数学专业外语之二: 阅读理解与翻译初步
企业开发
2023-04-07 14:35:46
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一、比、率与比例
number:数;number axis:number theory:数论;the number of:…的数量
quantity: 量;数量.
Unit: 单位;单元;可逆元素; unit angle:单位角;unit circle: 单位圆; unit area: 单位面积; unit element:单位元素,幺元
dimension:维数,尺寸,大小;dimension of linear space:线性空间的维数;dimension theory: 维数定理 dimensional: 维数的;3-dimensional:三维的;n-dimensional:n维的
length:长度,长;unit length:单位长度;length of arc:弧长;length of curve:曲线长;
quotient:商;quotient set:商集;quotient space:商空间;quotient group:商群;quotient map: 商映射
measurement:测量,测定。measurement of area: 面积的测量; measurement range:测量范围;measurement system:测量系统
Measure: n. 测度; v. 度量。measure space:测度空间;measure zero:零测度;measure of length:长度的度量;measure function:度量函数.
Measurable: a. 可测的. measurable space:测度空间;measurable set:可测集;measurable function:可测函数;measurable transformation:可测变换
angle:角度,角;angle between two straight line: 直线之间的夹角;angle between two planes:面之间的夹角;interior angle:内角;exterior angle: 外角
Angular: 角度的,角的;angular bisector:角平分线;angular acceleration: 角加速度
Ratio: 比,比率; ratio diagram: 比例图;ratio of equality: 等比;ratio of similitude:相似比;ratio scale:比例尺度;ratio method: 比率法;ratio of circumference: 圆周率;
proportion:比例,比例式;proportional:成正比例的;inverse proportional:成反比的
corresponding:adj. 对应的; corresponding angle: 对应角;corresponding side:对应边;corresponding point: 对应点
correspond: v. 对应,常用correspond to sth. 对应于某物
correspondence: n. 对应
二、三角函数与解三角函数
triangle: 三角形;right triangle: 直角三角形;isosceles right triangle: 等腰直角三角形;acute triangle:锐角三角形;obtuse triangle:钝角三角形
side: 边,侧;side of angle:角的边;side opposite of an angle: 角的对边;side face:侧面;
rotation: 旋转,旋度; rotation axis: 旋转轴; rotation of the coordinate system: 坐标轴的旋转; rotation of coordinate: 坐标旋转;rotation surface:旋转曲面;rotation transformation: 旋转变换
vertex:顶点; vertex angle:顶角;vertex of an angle: 角的顶点;vertex of cone:锥顶;vertex of a triangle:三角形的顶点
solution:n. 解,解法。solution approach:解题方法; solution set: 解集
Solve: 解决;solve equation:解方程;solve problem:解题
Unknown: n. 未知元,未知数,未知量;a. 未知的; unknown function:未知函数;unknown number: 未知数;unknown quantity: 未知量; unknown term:未知项
known: a. 已知的; given: a. 已知的,给定的
elementary:a. 初等的,基本的;elementary algebra: 初等代数;elementary geometry: 初等几何学;elementary number theory: 初等数论;elementary transformation: 初等变换;elementary operation:初等算子;elementary event: 基本事件
denote: vt. 表示,记作;多数情况下采用被动, be denoted as 或 be denoted by;祈使句时用主动式
define:vt. 定义。可用主动式,但多数用被动式 be defined as…
compose: vt. 组成; be composed of: 由…组成,可用consist of … 代替,后者是主动式
include: vt. 包含. be included by 被包含;同义词,contain, involve
inverse 和 converse都表示逆的,但是inverse通常只放在名次之前作定语,不做表语,后者都可作。 converse theorem: 逆定理;converse proposition:逆命题; Inverse function: 逆问题;inverse matrix:逆矩阵;inverse of a number: 倒数
三、素数与辗转相除法
division: 除法;division algorithm:辗转相除法;division by factor:因子除法;division with remainder:带余除法
dividend: 被除数;division:除数;quotient:商;remainder:余数;
addition:n. 加法; addition of vectors: 向量的加法;addition theorem: 加法定理
square:平方,二次幂,正方形;square brackets: 方括号;square root: 平方根,二次根;square matrix:方阵
factor: 因数;因子; the highest common factor (H.C.F):最大公因子;the greatest common divisor: (G.C.D) 最大公因子;
multiple: n. 倍数,倍式,多重;multiple angle:倍角;multiple arithmetic:多重运算;multiple divisor: 重因子;multiple integral: 多重积分;multiple numbers: 重数;multiple point:重点;multiple root:重根;multiple valued function:多值函数;the lowest common multiple: 最小公倍数, L.C.M
prime: 素数,质数;prime factor:素因子;prime field:素域;prime ideal:素理想;prime number: 素数
countable: 可数的;countable axiom:可数公理;countable additivity:可数可加的;countable set: 可数集
countably adv. 可数地; countably infinite: 可数无限的
uncountable: 不可数的; uncountable set: 不可数集
count:v. 计数
finite: 有限的;finite additively: 有限可加性;finite bias: 有限基;finite cover: 有限覆盖;finite dimensional space:有限维空间;finite element: 有限元;finite group:有限群;finite set: 有限集
infinite: 无限的; infinitely adv. 无限地
determine: vt. 确定. 表示经过判断而做出的一种选择行为,在数学英语中经常出现,如表示某一种情形或确定某个值等都用determine作动词。后常接宾语从句。
四、集合论简介
composite: n. 合数;a. 合成的,复合的;composite function: 复合函数;composition graph: 合成图;composition mapping: 复合映射,合成映射;composition vector:合成向量
correspondence:n. 对应.
