Your 8-Bit Glossary for Computer Science Mathematics
Describes the value that a function approaches as the input approaches some value 'a'.
Represents the instantaneous rate of change of a function, or the slope of the tangent line.
Calculates the net area under the curve of a function $f(x)$ from $x=a$ to $x=b$.
Represents the sum of a sequence of terms, from index $i=1$ to $n$.
Used in the formal definition of limits to represent arbitrarily small positive numbers.
A concept representing a quantity without bound or end.
The derivative of a multivariable function with respect to one variable, holding others constant.
A vector of all partial derivatives of a function. It points in the direction of the steepest ascent.
Calculates the volume under the surface $z=f(x,y)$ over a region R in the xy-plane.
An integral evaluated along a closed curve or path, often used in vector calculus theorems.
Measures the magnitude of a vector field's source or sink at a given point.
Measures the rotation or circulation of a vector field at a given point.
Represent the first and second derivatives of a function y with respect to its variable (e.g., x or t).
A special function used to solve linear first-order differential equations by making them integrable.
Transforms a function of time $f(t)$ into a function of complex frequency $F(s)$. Used to simplify solving ODEs.
Transpose ($A^T$) swaps rows and columns. Inverse ($A^{-1}$) is a matrix that, when multiplied by A, yields the identity matrix.
A scalar value that provides information about a square matrix, such as whether it's invertible.
An object with both magnitude and direction, often represented as an array of numbers.
An eigenvector $\mathbf{v}$ of a matrix A is a vector that is only scaled by a factor $\lambda$ (the eigenvalue) when A is applied to it.
A way to multiply two vectors to get a scalar, related to the projection of one vector onto another.
The length or size of a vector, calculated as the square root of the inner product of the vector with itself.
NOT, AND, OR, IMPLIES, and IF AND ONLY IF (IFF). Used to build logical statements.
"For All" ($\forall$) and "There Exists" ($\exists$). Used to specify the scope of a logical statement.
"Is an element of", Union, Intersection, and "Is a subset of".
"n choose k". Represents the number of ways to choose k items from a set of n items without regard to order.
A number between 0 and 1 representing the likelihood that event A will occur.
The probability of event A occurring, given that event B has already occurred.
The long-run average value of a random variable X; its probability-weighted average.
Measures the spread or dispersion of a random variable around its expected value.
Typically represent the mean ($\mu$) and standard deviation ($\sigma$) of a population or probability distribution.
Represent the mean ($\bar{x}$) and standard deviation ($s$) calculated from a sample of data.
"a is congruent to b modulo n". Means a and b have the same remainder when divided by n.
The largest positive integer that divides both a and b without leaving a remainder.
Counts the positive integers up to a given integer n that are relatively prime to n.
Describes the upper bound on the time or space complexity of an algorithm as the input size n grows.
Describes the lower bound on the complexity of an algorithm.
Describes a tight bound on the complexity, where the algorithm's growth is bounded both above and below.