高等数学英语词汇(精简3篇)
高等数学英语词汇 篇一
Important Mathematical Terms in English
Mathematics is a universal language, and understanding mathematical terms in English is crucial for students studying advanced mathematics. In this article, we will explore some important mathematical terms and their English translations.
1. Function - 函数
A function is a relationship between two sets of numbers, where each input has exactly one output. In English, we use the term "function" to describe this concept.
2. Derivative - 导数
The derivative of a function measures how a function changes as its input changes. In English, we refer to the derivative of a function as its "derivative."
3. Integral - 积分
The integral of a function is the area under the curve of the function. In English, we use the term "integral" to describe this concept.
4. Limit - 极限
The limit of a function is the value that the function approaches as its input approaches a certain value. In English, we use the term "limit" to describe this concept.
5. Vector - 向量
A vector is a quantity that has both magnitude and direction. In English, we use the term "vector" to describe this concept.
6. Matrix - 矩阵
A matrix is a rectangular array of numbers. In English, we use the term "matrix" to describe this concept.
7. Differential Equation - 微分方程
A differential equation is an equation that relates a function to its derivatives. In English, we use the term "differential equation" to describe this concept.
8. Series - 级数
A series is the sum of the terms of a sequence. In English, we use the term "series" to describe this concept.
9. Convergence - 收敛
Convergence refers to the behavior of a sequence or series as it approaches a certain value. In English, we use the term "convergence" to describe this concept.
10. Divergence - 发散
Divergence refers to the behavior of a sequence or series as it does not approach a certain value. In English, we use the term "divergence" to describe this concept.
Understanding these important mathematical terms in English is essential for students studying advanced mathematics. By familiarizing themselves with these terms, students can better communicate and understand mathematical concepts in an English-speaking academic environment.
高等数学英语词汇 篇二
Strategies for Learning Advanced Mathematical Terms in English
Learning advanced mathematical terms in English can be challenging for non-native English speakers. However, with the right strategies and practice, it is possible to overcome this difficulty. In this article, we will discuss some effective strategies for learning advanced mathematical terms in English.
1. Build a strong foundation in basic mathematical vocabulary
Before diving into advanced mathematical terms, it is important to have a strong foundation in basic mathematical vocabulary. By familiarizing yourself with terms such as "addition," "subtraction," "multiplication," and "division," you can better understand and relate to advanced mathematical concepts.
2. Use visual aids and diagrams
Mathematics is a visual subject, and using visual aids and diagrams can greatly enhance your understanding of mathematical terms. When learning a new term, try to visualize it on a graph or draw a diagram to represent its meaning. This visual representation will help you connect the term with its concept and remember it more effectively.
3. Practice reading and listening to mathematical texts in English
Reading and listening to mathematical texts in English can significantly improve your understanding of mathematical terms. Look for textbooks, articles, and online resources that provide mathematical explanations in English. By exposing yourself to mathematical language in various contexts, you will become more comfortable with using and understanding mathematical terms in English.
4. Engage in mathematical discussions in English
Engaging in mathematical discussions with your peers or teachers in English can greatly enhance your ability to use mathematical terms effectively. Participate in group discussions, ask questions, and explain mathematical concepts using English terminology. This practice will not only improve your understanding of mathematical terms but also enhance your overall communication skills.
5. Create flashcards and practice regularly
Creating flashcards with mathematical terms and their English translations can be an effective way to memorize and review these terms. Review your flashcards regularly, testing yourself on the terms and their meanings. This repetition will help reinforce your knowledge of mathematical terms in English.
6. Seek help from a tutor or teacher
If you are struggling to understand certain mathematical terms in English, do not hesitate to seek help from a tutor or teacher. They can provide explanations and examples in English, helping you better grasp the meaning and usage of these terms.
Learning advanced mathematical terms in English may seem daunting at first, but with consistent practice and the right strategies, you can overcome this challenge. By building a strong foundation, using visual aids, practicing reading and listening, engaging in discussions, creating flashcards, and seeking help when needed, you will gradually become more confident in your ability to use and understand advanced mathematical terms in English.
