Topics in a Pre-Calculus Course

To learn more about a topic listed below, click the topic name to go to the corresponding MathWorld classroom page.

General

Asymptote	A line or curve that approaches a given curve arbitrarily closely.
Curve	A continuous map from a one-dimensional space to an n-dimensional space. Loosely speaking, the word "curve" is often used to mean the function graph of a two- or three-dimensional curve.
Determinant	(1) A function that assigns a scalar to a square matrix (or, equivalently, its linear transformation). (2) The value of this function for a particular matrix. The matrix has an inverse if and only if its determinant is nonzero.
Parametric Equations	A set of equations that together express a set of quantities as explicit functions of a number of independent variables, which are known as parameters.
Plane	A two-dimensional surface defined by linear equations.
Plane Curve	A curve that lies in a single plane. A plane curve may be closed or open.
Polar Coordinates	A two-dimensional coordinate system in which points in two dimensions are given by an angle and a distance from the origin.
Rational Function	A function that can be written as the quotient of two polynomials.
Reflection	The operation of exchanging all points of a mathematical object with their mirror images.
Rotation	The turning of an object or coordinate system about a fixed point.
Rotation Matrix	A matrix that corresponds to the linear transformation of a rotation.
Scalar	A value (such as a measurement) that has only magnitude but not direction. This contrasts with a vector, which has direction as well as magnitude.
Spherical Coordinates	A coordinate system in which points in three-dimensional space are given by two angles and a distance from the origin.
Tangent Line	A line that touches but does not cross a curve at a given point.
Translation	A transformation consisting of a constant shift with no rotation or stretching.

Complex Numbers

Complex Conjugate:	The result of changing the sign of the imaginary part of a complex number.
Complex Number:	A number consisting of a real part and an imaginary part. A complex number is an element of the complex plane.
Complex Plane:	The set of all complex numbers. Just as all real numbers can be imagined as sitting on a line, all complex numbers can be thought of as points in a plane.
i:	The symbol used to denote the square root of -1.
Imaginary Number:	A multiple of the imaginary unit i (the square root of -1).

Conic Sections

Conic Section:	The nondegenerate curves generated by the intersections of a plane with one or two nappes of a cone. A conic section can also be realized as the zero set of a quadratic equation in two variables.
Ellipse:	A conic section with eccentricity less than one. It resembles a squashed circle.
Hyperbola:	A conic section with eccentricity greater than one. A hyperbola consists of two separate branches.
Locus:	The set of all points (usually forming a curve or surface) satisfying some condition. For example, the locus of points in a plane that are equidistant from a given point is a circle.
Parabola:	A conic section with eccentricity equal to one. Parabolas appear as the graphs of quadratic equations and the trajectories of projectiles.

Exponents and Logarithms

e:	The base of the natural logarithm, approximately equal to 2.718. After pi, e is the most important constant in mathematics.
Exponential Function:	The function consisting of the base of the natural logarithm e taken to the power of the variable.
Logarithm:	The power to which a number (called the base) is raised to produce a given number; e.g., the logarithm of 100 to the base 10 is 2.
Natural Logarithm:	The logarithm having base e.

Functions

Domain:	(1) The set of values for which a function is defined. (2) In topology, a connected, open set.
Function:	A relation that uniquely associates members of one set with members of another set. The term "function" is sometimes implicitly understood to mean continuous function, linear function, or function into the complex numbers.
Inverse Function:	For a function f, the function f-1 for which f(f-1(x)) = x for any x.
Range:	(1) The set of all values that a function can take. (2) The difference between the minimum and the maximum values of a data set.

Vectors

Cross Product:	A product of two vectors that results in a vector perpendicular to both.
Dot Product:	A product of two vectors, which results in a scalar.
Normal Vector:	A vector perpendicular to a surface.
Vector:	(1) A mathematical entity that has both magnitude (which can be zero) and direction. (2) An element of a vector space. MathWorld