C2级单词表 - Mathematics

在这里，您将学习所有关于数学的基本词汇，这些词汇是专门为C2级别的学习者收集的。

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algorithm

[名词]

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

算法

Ex: The Fast Fourier Transform ( FFT ) algorithm efficiently computes the discrete Fourier transform of a sequence or its inverse .快速傅里叶变换（FFT）**算法**高效地计算序列或其逆的离散傅里叶变换。

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variance

[名词]

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

方差

Ex: Variance is an important concept in probability theory and is used in various statistical analyses, such as hypothesis testing and regression analysis.**方差**是概率论中的一个重要概念，用于各种统计分析，如假设检验和回归分析。

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derivative

[名词]

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

导数, 微分

Ex: The chain rule allows finding the derivative of composite functions, crucial for analyzing complex mathematical expressions.链式法则允许找到复合函数的**导数**，对于分析复杂的数学表达式至关重要。

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integral

[名词]

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

积分, 定积分

Ex: The definite integral of a probability density function gives the probability of an event occurring within a specified range.概率密度函数的定**积分**给出了事件在指定范围内发生的概率。

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limit

[名词]

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

极限

Ex: Evaluating the limit of a difference quotient leads to the definition of a derivative in calculus .评估差商的**极限**导致了微积分中导数的定义。

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catastrophe theory

[名词]

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

灾变理论, 突变理论

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 .**灾难理论**也被用来分析生态系统的稳定性、动物行为的动态以及精神障碍的发作，提供了对这些现象背后驱动机制的见解。

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differential

[名词]

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

微分, 无限小变化

Ex: Differential equations describe relationships involving derivatives.**微分**方程描述了涉及导数的关系。

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logarithm

[名词]

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

对数

Ex: Astronomers apply logarithms to express stellar magnitudes and measure the brightness of celestial objects .天文学家应用**对数**来表示星等和测量天体的亮度。

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prime

[名词]

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

素数, 质数

Ex: The number 7 is a prime, as it can only be divided by 1 and 7 .数字7是一个**质数**，因为它只能被1和7整除。

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vector

[名词]

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

向量, 矢量

Ex: The force exerted by a tensioned rope can be represented as a vector in mechanics .由张紧的绳子施加的力可以在力学中表示为**矢量**。

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theorem

[名词]

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

定理

Ex: Students often encounter various theorems while studying advanced mathematics .学生在学习高等数学时经常会遇到各种**定理**。

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permutation

[名词]

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

排列, 序列

Ex: Permutations are used to count different ways to arrange objects .**排列**用于计算排列物体的不同方式。

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eigenvalue

[名词]

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

特征值, 本征值

Ex: The eigenvalues of a symmetric matrix are always real numbers .对称矩阵的**特征值**总是实数。

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set theory

[名词]

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

集合论, 集理论

Ex: Set theory forms the basis for defining functions and relations.**集合论**为定义函数和关系奠定了基础。

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polynomial

[名词]

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

多项式, 多项式表达式

Ex: Simple expressions like 5x are considered polynomials.像5x这样的简单表达式被认为是**多项式**。

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integration

[名词]

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

积分

Ex: Physicists use integration to solve problems in mechanics .物理学家使用**积分**来解决力学中的问题。

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matrix multiplication

[名词]

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

矩阵乘法

Ex: In finance , matrix multiplication is used for portfolio optimization and risk analysis .在金融中，**矩阵乘法**用于投资组合优化和风险分析。

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quadratic equation

[名词]

an equation involving the square of a variable

二次方程, 平方方程

Ex: Factoring is a common method to solve quadratic equations when possible .**因式分解**是解**二次方程**时常用的一种方法。

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C2级单词表

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C2级单词表 - Mathematics