Title 
Description 

Calculus 
Calculus is the branch of mathematics concerned with the rates of changes between variables (derivatives) as well as areas under curves that represent functions (integrals). 

Cardinal Number 
The number of objects or elements within a set is the Cardinal Number of the set. 

Cardioid 
A heartshaped curve formed by rotating a circle and graphing the movement of that point as the "outside" circle traces around the inside circle. 

Cartesian Coordinates 
The familiar xy coordinate plane is called the plane of Cartesian Coordinates; it is named for Rene Descartes.


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

Catenary Curve 
The curve formed by hanging a rope or chain between two posts is a Catenary Curve. Its math function is that of the hyperbolic cosine function. 

Center of Mass 
The Center of Mass of an object is the point at which forces acting on the object may be considered to be balanced or concentrated. In a triangle it is at the centroid, the point of concurrence where the medians of the triangle meet. 

Center of Rotation 
A point around which the rest of a body or object rotates is termed the Center of Rotation. 

Center of Rotation 2 
The point around which an object revolves or rotates is called the Center of Rotation. 

Central Angle 
A Central Angle is formed at the center of a circle. Think of the angle formed by cutting a slice of pie or cake from the center of a round baked good. 

Centroid 
The Center of Mass of a triangle (made from some flat material) is its Centroid. It is the point at which the medians of the triangles intersect, also called the point of concurrence. 

Chain Rule 
The Chain Rule is a basic rule in calculus to find the derivative of a composite function. 

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

Chi 
The twentysecond letter of the Greek alphabet. 

Chord 
A line (line segment) across a circle that does not pass through the center of the circle is termed a Chord. 

Circular Cone 
A Circular Cone need not have its apex directly above the center of its base. 

Circular Cylinder 
A Circular Cylinder does not have to have sides perpendicular to its base; its side may be oblique. 

Circular Functions 
Circular Functions are based on the properties of circles, which are plane figures where every point on the circle is equidistant from a center point. 

Circumcenter 
The center of a circumscribed circle is called its Circumcenter. All regular polygons have a circumcenter, but most polygons do not. All triangles have a circumcenter. 

Circumcircle 
Also called the Circumscribed Circle, the Circumcircle encompasses a polygon and all vertices of the polygon are on the circle. 

Circumference 
The distance around a circle is its Circumference. It is the product of pi times the diameter, or twice the product of pi and the radius of the circle. 

Circumscribed Circle 
A circle around a polygon that contains all the vertices of that polygon is termed a Circumscribed Circle, also called a Circumcircle. 

Clockwise 
Rotation in the same direction as the hands of a traditional clock. 

Closed Interval 
A segment of the real number line including the endpoints. 

Coefficient 
A number that indicates the multiple of an algebraic term. 

Coefficient Matrix 
A matrix comprised of coefficients which can be used to solve a system of equations. 

Cofactor 
Typically the result of taking a determinant, it is a number associated with an element in a matrix. 

Cofunctions 
Each of the six basic trigonometric functions have a cofunction. Their names tell the story: sine and cosine, tangent and cotangent, secant and cosecant are each pairs of cofunctions. 

Collinear 
Lined up perfectly; exactly aligned. In the same line are collinear points. 

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. 

Combinations 
Combinations are calculated to be the number of ways that a number of objects may be selected from a group of objects. 

Combinatorics 
The branch of math that provides calculations for the selection of a number of elements from a set is called Combinatorics. 

Common Logarithm 
The baseten logarithm is often called the Common Logarithm. 

Common Ratio 
In a geometric progression, subsequent terms are obtained by multiplication of terms by a constant called the Common Ratio. 

Commutative Law of Addition 
When adding terms the order in which we add them matters not at all. 

Commutative Law of Multiplication 
The order in which we multiply any number of factors (to obtain the product of those factors) matters not at all. 

Complement of an Angle 
Complementary Angles sum to 90 degrees or pi/2 radians. So the complement of an angle with measure x is (90  x) degrees or (pi/2  x) radians. 

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. 

Complementary Angles 
Complementary Angles sum to 90 degrees or pi/2 radians. 

Complex Conjugate 
The Complex Conjugate of (a + bi) is (a  bi). The Complex Conjugate of (c  di) is (c + di). 

Complex Number 
All numbers, as it turns out, are complex. When the "imaginary part" has a zero coefficient, the number is purely real. 

Complex Plane 
The complex number plane is required to map or plot complex numbers because the complex numbers themselves have two components. 

Composite Number 
Composite Numbers relate to positive integers that are not prime. If a positive integer has factors other than itself and one, it is a Composite Number. 

Compound Interest 
When the Time Value of Money generates interest and that interest is added to the principal to increase the amount of money to which subsequent interest is added, this is Compound Interest. 

Computation 
Computation is the act of taking values and logical mathematical steps to make a calculation. 

Concave 
Bending inward or with an indentation. The opposite of convex, Concave applies to physical objects such as lenses or mirrors, as well as to polygons or solids. 

Concave Polygon 
A Concave Polygon has an "indentation." In moving around the perimeter of the polygon, at least one interior angle will be greater than 180 degrees. 

Concenric Circles 
Circles having the same centers but different radii are termed Concentric Circles. 

Concentric 
Literally having the same center point; centered at the same point. 

Conclusion 
When mathematical conclusions are valid the laws of math and science have been adhered to, and a logical approach has been taken. Sometimes conclusions are invalid because scientific or mathematic rigor has not been adhered to. Reason and judgment are often important to reaching sound or valid conclusions. 

Concurrent 
At the same point. Concurrent geometric entities occupy the same place, the same space. 

