# Math Glossary of Terms

## Absolute Value of a Complex Number

Also known as the modulus of a complex number in the form of a+bi. It tells you the distance between the origin and a point (a,b) that's on a complex plane. It is a measure of distance from 0 measured on the complex number plane, rather than using a number line as per usual absolute values.## Absolute Value Rules

Absolute value rules tell you how you should go about taking the absolute value of a number. Absolute values always leave you with a postive number, whether or not the output is positive or negative. You will turn any negative numbers into positive ones for absolute values.## Absolutely Convergent

Also known as absolute convergence, this refers to an infinite series that converges when its terms are changed to their absolute values. This is done by changing any subtraction signs in the series to additions, then checking if the new series converges.## Acceleration

Can be thought of as the increase of something's speed. Acceleration tells you the rate of change in veolicty of an object in relation to time. A positive acceleration means there is an increase in acceleration (speed) and a negative acceleration means there is a decrease in speed.## Accuracy

Tells you how close an estimation or an approximation is to its real value. Commonly compared against precision, which tells you how much information is conveyed by a number, accuracy reflects correctness. An example is the number of pi. 3.14 is accurate, but not precise.## Bernoulli Trials

A trial in probability in which a random experiment with precisely two possible outcomes are repeated and it consistently gives the same probabilty of success. The binomial probability formula can help you find probabilites for Bernoulli trials.## Beta (β)

The second letter in the Greek alphabet. In math, the beta function helps to reduce complex integrals into exprsesions. The beta function is also known as Euler's integral of the first time and is closely connected to the gamma function.## Between

When you have a line with endpoints X and Z, a point Y is between points X and Z if it is on the XZ line segment. The idea of a number being between two other numbers is used in Euclid's proofs.## Biconditional

When two conditionals (a conditional and its converse) are written both at once. Also known as the if and only if condition. In order for two propositions to be true, they must both be simultaneously true. The same goes for it being false. The symbol for biconditionals is ↔.## Binomial

A polynomial that is made up of two terms. It is an algebraic expression that is made up of the sum or differences of two seperate terms. Therefore, each of the seperate terms can be seen as monomials when they are alone. An example of this would be 2x + y.## Cartesian Form

Also known as rectagular form. The cartesian form is used to indicate a position of a point on a two-dimensional or three-dimensional space. The cartesian coordinates were first used by René Descartes and therefore named after him.## Cartesian Plane

Named after René Descartes who first used the plane formally in mathematics. Points can be located on a Cartesian plane by using the x-axis and y-axis to give you its horizontal and vertical locations. The x-axis and y-axis intersects at the origin in a Cartesian plane.## Catenary

In geometry, it is a curve that looks like a slack hanging rope that is held up at its ends on two sides and pulled down by gravity. Its name cames from the latin word for "chain". Be cautious that a cartenary is not a parabola.## Cavalieri's Principle

This principle tells us that if there are two solids with the same altitude, the section that come about from the planes that are parallel and the same distance from the two solids' bases are always equal. The volumes of the solids are also the same.## Ceiling Function

The ceiling function maps out x's smallest integer that is greater than or equal to x. The ceiling has a domain of all real numbers and the set of all integers is its range. Sometimes, the ceiling function is also called the least integer function.## Definite Integral Rules

Defnite integrals are integrals that have start and end values. The definite integral rules tell you how to treat definite integrals in different situations. Keep in mind that these rules only apply when the integrals exist.## Degenerate

When an object's nature is so changed that it should be classifed as another class. It is qualitatively different from the rest of its original class. An example of a degenerate form is a point being the degenerate form of a circle. Degenerate objects are used to test if certain formulas can be applied to objects that have been stretched from its original definition.## Degenerate Conic Sections

Made up of a point, a line, and intersecting lines. Degenerate conic sections refer to plane figures that you get from the intersection of a double cone that has a plane passing through its apex.

