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 Euclidean algorithm is used to find the greatest common divisor of two integers.

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: In statistics, variance is a measure of how spread out the values in a data set are around the mean.

derivative

[noun]

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

Ex: Calculating the derivative of a position function yields the velocity function, describing the rate of change of position with respect to time.

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 velocity function over a time interval gives the total displacement of an object during that time.

limit

[noun]

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

Ex: In calculus, the concept of a limit is essential for defining derivatives, as it involves understanding how a function behaves near a given point.

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, introduced by French mathematician René Thom in the 1960s, is a branch of mathematics that studies sudden changes in the behavior of systems as a result of small changes in inputs or parameters.

differential

[noun]

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

Ex: The differential dx represents a small change in the variable x.

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: In the logarithm log₂(8) = 3, the base 2 raised to the power of 3 equals 8.

prime

[noun]

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

Ex: Seven is a prime because it's only divisible 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: In physics, force is often represented as a vector, considering both its magnitude and direction.

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: Mathematicians often prove theorems to establish mathematical truths.

permutation

[noun]

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

Ex: The number of permutations of three distinct objects is six.

eigenvalue

[noun]

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

Ex: Eigenvalues help us understand how matrices transform vectors.

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 helps define relationships between different groups of numbers.

polynomial

[noun]

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

Ex: Polynomials are used to represent curves in algebraic geometry.

integration

[noun]

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

Ex: Integration helps find the area under curves in math.

matrix multiplication

[noun]

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

Ex: Matrix multiplication is essential for solving systems of linear equations.

quadratic equation

[noun]

an equation involving the square of a variable

Ex: Quadratic equations involve squared terms like x^2.

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