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فهرست واژگان سطح C2 - ریاضیات

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شروع یادگیری
CEFR C2 Vocabulary
algorithm
algorithm
[اسم]

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

دستورالعمل‌های ریاضی

دستورالعمل‌های ریاضی

Ex: The Euclidean algorithm is used to find the greatest common divisor of two integers. 
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variance
variance
[اسم]

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

واریانس

واریانس

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

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

مشتق

مشتق

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

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

انتگرال

انتگرال

Ex: The definite integral of a velocity function over a time interval gives the total displacement of an object during that time. 
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limit
limit
[اسم]

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

حد (ریاضی)

حد (ریاضی)

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. 
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catastrophe theory

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

نظریه فاجعه

نظریه فاجعه

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. 
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differential
differential
[اسم]

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

دیفرانسیل (ریاضیات)

دیفرانسیل (ریاضیات)

Ex: The differential dx represents a small change in the variable x. 
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logarithm
logarithm
[اسم]

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

لگاریتم

لگاریتم

Ex: In the logarithm log₂(8) = 3, the base 2 raised to the power of 3 equals 8. 
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prime
prime
[اسم]

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

عدد اول

عدد اول

Ex: Seven is a prime because it's only divisible by 1 and 7. 
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vector
vector
[اسم]

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

بردار (ریاضیات)

بردار (ریاضیات)

Ex: In physics, force is often represented as a vector, considering both its magnitude and direction. 
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theorem
theorem
[اسم]

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

قضیه

قضیه

Ex: Mathematicians often prove theorems to establish mathematical truths. 
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permutation
permutation
[اسم]

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

جایگشت

جایگشت

Ex: The number of permutations of three distinct objects is six. 
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eigenvalue
eigenvalue
[اسم]

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

مقدار ویژه

مقدار ویژه

Ex: Eigenvalues help us understand how matrices transform vectors. 
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set theory
set theory
[اسم]

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

نظریه مجموعه‌ها

نظریه مجموعه‌ها

Ex: Set theory helps define relationships between different groups of numbers. 
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polynomial
polynomial
[اسم]

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

چندجمله‌ای

چندجمله‌ای

Ex: Polynomials are used to represent curves in algebraic geometry. 
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integration
integration
[اسم]

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

انتگرال‌گیری, ادغام عددی

انتگرال‌گیری, ادغام عددی

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

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

ضرب ماتریسی, ضرب ماتریس

ضرب ماتریسی, ضرب ماتریس

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

an equation involving the square of a variable

معادله درجه‌دو, معادله مربعی

معادله درجه‌دو, معادله مربعی

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