## Degree (angle measure)

Indicated in math by the ° symbol. It is a unit for measuring angles (not to be confused with the degree that measures temperature and also uses the same symbol). It takes 360 degrees to make a full rotation in a circle. Each degree is equal to 1/360 of a revolution. Degrees are usually measured using a protractor.## Degree of a Polynomial

Refers to the highest degree in a polynomial. The degree in an expression tells us the order of an equation. They are represented by small numbers above and slightly beside a variable telling you that variable is raised to a certain degree.## Element of a Set

The objects that make up a set. A set is usually made up of numbers or objects which individually, are each different entities. Elements can be, for example, letters, numbers or points. In the set {1, 2, 3}, the elements of the set would be 1, 2, and 3.## Ellipse

A shape that looks like a stretched circle, giving it the appearance of an oval (keep in mind though that in mathematics, an ellipse is not an oval). It is a curve that is surrounded by two focal points of which the sum of the distances of the two foci are constant no matter which point you are at on the curve.## Ellipsoid

A deformed sphere whose cross sections (no matter where you cut it) is either an ellipse, empty, or just a single point. It has three pairwise perpendicular axes of symmetry that intersect at a center of symmetry. A prominent object that is an ellipsoid is the earth, as it resembles a slightly flattened sphere more than a perfect sphere.## Elliptic Geometry

Also known as Riemannian Geometry. An elliptic geometry is a non-Euclidean geometry that has a positive curvature of which Euclid's parallel postulate does not apply to. This geometry happens on the surface of a sphere where all the lines are great circles (circles on the surface of a sphere) and points are pairs of points that are directly opposite of one another. Therefore, all lines intersect.## Empty Set

Sometimes known as a null set. It is a set that does not contain any elements within it. Therefore it has a size and cardinality of zero. The notation for empty sets are written as: "{ }" or "∅"## Factorial

It is the product of an integer with the rest of its smaller positive integers. A factorial is represented by a "!" sign after a number. It indicates that you should multiply a series of descending numbers. For example, 5! (read as "5 factorial") means you should carry out: 5 x 4 x 3 x 2 x 1 = 120.## Factoring Rules

Rules that tell you how to properly handle different types of formulas when you're carrying out factoring. Examples of factoring rules include difference of squares, difference of cubes, and sum of squares. By observing the question you're dealing with, you can refer to the below rules to see how you can factor your formula.## Falling Bodies

Also known as projectile motion. It is a formula that helps to find the vertical motion of an object that is throwing straight up or down, or simply dropped under gravitational force on Earth. The formula contains the variables of height, time, acceleration (due to gravity), initial veolocity and initial height.## Identity (Equation)

An identity is an equation that stays true no matter what values are substituted for any of its variables. It is an equality between functions that are defined differently. An example of this is tan θ = sin θ/cos θ. Both sides of this equation will produce the same values regardless of what θ¸ ends up becoming.## Identity Function

A function that always gives you the same value as its argument. That means you're working with a function that looks like f(x) = x, where every real number x that is inputted gives you that same number x as the output. The graphs of identity functions all looks like a straight diagonal line that rises upwards from left to right.## Identity Matrix

Sometimes known as a unit matrix. The n x n identity matrix has n rows and n columns. The upper left and bottom right diagonal consists of 1s, and the other entries in the matrix are all 0s. By multiplying another matrix by an identity matrix, it'll leave the original matrix the same.## Identity of an Operation

A number where if you combine it with another quantity via an operation allows that quanity to remain the same. For addition, you have the additive identity of 0 since adding 0 to anything does not alter it. In multiplication, it is 1 since multiplying anything by 1 allows it to remain the same.## if and only if

Also known as biconditional or shortened to iff. It means that a statement being true requires another statement to also be true. The inverse is true too. If one statement is false, it requires that the other statement is too. It plays on the fact that there is a neccessary and a sufficient condition for the statements.## Lateral Area

The surface area of 3D objects without its top and bottom base. The surface area is found by finding the area of the individual faces of an object and then summing it together to find the total surface area. In order to find just the lateral area, do not sum up the areas of the top and bottom base when totalling up the surface area.## Lateral Surface Area