Cone 
A Cone is a geometric shape where a simple closed curve is connected to an apex (a point) with smooth lateral sides. 

Congruence Test 
There are various tests for congruence, which is the state of having identical size and shape. 

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. 

Conjugates 
Conjugates multiply to simpler entities based on changing the operator between terms of each conjugate from positive to negative, or vice versa. 

Consecutive Interior Angles 
When two parallel lines are cut by a transversal, the two angles formed on one side of the transversal between the parallel lines are termed Consecutive Interior Angles; they are supplementary. 

Consistent System of Equations 
When a system of equations has at least one solution (and most often a unique solution) the equations are said to be Consistent. 

Constant 
A mathematical value that never changes is said to be constant. Real numbers are constants because their value never changes. In a polynomial, a term with a variable (or variables) raised to the zero power is constant. 

Continuous 
A function is considered Continuous if its graph has no gaps, no holes, no steps, and no cusps or discontinuities. 

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. 

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. 

Continuously Differentiable 
When a function is Continuously Differentiable it is both continuous and smooth. 

Contraction 
Contraction is the process by which some object or entity is shrunk or diminished in size or extent. It may be diminished in one dimension, or reduced proportionally if it is a two or threedimensional object. A Contraction can also be the result of such a process. 

Contrapositive 
Given a conditional statement, its Contrapositive is logically equivalent and is obtained by negating the original hypothesis and conclusion as well as reversing their order. 

Convergence 
To approach a limit is to experience Convergence. Mathematical series experience convergence when the sum of their expanded terms reaches a boundary or limit. 

Convergent Series 
A series is said to be Convergent when its sum approaches a limit. 

Converse 
Given a conditional statement, as "If A, then B," the Converse results from switching the order of the hypothesis and conclusion: "If B, then A." The Converse may or may not be true given a true original statement. 

Convex 
When a geometric or physical entity has no indentations. Or, when a polygon has the property where no line segment across it leaves the interior of the polygon, the polygon is said to be Convex. 

Coordinate 
A value associated with the location of a point is a Coordinate. In one dimension a Coordinate is a single value. In two dimensions, a point is defined by two Coordinates as an ordered pair. 

Coordinate Geometry 
This branch of mathematics is a combination of algebra and geometry; it is analytic geometry. 

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

Coplanar 
In the same plane; of the same plane. Most generally, points within the same plane are said to be Coplanar. 

Corollary 
A Corollary is like a baby theorem. 

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. 

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. 

Corresponding Angles 
Sometimes Corresponding Angles refer to the "same" angle in two similar (or congruent) polygons. Or, when parallel lines are cut by a transversal, Corresponding Angles are "on the same corner of the intersections." 

Cosecant 
One of the six basic trig functions, the Cosecant function is the reciprocal of the sine function, and the cofunction of the secant. The Cosecant of theta can be expressed as (r/y) for an angle in standard position, or the ratio of hypotenuse over opposite side in a right triangle. 

Cosine 
One of the six basic trig functions, the Cosine is the cofunction of the sine function and the reciprocal of the secant function. In standard position the Cosine of theta is (x/r). In a right triangle the cosine of an angle is the ratio of the adjacent side to the hypotenuse. 

Cotangent 
One of the six basic trig function, Cotangent is both the reciprocal function and the cofunction of the tangent function. For a right triangle, the Cotangent of an angle is the ratio of adjacent side to the opposite. In standard position for angle theta, the Cotangent can be expressed as (x/y). 

Coterminal 
When one angle is in the same position as another, as adding or subtracting 360 degrees or 2 pi radians puts a rotating angle in the same position as the previous angle, we say the angles are Coterminal. 

Countable 
In common language, countable just means reasonably enumerated or countable, as in there are not too many objects to physically count. In human terms, the grains of sand in the Sahara Desert are not countable. But mathematically they actually are. So Countable means something a little different to the mathematicians. 

Counterclockwise 
For angles in standard position, we use a Counterclockwise rotation for positive measurement of the angle's rotation. This is the direction opposite the traditional movement of analog clock hands. 

Counting Numbers 
The set of Counting Numbers is (usually) identical to the set of Natural Numbers, the positive integers that we begin to count with when we're little kids. Watch out, however: some people include zero in this set. 

CPCTC 
In geometry class we use this shorthand for "Corresponding Parts of Congruent Triangles are Congruent." 

Cramer's Rule 
Cramer's Rule provides a matrix manipulation to solve simultaneous equations. 

Critical Number 
While there are many ways to define Critical Numbers, depending on the circumstances, most generally we're interested in places where a function generates either an extreme value or a discontinuity. 

Cross Product 
A product of vectors that generates another vector is often a Cross Product. 

Cube 
A sixsided orthogonal box with square faces; a right square parallelepiped. The result of raising a real value to its third power. The process of multiplying a number times itself and times itself again. 

Cube Root 
The Cube Root of a real value is the number that when raised to the third power equates to the original real value. 

Cubic 
A Cubic is a thirdorder polynomial. 

Curve 
Beware that mathematicians consider straight lines to be Curves! 

Cusp 
When the graph of a function comes to a sharp point, we say that point on the graph is a Cusp. 

Cycloid 
The path that a point on the outside of a rolling wheel makes is termed a Cycloid. 

Cylinder 
A Cylinder may or may not have circular bases. The lateral sides are connected with congruent, parallel bases that may be the shape of any closed curve. 

Cylindrical Shell 
A method for volumetric calculations especially for rotated bodies around an axis. The small thickness of the shell is typically the differential "dx" (or dy or whatever differential represents the incremental thickness of the cylinder). 