高等数学英语词汇 篇三
高等数学英语词汇
引导语：高等数学指相对于初等数学而言，数学的对象及方法较为繁杂的'一部分。以下是百分网小编分享给大家的高等数学英语词汇，欢迎阅读!
A
abelian group：阿贝尔群; absolute geometry：绝对几何; absolute value：绝对值; abstract algebra：抽象代数; addition：加法; algebra：代数; algebraicclosure：代数闭包; algebraic geometry：代数几何;algebraic geometry and analytic geometry：代数几何和解析几何; algebraic numbers：代数数; algorithm：算法; almost all：绝大多数; analytic function：解析函数; analytic geometry：解析几何; and：且;angle：角度; anticommutative：反交换律; antisymmetric relation：反对称关系; antisymmetry：反对称性; approximately equal：约等于; Archimedean field：阿基米德域; Archimedean group：阿基米德群; area：面积; arithmetic：算术; associative algebra：结合代数; associativity：结合律; axiom：公理; axiom of constructibility：可构造公理; axiom of empty set：空集公理;axiom of extensionality：外延公理; axiom of foundation：正则公理; axiom of pairing：对集公理; axiom of regularity：正则公理; axiom of replacement：代换公理; axiom of union：并集公理; axiom schema of separation：分离公理; axiom schema of specification：分离公理;axiomatic set theory：公理集合论; axiomatic system：公理系统;
B
Baire space：贝利空间; basis：基; Bézout's identity：贝祖恒等式; Bernoulli's inequality：伯努利不等式 ; Big O notation：大O符号; bilinear operator：双线性算子; binary operation：二元运算; binary predicate：二元谓词; binary relation：二元关系; Boolean algebra：布尔代数;Boolean logic：布尔逻辑; Boolean ring：布尔环; boundary：边界; boundary point：边界点;bounded lattice：有界格;
C
calculus：微积分学; Cantor's diagonal argument：康托尔对角线方法; cardinal number：基数;cardinality：势; cardinality of the continuum：连续统的势; Cartesian coordinate system：直角坐标系; Cartesian product：笛卡尔积; category：范畴; Cauchy sequence：柯西序列; Cauchy-Schwarz inequality：柯西不等式; Ceva's Theorem：塞瓦定理; characteristic：特征;characteristic polynomial：特征多项式; circle：圆; class：类; closed：闭集; closure：封闭性 或 闭包; closure algebra：闭包代数; combinatorial identities：组合恒等式; commutativegroup：交换群; commutative ring：交换环; commutativity:：交换律; compact：紧致的;compact set：紧致集合; compact space：紧致空间; complement：补集 或 补运算; completel
D
de Morgan's laws：德·摩根律; Dedekind completion：戴德金完备性; Dedekind cut：戴德金分割;del：微分算子; dense：稠密; densely ordered：稠密排列; derivative：导数; determinant：行列式; diffeomorphism：可微同构; difference：差; differentiable manifold：可微流形;differential calculus：微分学; dimension：维数; directed graph：有向图; discrete space：离散空间; discriminant：判别式; distance：距离; distributivity：分配律; pidend：被除数;piding：除; pisibility：整除; pision：除法; pisor：除数; dot product：点积;
E
eigenvalue：特征值; eigenvector：特征向量; element：元素; elementary algebra：初等代数;empty function：空函数; empty set：空集; empty product：空积; equal：等于; equality：等式 或 等于; equation：方程; equivalence relation：等价关系; Euclidean geometry：欧几里德几何;Euclidean metric：欧几里德度量; Euclidean space：欧几里德空间; Euler's identity：欧拉恒等式;even number：偶数; event：事件; existential quantifier：存在量词; exponential function：指数函数; exponential identities：指数恒等式; expression：表达式; extended real number line：扩展的实数轴;
F
false：假; field：域; finite：有限; finite field：有限域; finite set：有限集合; first-countablespace：第一可数空间; first order logic：一阶逻辑; foundations of mathematics：数学基础;function：函数; functional analysis：泛函分析; functional predicate：函数谓词;fundamental theorem of algebra：代数基本定理; fraction：分数;