The surface area of 3D objects without its top and bottom base. The surface area is found by finding the area of the individual faces of an object and then summing it together to find the total surface area. In order to find just the lateral area, do not sum up the areas of the top and bottom base when totalling up the surface area.## Lateral Surface/Face

A solid's surface that can be considered a face. This excludes the bases of the solid. In the case of a cylinder, for example, its lateral surface is the side of the cylinder. The top and bottom circles would not be considered a part of its lateral face.## Latus Rectum

It is a segment of a line that perpendicular to the principal axis of a parabola, hyperbola, or ellipse. It starts and ends on the curve, so its endpoints sit on the curve. Different conics have different ways of determining its latus rectum.## Law of Cosines

Also known as the cosine rule. The law of cosines relates the cosine of an interior angle in a triangle to its sides. It helps us find aspects to a triangle such as its third side when we know two sides and the angle between them, or we can even find the angles inside a triangle if we have all three sides of the triangle.## Magnitude of a Vector

A magnitude in mathematics refers to the size of some quantity or object. It helps you compare if something is larger or smaller to another object. For the magnitude of a vector, it tells you the length of the vector. Along with telling you a magnitude, vectors also have a direction.## Main Diagonal of a Matrix

Refers to a diagonal set of elements in a matrix. The main diagonal can be found by going from the upper left corner of a matrix and then diagonally going down and to the right.## Major Arc

In situations where you have two arcs in a circle, the larger arc is referred to as the major arc. It is an arc that measures to or is greater than 180 degrees, which is also π in radians. Summing up the major arc and the minor arc (the arc that is smaller) gives you 360 degrees or 2π radians.## Major Axis of a Hyperbola

The principle axis of symmetry in a hyperbola that seperates it into two mirrored halves. It is a line that passes through the vertices, center, and the foci of a hyperbola that ends at the widest points of a hyperbola's perimeter.## Major Axis of an Ellipse

The principle axis of symmetry in an ellipse. It is a line that passes through the vertices, center, and the foci of an ellipse. It can also be considered the longest diameter that can be measured in an ellipse. One half of a major axis is called a the semi-major axis.## Natural Domain

Is the maximum set of plausible values in a defined function which does not have an imposed domain. Each value in the set, when used with the function, will output a real value. An imposed domain on a function would cause it to have an unnatural domain.## Natural Logarithm

A logarithm to the special base of base e (e = 2.7182818...). You may see it being written as ln(x) or logₑ(x). Natural logarithm functions are the inverse functions of exponential functions, which allows you to rewrite a natural logarithm in exponential form by converting back and forth.## Natural Numbers

Positive whole numbers that are commonly used for counting and putting things in order. Natural numbers contains no negative numbers or numbers that are in fractions. The numbers 1, 2, 3, 4, 5 demonstrates this. 0 is a number that cannot be universally agreed on whether it is a natural number or not.## Negative Direction

A descriptor of data on a plot. Negative direction is usually describing a downward slope on a plot, where one value is decreasing and the other value is increasing or vice versa.## Negative Exponents

Another way to display reciprocals. Negative exponents allow you to write powers without having to use decimals or fractions. When you have a negative exponent, flipping it to the other side of the division line allows you to rewrite it as a number with a positive exponent.## Oblique Asymptote

An asymptote that is not not horizontal or vertical. It is a slanted line where a function approaches when x approaches infinity. A function is able to have a maximum of two oblique asymptotes. Some rational functions have oblique asymptotes if the degree in the numerator is one degree more than the degree in the denominator, an oblique asymptote will exist.## Oblique Cone

A cone whose altitude does not intersect with the center of the cone's base. Its altitude is still perpendicular to the base, but it is not in the center. A oblique cone can be summarized as a 3D figure that has a lateral surface with altitude, a base that is circular, and a vertex.## Oblique Cylinder

