Mathematics

Encryption relies on sophisticated algorithms to secure data.

差异, 方差

The temperature variance this year was higher than usual.

今年的温度方差比往常高。

导数, 微分

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

计算位置函数的导数可以得到速度函数，描述位置随时间的变化率。

整体的, 基本的

Effective communication is integral to a successful team.

有效的沟通是成功团队的不可或缺部分。

极限, 界限

The engineer's innovative designs pushed the limits of modern technology.

工程师的创新设计推动了现代技术的极限。

灾变理论, 突变理论

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.

灾变理论由法国数学家勒内·托姆在20世纪60年代提出，是数学的一个分支，研究由于输入或参数的微小变化而导致的系统行为的突然变化。

差异的

The company offers employees a higher salary based on their level of experience, creating a pay scale with differential wages.

公司根据员工的经验水平提供更高的薪水，创建一个具有差异工资的工资等级。

对数

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

在对数 log₂(8) = 3中，底数2的3次方等于8。

主要的, 首要的

The prime objective of the mission was to ensure the safety of all crew members.

任务的主要目标是确保所有船员的安全。

Mosquitoes are the primary vector of malaria.

定理

Mathematicians often prove theorems to establish mathematical truths.

数学家经常证明定理以建立数学真理。

The city underwent a permutation after the new government took power.

特征值, 本征值

Eigenvalues help us understand how matrices transform vectors.

特征值帮助我们理解矩阵如何变换向量。

集合论, 集理论

Set theory helps define relationships between different groups of numbers.

集合论有助于定义不同数字组之间的关系。

多项式, 多项式表达式

Polynomials are used to represent curves in algebraic geometry.

多项式用于在代数几何中表示曲线。

The civil rights movement promoted school integration.

矩阵乘法

Matrix multiplication is essential for solving systems of linear equations.

矩阵乘法对于解线性方程组至关重要。

二次方程, 平方方程

Quadratic equations involve squared terms like x^2.

二次方程涉及像x^2这样的平方项。