G
gauge space：规格空间; general linear group：一般线性群; geometry：几何学; gradient：梯度;graph：图; graph of a relation：关系图; graph theory：图论; greatest element：最大元;group：群; group homomorphism：群同态;
H
Hausdorff space：豪斯多夫空间; hereditarily finite set：遗传有限集合; Heron's formula：海伦公式; Hilbert space：希尔伯特空间; Hilbert's axioms：希尔伯特公理系统; Hodge decomposition：霍奇分解; Hodge Laplacian：霍奇拉普拉斯算子; homeomorphism：同胚; horizontal：水平;hyperbolic function identities：双曲线函数恒等式; hypergeometric function identities：超几何函数恒等式; hyperreal number：超实数;
I
identical：同一的; identity：恒等式; identity element：单位元; identity matrix：单位矩阵;idempotent：幂等; if：若; if and only if：当且仅当; iff：当且仅当; imaginary number：虚数;inclusion：包含; index set：索引集合; indiscrete space：非离散空间; inequality：不等式 或 不等; inequality of arithmetic and geometric means：平均数不等式; infimum：下确界; infiniteseries：无穷级数; infinite：无穷大; infinitesimal：无穷小; infinity：无穷大; initial object：初始对象; inner angle：内角; inner product：内积; inner product space：内积空间; integer：整数; integer sequence：整数列; integral：积分; integral domain：整数环; interior：内部;interior algebra：内部代数; interior point：内点; intersection：交集; inverse element：逆元;invertible matrix：可逆矩阵; interval：区间; involution：回旋; irrational number：无理数;isolated point：孤点; isomorphism：同构;
J
Jacobi identity：雅可比恒等式; join：并运算;
K
格式： Kuratowski closure axioms：Kuratowski 闭包公理;
L
least element：最小元; Lebesgue measure：勒贝格测度; Leibniz's law：莱布尼茨律; Liealgebra：李代数; Lie group：李群; limit：极限; limit point：极限点; line：线; line segment：线段; linear：线性; linear algebra：线性代数; linear operator：线性算子; linear space：线性空间; linear transformation：线性变换; linearity：线性性; list of inequalities：不等式列表; list oflinear algebra topics：线性代数相关条目; locally compact space：局部紧致空间; logarithmicidentities：对数恒等式; logic：逻辑学; logical positivism：逻辑实证主义; law of cosines：余弦定理; L??wenheim-Skolem theorem：L??wenheim-Skolem 定理; lower limit topology：下限拓扑;
M
magnitude：量; manifold：流形; map：映射; mathematical symbols：数学符号; mathematicalanalysis：数学分析; mathematical proof：数学证明; mathematics：数学; matrix：矩阵;matrix multiplication：矩阵乘法; meaning：语义; measure：测度; meet：交运算; member：元素; metamathematics：元数学; metric：度量; metric space：度量空间; model：模型; modeltheory：模型论; modular arithmetic：模运算; module：模; monotonic function：单调函数;multilinear algebra：多重线性代数; multiplication：乘法; multiset：多样集;
N
naive set theory：朴素集合论; natural logarithm：自然对数; natural number：自然数; naturalscience：自然科学; negative number：负数; neighbourhood：邻域; New Foundations：新基础理论; nine point circle：九点圆; non-Euclidean geometry：非欧几里德几何; nonlinearity：非线性; non-singular matrix：非奇异矩阵; nonstandard model：非标准模型; nonstandardanalysis：非标准分析; norm：范数; normed vector space：赋范向量空间; n-tuple：n 元组 或 多元组; nullary：空; nullary intersection：空交集; number：数; number line：数轴;
O
object：对象; octonion：八元数; one-to-one correspondence：一一对应; open：开集; openball：开球; operation：运算; operator：算子; or：或; order topology：序拓扑; ordered field：有序域; ordered pair：有序对; ordered set：偏序集; ordinal number：序数; ordinarymathematics：一般数学; origin：原点; orthogonal matrix：正交矩阵;