A cylinder that has two end planes that are parallel to one another. However, unlike a right cylinder, its lateral surface is not perpendicular to these end planes. These end planes (also known as its bases) don't align perfectly on top of one another.## Oblique Prism

A prism whose end planes are parallel but not aligned on top of one another perfectly. An oblique prism's lateral faces (its sides) are parallelograms. Since its bases don't align perfectly, the prism looks like it is slanted (oblique means "slanting").## Oblique Pyramid

A pyramid whose apex is not above the center of the pyramid's base. The pyramid looks as if it is tilted to one side (oblique means "slanting"). In order to calculate a oblique pyramid's surface area, you cannot use the regular formula anymore and must instead cauculate each of the faces seperately.## Pappus's Theorem

A geometry theorem that helps you identify the surface area and volume of surfaces of a solid of revolution. It uses the distance travelled by the centroids of a curve and the region that experiences revolution. Named after Pappus of Alexandria who is attributed to this theorem.## Parabola

A two-dimensional u-shaped curve. A parabola is made up of the focus (a point) and a directrix (a line). The focus does not lie on the directrix and the locus of points in the plane is such that the distance to the focus is the same as the distance to the directrix.## Parallel Cross Sections

Cross sections that are parallel with the base of a solid. Cross sections can be thought of as slices of a shape - imagine slicing through a loaf of bread. The other orientation for cross sections is that they can be perpendicular to the base.## Parallel Lines

Two lines that are always an equal distance apart and never touches each other. These two lines lie on the same plane and must lie on a perfectly flat surface. Note that lines that are parallel have the same slope. The symbol to signify that lines are "parallel to" one another is ||.## Parallel Planes

Two planes in the same three-dimensional space that do not intersect and are parallel to the same line. The symbol to show that a plane is "parallel to" another is ||. There are proofs for you to find out if two planes are parallel to one another.## Q1

In statistics, Q1 is known as the first quartile or lower quartile. Quartiles divide up a data set into four equal sections. Q1 is the middle value in the first half of the data set. It is also known as the first 25% of a data set. Remember that the data has to be sorted first before quartiles can be found.## Q3

In statistics, Q3 is known as the third quartile or higher quartile. Quartiles divide up a data set into four equal sections. Q3 is also known as the 75th percentile of a data set. Remember that the data has to be sorted first before quartiles can be found.## QED

An abbreviation of the latin phrase quod erat demonstrandum ("that which was to be demonstrated"). It signifies that we have come to the end of a proof. This is especially useful when it's not obvious that a proof has been completed.## Quadrangle

Another name for a quadrilateral. This is a two dimensional shape that has four sides. Examples of quadrangles include parallelograms, rectangles, and squares.## Quadrantal Angle

Angle in the standard position with a terminal side that lies on the x-axis or y-axis. This means that the angle will be multiples of 90°. Examples include 0°, 270°, -90° and so forth.## Radian

A way to measure angles, as opposed to using degrees. You can equate radians to degrees as ½π radians equals 90°. This means that 360° is the same as 2π. Radians measure angles using the number of radii required to measure an arc that is described by that angle.## Radical

What is referred to when you see the square root sign (√). Radical expressions have at least one number under a radical. The sign can mean square root, but it can also mean some other root. Radicals that aren't square roots will have a smaller number (a subscript) that allows you to identify which root you're dealing with.## Radical Rules

Rules that tell you how to carry out operations on radicals. Keep in mind that radicals can be rewritten with exponents, so some of the rules you'll encounter will move the radicals into a number's exponent.## Radicand

A number under the radical symbol (sometimes known as the square root symbol). It is the number that is having its root taken. It could be a square root, but you likely will encounter cube roots and more. A subscript outside the radical sign will allow you to identify which root you're dealing with.## Radius of a Circle or Sphere

The line that connects the center of a circle to the circumference of the circle or sphere. Its plural form is radii. Two radii will give you the diameter of a circle, since the diameter is a line that touches two points on a circle's circumference that passes through the center.## SAA Congruence

