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algorithm
2-
variance
3-
derivative
4-
integral
5-
limit
6-
catastrophe theory
7-
differential
8-
logarithm
9-
prime
10-
vector
11-
theorem
12-
permutation
13-
eigenvalue
14-
set theory
15-
polynomial
16-
integration
17-
matrix multiplication
18-
quadratic equation
algorithm
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(metodă de calcul)

(metodă de calcul)

algoritm

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/ˈæɫɡɝˌɪðəm/
substantiv

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

example
Exemplu
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The Sieve of Eratosthenes is an algorithm for finding all prime numbers up to a given limit.
The Fast Fourier Transform (FFT) algorithm efficiently computes the discrete Fourier transform of a sequence or its inverse.
The Euclidean algorithm is used to find the greatest common divisor of two integers.
variance
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variabilitate

variabilitate

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/ˈvɛɹiəns/
substantiv

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

example
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The variance of a random variable is the expectation of the squared deviation of that variable from its mean.
In statistics, variance is a measure of how spread out the values in a data set are around the mean.
The variance formula involves summing the squared differences between each data point and the mean, divided by the number of data points.
derivative
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derivată

derivată

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/dɝˈɪvətɪv/, /dɝˈɪvɪtɪv/
substantiv

the rate at which a function changes with respect to its independent variable, representing the slope of the tangent line to the function's graph

synonymderived function
synonymdifferential
synonymdifferential coefficient
synonymfirst derivative
example
Exemplu
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Finding the derivative of a distance function results in the instantaneous speed function, representing the speed of an object at a specific moment.
The derivative of a revenue function provides the marginal revenue, indicating the additional revenue gained from selling one more unit.
In economics, the elasticity of a demand function is determined by finding the derivative with respect to price.
integral
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(integrare)

(integrare)

integrală

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/ˈɪnəɡɹəɫ/, /ˈɪntəɡɹəɫ/
substantiv

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

example
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Calculating the integral of a rate of change function provides the total change in the quantity over a given period.
limit
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limită

limită

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/ˈɫɪmət/
substantiv

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

synonymlimit point
synonympoint of accumulation
example
Exemplu
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The limit of a sequence is the value it approaches as the index goes to infinity.
Evaluating the limit of a difference quotient leads to the definition of a derivative in calculus.
The limit of a fraction where the numerator and denominator both approach infinity may involve applying L'Hôpital's Rule.
catastrophe theory
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(teoria catastrofei)

(teoria catastrofei)

teoria catastrofelor

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/kɐtˈæstɹəfi θˈiəɹi/
substantiv

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

example
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Applications of catastrophe theory range from biology and ecology to economics and psychology, where it helps explain abrupt shifts in phenomena such as population dynamics, market crashes, and sudden changes in behavior.
Catastrophe theory models complex systems using mathematical structures called catastrophe manifolds, which describe the possible states of the system and the transitions between them.
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.

Informații Gramaticale:

Substantiv Compozit
differential
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(diferențial)

(diferențial)

diferential

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/ˌdɪfɝˈɛnʃəɫ/
substantiv

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

synonymderivative
synonymderived function
synonymdifferential coefficient
synonymfirst derivative
example
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Calculus involves studying differentials to understand rates of change.
logarithm
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logaritm

logaritm

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/ˈɫɑɡɝˌɪðəm/
substantiv

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

example
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Engineers often apply logarithms in signal processing for efficient data representation.
She used the logarithm to solve complex exponential equations in her mathematics class.
Astronomers apply logarithms to express stellar magnitudes and measure the brightness of celestial objects.
prime
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(prim)

(prim)

număr prim

flag
/ˈpɹaɪm/
substantiv

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

synonymprime quantity
example
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The number 29 is a prime because it has no divisors other than 1 and 29.
Seven is a prime because it's only divisible by 1 and 7.
vector
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vector

vector

flag
/ˈvɛktɝ/
substantiv

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

example
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Acceleration, a vector in kinematics, represents the rate of change of velocity over time.
Velocity, a vector quantity, describes an object's speed and the direction in which it is moving.
In physics, force is often represented as a vector, considering both its magnitude and direction.
theorem
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teoremă

teoremă

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/ˈθɪɹəm/
substantiv

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

example
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The Pythagorean theorem is a well-known principle in geometry.
One fundamental aspect of mathematical reasoning is establishing the validity of theorems.
Students often encounter various theorems while studying advanced mathematics.
permutation
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permutare

permutare

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/ˌpɝmjuˈteɪʃən/
substantiv

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

example
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Permutations are often used in probability calculations.
Combinatorics relies on permutations to count arrangements without repetition.
The number of permutations of three distinct objects is six.
eigenvalue
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valoare proprie

valoare proprie

flag
/ˈaɪɡənˌvæɫju/
substantiv

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

synonymcharacteristic root of a square matrix
synonymeigenvalue of a matrix
synonymeigenvalue of a square matrix
example
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Engineers use eigenvalues to understand structural stability in bridges.
The eigenvalues of a symmetric matrix are always real numbers.
Eigenvalues help us understand how matrices transform vectors.
set theory
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(teoria mulțimilor matematice)

(teoria mulțimilor matematice)

teoria mulțimilor

flag
/sˈɛt θˈiəɹi/
substantiv

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

Informații Gramaticale:

Substantiv Compozit
polynomial
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polinom

polinom

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/ˌpɑˌɫiˈnoʊmiəɫ/
substantiv

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

synonymmultinomial
example
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Simple expressions like 5x are considered polynomials.
The expression 2x+3 is a simple polynomial.
Adding or subtracting polynomials involves combining like terms.
integration
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(operație de integrare)

(operație de integrare)

integrare

flag
/ˌɪnəˈɡɹeɪʃən/, /ˌɪntəˈɡɹeɪʃən/
substantiv

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

example
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Integration helps find the area under curves in math.
Physicists use integration to solve problems in mechanics.
In math, integration helps calculate probabilities.
matrix multiplication
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(produsul matricelor)

(produsul matricelor)

înmulțirea matricelor

flag
/mˈeɪtɹɪks mˌʌltɪplɪkˈeɪʃən/
substantiv

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

example
Exemplu
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Data scientists apply matrix multiplication in machine learning algorithms for data analysis.
In finance, matrix multiplication is used for portfolio optimization and risk analysis.
Matrix multiplication is essential for solving systems of linear equations.

Informații Gramaticale:

Substantiv Compozit
quadratic equation
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(ecuație de gradul al doilea)

(ecuație de gradul al doilea)

ecuație cuadratică

flag
/kwɑːdɹˈæɾɪk ɪkwˈeɪʒən/
substantiv

an equation involving the square of a variable

synonymquadratic
example
Exemplu
click on words
Quadratic equations involve squared terms like x^2.
Quadratic equations often have two solutions, called roots.
Quadratic equations are useful for calculating areas of squares and rectangles.

Informații Gramaticale:

Substantiv Compozit
pattern

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