Mathematics: English Vocabulary List

a measure of the dispersion or spread of a set of data points in statistics, representing the average squared deviation from the mean

"There was a slight variance between the two sets of test results."

"Variance is a statistical measure of the dispersion of a set of data points around their mean value"

a branch of mathematics that studies and classifies phenomena characterized by sudden shifts in behavior arising from small changes in circumstances

"Catastrophe theory models sudden changes in systems."

"Catastrophe theory uses mathematical models to describe how small changes can suddenly cause large dramatic shifts."

a mathematical function that represents the exponent to which a fixed number, called the base, must be raised to produce a given number

"Calculate the logarithm now."

"The logarithm of 100 to the base 10 is 2, because 10 raised to the power of 2 equals 100."

first in importance or rank

"This is a prime example."

"The prime location of the hotel meant that guests could walk to the beach and the shops without needing a car."

a statement or proposition that has been proven to be true based on previously established axioms, definitions, and other theorems within a particular mathematical or logical system

"The theorem was proven."

"Pythagoras' theorem, stating that the square of the hypotenuse is equal to the sum of the squares of the other two sides, is a fundamental geometric theorem."

(mathematics) a rearrangement of a set of elements in a specific order or sequence

"Students learned permutation formulas in mathematics class"

"There are over three hundred thousand possible permutations of the letters in the word "math"."

a special number used in linear algebra to describe how vectors change during transformations

"Find the eigenvalue."

"Engineers calculate the eigenvalues of a bridge design to predict how it will vibrate during an earthquake."

a branch of mathematics that deals with the study of sets, which are collections of distinct objects, and their properties, relationships, and operations

"Set theory is fundamental."

"Set theory is the branch of mathematics that studies collections of objects and their relationships."

a mathematical expression with variables raised to powers and combined using arithmetic operations

"Factor the polynomial."

"A quadratic is a polynomial of degree two."

a mathematical operation that combines two matrices to produce a new matrix, calculated by multiplying rows and columns

"Matrix multiplication is key."

"Matrix multiplication is not commutative."

an equation involving the square of a variable

"Solve the quadratic equation."

"Students learn to solve quadratic equations like x squared minus four equals zero."

a finite sequence of well-defined, mathematical instructions for completing a specific task or solving a problem

"The algorithm solved the problem quickly."

"An algorithm is a finite sequence of precise"

the rate at which a function changes with respect to its independent variable

"The derivative measures how a function changes."

"A derivative in calculus is the instantaneous rate of change of a function"

a mathematical concept representing the total accumulation of a quantity, often represented by the area under a curve on a graph

"The integral calculates the area under a curve."

"An integral in calculus is the continuous sum of infinitesimal parts"

the value that a function or sequence approaches as its input or index gets close to a particular value

"The limit of the function is zero."

"In calculus, finding the limit of a function is a fundamental concept to master."

(mathematics) a really small change in a function or variable

"A small differential occurred."

"In calculus, the differential represents an infinitesimally small change in a variable or function's value."

a natural number greater than 1 that has no positive divisors other than 1 and itself

"Seven is a prime number."

"A prime number is only divisible by one and itself, a fundamental concept in number theory."

an ordered set of numbers that describes both magnitude and direction, commonly used to represent quantities like displacement, velocity, or force in physics and engineering

"The vector points north."

"In physics, a velocity vector indicates both the speed and the direction of an object's motion."

a mathematical operation that calculates the accumulation of quantities, represented as the area under a curve on a graph

"We need integration."

"The integration of these functions reveals the total accumulated value across the entire interval."