Stands for side-angle-angle congruence. Sometimes also known as AAS congruence (angle-angle-side). If two triangles have two angles and a non-included side that are the same, SAA can prove that the two are congruent.## Sample Space

All the possible outcomes or results for an experiment. Sample space is usually written as a set where the possible results are listed out as elements. As an example, if you're rolling a die, you have 6 possible outcomes and you will get a sample space of {1, 2, 3, 4, 5, 6}.## Sandwich Theorem

Also known as the pinching or squeeze theorem. It tells you that if a function that is between two functions that approach the same limit, it too must also approach that limit. In other words, a function is "sandwich"-ed between two other ones.## SAS Congruence

Stands for side-angle-side congruence. If two of a pair of triangles' corresponding sides and one of their included angles are the same, you can use SAS to prove that the two are congruent.## SAS Similarity

Stands for side-angle-side similarity. If two triangles have a corresponding angle that is equal and two sides are the same proportion to the other triangle's corresponding sides, you can use SAS to prove that the two are similar.## Table of Integrals

Helps with integration in calculus. The table of integrals lists out common antiderivatives so that you can carry out calculations that involve integrations. It also lists out the integrals in different categories to make it easier for you to find the ones you'll need.## Takeout Angle

The angle you would cut out from a piece of paper so that it will turn into a right circular cone. Depending on how large the angle is, it can affect how spread out your cone is or how narrow its base is.## tan

Known as tangent, and usually written as tan θ¸ in trigonometry. Tan can be represented as sine and cosine, since tan θ = sin θ/cos θ. Simplifying down sin θ¸ divided by cos θ, you will be left with tan = opposite/adjacent. The memory device SOHCAHTOA can help you to remember this.## tan₋₁

Tangent's inverse function. It can help you calculate angles when certain information is given to you. When you know the sides of a right triangle, but not the angle, inverse tangent comes into use. The inverse tangent performs the opposite of the tangent function.## u-Substitution

An integration technique that can help make integration easier to carry out. It is used when an integral contains a function and it derivative. It involves using the chain rule in reverse.## Unbounded Set of Numbers

Set of numbers that do not have either a lower or upper bound. Bounded sets are finite, whereas unbounded sets can be considered not. To demonstrate this, the sequence of 1, 2, 3, 4, 5... does not have an upper bound to it and is therefore an unbounded set of numbers.## Uncountably Infinite

An infinite set that has too many elements in it that it is considered uncountable. This happens if a set's cardinal number is bigger than the set of all natural numbers. The best known example of a set of uncountable numbers is the set of all real numbers.## Undecagon

A polygon that has 11 sides. It is more commonly known as a hendecagon. Hendecagons that have 11 equal number of angles are regular hendecagons. It will have internal angles of 147.27 degrees each.## Variable

An alphabetical character in mathematics that can take on different number values. It also can mean a quantity that is subject to change or can be regarded as different quantities.## Varignon Parallelogram of a Quadrilateral

The shape that you get when you take the midpoints of the sides of a quadrilateral and join them together to make a new four sided shape. Varignon's theorem tells us that this shape that ends up being formed is a parallelogram.## Vector

A line with an arrowhead at its end in mathematics that has both a direction and a magnitude (a size) associated with it. The length of the arrow can tell you the magnitude and the arrowhead shows you the direction.## Vector Calculus

Also known as multivariable calculus. Multivariable calculus has to do with functions whose outputs and inputs exist in two or more dimensions. Therefore, it will have two (or more) independent variables and dependent variables.## Velocity

Tells you the rate of change of position of an object. It is speed with a direction attached to it. Commonly used to define how fast an object is moving, such as calculations that involve a car driving down a road. To make the car's speed a velocity, it should also specify which direction it is heading.## Washer

A washer, or an annulus (in latin, this means little ring), is a ring shaped object. Its area is bounded by two concentric circles that has different radii. Both of the circles has the same center point. You are able to find the area of the annulus by subtracting the hole in the middle from the total area of the bigger circle.## Washer Method