P
p-adic number：p进数; paracompact space：仿紧致空间; parallel postulate：平行公理;parallelepiped：平行六面体; parallelogram：平行四边形; partial order：偏序关系; partition：分割; Peano arithmetic：皮亚诺公理; Pedoe's inequality：佩多不等式; perpendicular：垂直;philosopher：哲学家; philosophy：哲学; philosophy journals：哲学类杂志; plane：平面; pluralquantification：复数量化; point：点; Point-Line-Plane postulate：点线面假设; polarcoordinates：极坐标系; polynomial：多项式; polynomial sequence：多项式列; positive-definitematrix：正定矩阵; positive-semidefinite matrix：半正定矩阵; power set：幂集; predicate：谓词; predicate logic：谓词逻辑; preorder：预序关系; prime number：素数; product：积;proof：证明; proper class：纯类; proper subset：真子集; property：性质; proposition：命题; pseudovector：伪向量; Pythagorean theorem：勾股定理;
Q
Q.E.D.：Q.E.D.; quaternion：四元数; quaternions and spatial rotation：四元数与空间旋转;question：疑问句; quotient field：商域; quotient set：商集;
R
radius：半径; ratio：比; rational number：有理数; real analysis：实分析; real closed field：实闭域; real line：实数轴; real number：实数; real number line：实数线; reflexive relation：自反关系; reflexivity：自反性; reification：具体化; relation：关系; relative complement：相对补集;relatively complemented lattice：相对补格; right angle：直角; right-handed rule：右手定则;ring：环;
S
scalar：标量; second-countable space：第二可数空间; self-adjoint operator：自伴随算子;sentence：判断; separable space：可分空间; sequence：数列 或 序列; sequence space：序列空间; series：级数; sesquilinear function：半双线性函数; set：集合; set-theoretic definitionof natural numbers：自然数的集合论定义; set theory：集合论; several complex variables：一些复变量; shape：几何形状; sign function：符号函数; singleton：单元素集合; social science：社会科学; solid geometry：立体几何; space：空间; spherical coordinates：球坐标系; squarematrix：方块矩阵; square root：平方根; strict：严格; structural recursion：结构递归;subset：子集; subsequence：子序列; subspace：子空间; subspace topology：子空间拓扑;subtraction：减法; sum：和; summation：求和; supremum：上确界; surreal number：超实数; symmetric difference：对称差; symmetric relation：对称关系; system of linearequations：线性方程组;
T
tensor：张量; terminal object：终结对象; the algebra of sets：集合代数; theorem：定理; topelement：最大元; topological field：拓扑域; topological manifold：拓扑流形; topological space：拓扑空间; topology：拓扑 或 拓扑学; total order：全序关系; totally disconnected：完全不连贯;totally ordered set：全序集; transcendental number：超越数; transfinite recursion：超限归纳法; transitivity：传递性; transitive relation：传递关系; transpose：转置; triangleinequality：三角不等式; trigonometric identities：三角恒等式; triple product：三重积; trivialtopology：密着拓扑; true：真; truth value：真值;
U
unary operation：一元运算; uncountable：不可数; uniform space：一致空间; union：并集;unique：唯一; unit interval：单位区间; unit step function：单位阶跃函数; unit vector：单位向量; universal quantification：全称量词; universal set：全集; upper bound：上界;
V
vacuously true：??; Vandermonde's identity：Vandermonde 恒等式; variable：变量;vector：向量; vector calculus：向量分析; vector space：向量空间; Venn diagram：文氏图;volume：体积; von Neumann ordinal：冯·诺伊曼序数; von Neumann universe：冯·诺伊曼全集;vulgar fraction：分数;
Z
Zermelo set theory：策梅罗集合论; Zermelo-Fraenkel set theory：策梅罗-弗兰克尔集合论; ZF settheory：ZF 系统; zero：零; zero object：零对象;
