C2 Level Wordlist - Mathematics

Here you will learn all the essential words for talking about Mathematics, collected specifically for level C2 learners.

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algorithm

[noun]

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

Ex: The Fast Fourier Transform ( FFT ) algorithm efficiently computes the discrete Fourier transform of a sequence or its inverse .

variance

[noun]

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

Ex: Variance is an important concept in probability theory and is used in various statistical analyses, such as hypothesis testing and regression analysis.

derivative

[noun]

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

Ex: The chain rule allows finding the derivative of composite functions, crucial for analyzing complex mathematical expressions.

integral

[noun]

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

Ex: The definite integral of a probability density function gives the probability of an event occurring within a specified range.

limit

[noun]

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

Ex: Evaluating the limit of a difference quotient leads to the definition of a derivative in calculus .

catastrophe theory

[noun]

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

Ex: Catastrophe theory has also been used to analyze the stability of ecosystems , the dynamics of animal behavior , and the onset of psychiatric disorders , providing insights into the underlying mechanisms driving these phenomena .

differential

[noun]

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

Ex: Differential equations describe relationships involving derivatives.

logarithm

[noun]

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

Ex: Astronomers apply logarithms to express stellar magnitudes and measure the brightness of celestial objects .

prime

[noun]

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

Ex: The number 7 is a prime, as it can only be divided by 1 and 7 .

vector

[noun]

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

Ex: The force exerted by a tensioned rope can be represented as a vector in mechanics .

theorem

[noun]

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

Ex: Students often encounter various theorems while studying advanced mathematics .

permutation

[noun]

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

Ex: Permutations are used to count different ways to arrange objects .

eigenvalue

[noun]

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

Ex: The eigenvalues of a symmetric matrix are always real numbers .

set theory

[noun]

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

Ex: Set theory forms the basis for defining functions and relations .

polynomial

[noun]

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

Ex: Simple expressions like 5x are considered polynomials.

integration

[noun]

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

Ex: Physicists use integration to solve problems in mechanics .

matrix multiplication

[noun]

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

Ex: In finance , matrix multiplication is used for portfolio optimization and risk analysis .

quadratic equation

[noun]

an equation involving the square of a variable

Ex: Factoring is a common method to solve quadratic equations when possible .

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