If you wanted to find the volume of a round shape with a hole in the center, the washer method can be used. This technique makes use of the disk method. A shape is cut into thin pieces (or disks) and then you can find the volume of the slices by subtracting out the hole in the middle.## Wavelength

It is the period of a sine wave. A period can be thought of the amount of distance over which a shape repeats its own shape. It is usually found by calculating the distance between corresponding points of the wave going through a certain phaseâ€”for example, at the troughs at of the waves.## Weighted Average

A method to find the mean in a set of numbers. The weighted average takes into consideration that some components in the set of numbers are more important than others. The average is calculated by multiplying each number with its assigned weight before adding them together and dividing it to find the average.## Whole Numbers

Numbers such as 1, 2, 3. These do not have decimals and are not fractions. There are also no negative in whole numbers. 0 is also considered a whole number.## Work

Tells you the amount of energy transer that occurs when something is moved over a certain distance by an external force. In mathematics, work can be found by finding the integral of the force over the distance that the object is displaced.## x-intercept

In graphing, it is a point where the graph intersects with the x-axis (the horizontal axis on a Cartesian plane).To find the x-intercept in a linear equation for example, substitute in 0 for the y value in your linear equation and you can then solve for x.## x-y Plane

Also known as the Cartesian plane. It is a plane that has its x and y axes defined. The values of x is called the x-coordinates (also known as the abscissae) and the values of y is called the y-coordinates (also known as the ordinates).## x-z Plane

Can be found in a 3 dimensional coordinate system. It is the plane formed by the x-axis and the z-axis. It has the standard equation of y = 0.## Xi (Ξ)

Xi is the Greek alphabet's fourteenth letter. Ξ or ξ represents the original Riemann Xi function. This function was named after B.G. Riemann, he wanted to estimate the number of primes less than a given number.## y-intercept

In graphing, it is a point where the graph intersects with the y-axis (the vertical axis on a Cartesian plane).To find the y-intercept in a linear equation for example, substitute in 0 for the x value in your linear equation and you can then solve for y.## y-z Plane

A part of the three dimensional coordinate system. It is the plane formed by the y-axis and the z-axis. It has the standard equation of x = 0.## z-intercept

In graphing, it is a point where the graph crosses the z-axis on a three dimensional coordinate system in a Cartesian grid.To find the z-intercept you will need to figure out where the x and y coordinates are equalled to 0.## Zero

A number that expresses something that has no size, quantity, or magnitude. If you see that something has the value of zero, it essentially means there is no amount. It is represented with the figure 0. It is regarded as being neither positive or negative.## Zero Dimensions

Also known as zero dimensional. A topological space that has zero dimensions. An example of something with zero dimensions is a point. In order to indentify a point on a line, you'll need one coordinate to find that point and therefore it has a dimension. But for a point of a point, you don't need to use any coordinates to identify where it is.## Zero Matrix

When you come across a matrix that has all 0's as its elements. They are also sometimes known as null matrices. "O" is used to denote a zero matrix and a small subscript next to it (i.e. 2x4) can depict the dimensions of the matrix if needed.## Zero of a Function

Refers to the x-value that makes the function equal to 0. In other words, what input to a function can produce the output of zero? In polynomial functions, the zero is known as the root. The Zero of a function can be a real or a complex number.## Zero Slope

Also known as the slope of a horizontal line. A horizontal line has all the same y-coordinates and therefore, when you attempt to find the slope of it usuing the slope formula, you'll get 0 no matter what. This is due to the "rise" of the line is always zero.## Zero Vector

Also known as a null vector. A vector that has the length of 0. This means that all its components are also equal to 0. Since it doesn't have a length, its magnitude is not pointing in any direction and therefore has an undefined direction.## Zeta (Ζ)

Zeta is the Greek alphabet's sixth letter. It is used in math in the Riemann zeta function that helps investigate the properties of prime numbers. This function is named after mathematician Bernhard Riemann.