
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Term In most mathematical expressions a single Term is isolated from other Terms by plus or minus signs.
A monomial is a Term.
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Terminal Side of an Angle When in standard position, an Angle has an initial side, a ray on the positive x-axis, and a Terminal Side where the rotation of the angle stops, at an angle of specific measure (in degrees or radians).
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Tessellate A planar pattern of repeating geometric shapes is a Tessellation; to produce these shapes is to Tessellate.
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Tetrahedron A polyhedron with four faces.
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Theorem A mathematical principle typically proved with some rigor is often a Theorem.
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Theta The eighth letter of the Greek alphabet is Theta, a common variable for an angle.
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Third Quartile For certain types of data, it is the 75th percentile.
Also high quartile or upper quartile.
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Three Dimensions The Dimensions of space or volume are Three Dimensions, typically labeled with rectangular, spherical, or cylindrical coordinates.
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Three-Dimensional Coordinates Three-Dimensional Coordinates require an ordered triple to label a point in space.
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Transcendental Number A Transcendental Number will not be the root of a polynomial with integer coefficients; it is an irrational number.
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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.
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Transpose (Matrix) When we interchange the rows and columns of a matrix we Transpose the Matrix.
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Triple Product (Scalar) Effectively, a Scalar Triple Product is akin to the determinant of a 3x3 matrix.
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Uncountable In human terms, Uncountable means too many to practically count or enumerate.
In math, an infinite function without a one-to-one correspondence to natural numbers.
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Uniform Constant and unchanging; fixed.
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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."
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Unit Circle A Circle of radius one centered at the origin is termed the Unit Circle.
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Unit Vector A vector of length one directed along one of the coordinate axes.
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Upper Bound The greatest permissible value of a function may be termed its Upper Bound.
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Upper Quartile Also the high quartile, the 75th percentile.
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Upper Quintile Also high quintile, the 80th percentile.
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Upsilon Upsilon is the 20th letter of the Greek alphabet.
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Vector Often represented with an arrow, a Vector is a quantity with both magnitude (size) and direction.
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Velocity Formally a vector in physics, Velocity has both magnitude (speed) and direction.
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Venn Diagram Most often graphics of overlapping circles and ovals, a Venn Diagram depicts sets, subsets, and their intersections and unions.
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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."
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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.
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Vertical Straight up, perpendicular to horizontal, is Vertical.
Vertical lines have an indeterminate or infinite slope.
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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.
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Volume The extent to which an object fills units of three-dimensional space is its Volume.
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Wavelength The length of a wave, literally, is its Wavelength.
Typically symbolized with Greek letter lambda, a Wavelength can be measured by actual length, or by the period, which may be the angle traversed through one complete cycle, or the time required to complete a cycle.
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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.
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Whole Numbers Most often, the set of positive integers and zero.
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Work Equivalent to energy, Work is the product of force and distance.
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Xi The 14th letter of the Greek alphabet.
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y-z Plane In three dimensions, the plane orthogonal to the x-axis.
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Zero Vector A Vector of length Zero. Play_video
Zero, Matrix Technically an identity Matrix for Matrix addition, the Zero Matrix is a Matrix with all elements equal to zero.
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