数学家的英语 (含例句)

1. 术语及符号

数学家在论文和教材中使用大量的术语和符号，这些术语和符号对于非数学专业的人来说可能很陌生。因此，学习数学家的英语需要了解和掌握相应的数学术语和符号。

例句：

- The equation f(x) = 0 has two real roots.

- The concept of limit is fundamental in calculus.

- The expression ∑n=1∞ 1/n diverges.

- The matrix A is invertible if and only if det(A) ≠ 0.

- The theorem states that every even integer greater than 2 can be expressed as the sum of two primes.

2. 逻辑推理

数学家在论文和教材中使用的语言通常比较严谨和精确，需要进行逻辑推理才能理解其含义。因此，学习数学家的英语需要具备一定的逻辑推理能力。

例句：

- By induction, we can prove that the statement holds for all positive integers.

- If A is a subset of B and B is a subset of C, then A is a subset of C.

- The function f(x) is continuous if and only if it is sequentially continuous.

- The theorem follows immediately from the definition of divergence.

- The proof of the proposition is by contradiction.

3. 抽象概念

数学家经常涉及抽象的概念和思维，这些概念和思维可能与日常生活中的经验和直觉相去甚远。因此，学习数学家的英语需要具备一定的抽象思维能力。

例句：

- The concept of integral is a generalization of the notion of area.

- Topology is the study of abstract properties of space.

- A ring is an abstract algebraic structure that satisfies certain axioms.

- The idea of morphism generalizes the notion of a function between two sets.

- A manifold is a mathematical object that locally resembles Euclidean space.

4. 计算能力

数学家在论文和教材中经常涉及复杂的计算和推导过程，需要具备一定的计算能力和技巧才能进行理解和学习。因此，学习数学家的英语需要具备一定的计算能力和技巧。

例句：

- The integral can be evaluated using the substitution u = sin(x).

- The eigenvalues of a matrix can be computed by solving the characteristic equation.

- The series can be approximated by truncating it at a certain term.

- The differential equation can be solved using the method of separation of variables.

- The limit can be computed using L'Hôpital's rule.

例句翻译：

1. The equation f(x) = 0有两个实根。

这个方程式的解包括两个实数。

2. The concept of limit is fundamental in calculus.

极限概念是微积分中的基础概念。

3. The expression ∑n=1∞ 1/n diverges.

这个无穷级数发散。

4. The matrix A is invertible if and only if det(A) ≠ 0.

当且仅当矩阵A的行列式不等于0时，A才有逆矩阵。

5. The theorem states that every even integer greater than 2 can be expressed as the sum of two primes.

这个定理表明每个大于2的偶数都可以表示成两个质数之和。