corresponding: a. 对应的; corresponding angle: 同位角,对应角;corresponding sides:对应边;corresponding angle: 对应角
symbolic: a. 符号的; symbolic logic:符号逻辑; symbolic computation: 符号运算; symbolic language:符号语言
symbol: n. 符号;symbol computation: 符号运算;symbol of numeral: 数字的符号
curve: n. 曲线;vt. 弯曲;curve of second order: 二次曲线;curve segment:曲线段
curved: adj. 弯曲的;curved line: 曲线;curved surface: 曲面
set: 集; empty set = null set: 空集;set theory:集论;the set of integers: 整数集;open set: 开集;closed set: 闭集
supplementary: a. 互补的;supplementary angle: 补角;supplementary conditions: 补充条件,辅助条件;supplementary set:补集;supplementary unknown: 补充未知数
reduce: vt. 简化,转化,缩减;常用reduce to表示: 简化为,转化为,缩减为
consist: v. 组成。常用consist of 表示由…组成,例如The right half plan consists of the points (x,y) satisfying x>0.
Indicate: vt. 指示,指明,表示。常作指明,其它用法不如denote高频。
Hold: 有效,成立,比be valid和 be true更常用。
under consideration: 名次后作定语,表示考虑中的
In advance: 实现,预先
In contrast to/with: 与…相对照
In the nature of: 具有…的性质
In (with) reference to: 关于,参考
A is said to be B; A is called B; (满足某种条件的)A被称为B.
B is defined as A. (新概念)B定义为(满足某种条件的)A
五、平面点集和圆锥曲线
coordinate: n. 坐标.; coordinate axis: 坐标轴;coordinate transformation: 坐标变换;coordinate of a point: 点的坐标;coordinate system:笛卡尔坐标系
abscissa: 横坐标;quadrant: 象限;ordinate: 纵坐标;axis: 轴;x-axis,y-axis, pole axis
Intersection: 交、交集;intersection point = point of intersection: 交点;intersection properly:正常相交;the intersection of sets A and B: 集合A和B的交集
degenerate: a. 退化的; degenerate conic: 退化二次曲线;degenerate matrix: 退化矩阵;degenerante differential equation: 退化微分方程;
vertical: a. 竖直的,垂直的;vertical line: 竖直线;
perpendicular: 垂线;垂直的,正交的;
Horizontal: a. 水平的;horizontal line: 水平线;horizontal plane: 水平面
Parabola: 抛物线;parabola formula: 抛物线公式;parabola method: 抛物线法
Parabolic: 抛物线的; parabolic differential equation: 抛物线微分方程
generating: a. 生成的; generating circle: 母圆; generating curve: 母曲线; generating element: 生成元素; generating function: 母函数; generating operator: 生成算子; generation subset: 生成子集
generator: n. 母线、生成元;generator matrix:生成矩阵;
quadratic: a. 二次的;quadratic convergence: 平方收敛;quadratic curve: 二次曲线;quadratic equation: 二次方程;quadratic form: 二次型;quadratic inequality: 二次不等式;quadratic transformation: 二次变换
comprise: vt. 组成;The points (x,y) satisfying x>0 comprise the right half plane.
constitute. vt. 组成;和comprise同义
obtain. vt. 得到, we obtain the conclusion.
mean. vt 指的是, by … is meant …:所谓…指的是
one-to-one: a. 一对一的,术语 one-to-one correspondence:一一对应
on the basis of: 在…基础上
六、空间的向量、直线与平面
Vector: n. 向量;unit vector: 单位向量;normal vector: 法向量;tangent vector: 切向量;position vector: 位置向量;displacement vector: 位移向量
geometrically: 在几何上,用几何方法;genometry: n. 几何;geometrical a.几何的.
perpendicular: 垂直的; perpendicular line: 垂线;perpendicular plan: 垂面;be perpendicular to: 垂直于
displacement: n. 位移; displacement vector: 位移向量;displacement operator: 位移算子
Component: n. 分量,分支,成分,连通区;component ideal: 支理想;component of a vector: 向量的分支
Parametric: a. 参数的;parametric equations: 参数方程;parametric analysis: 参数分析
Parallel: a. 平行的; parallel lines: 平行线;parallel planes: 平行平面;parallel to: 平行于 Parallelogram n. 平行四边形; nonparallel a. 不平行的
base: n. 基,底;base point: 基点,起点;base angle 底角;base for topology: 拓扑基;base of logarithm: 对数的底
Product: n. 乘积,积;dot product: 点积,内积;product rule: 乘法法则;product measure: 积测度;product metric: 积度量;product of paths: 道路的积
Point vt. 使尖锐;vi. 指,指向;n. 点
Compute: vt. 计算,compute from
Through: 通过,穿过
七、矩阵与线性变换
dependent a. 相关的;linear dependent: 线性相关的; dependent linear equations: 相关线性方程; dependent random variable: 相关随机分量; dependent variable: 因变量
dependence n. 相关,相关性;linear dependence 线性相关;
depend: v. 与有关,依赖于
scalar: n. 标量,数量,纯量; a. 标量的,数量的,纯量的;scalar multiple:纯量倍数;scalar product of vector: 向量的数量积,内积,点积;
hypothesis: n. 假设;hypothesis testing:假设检验;hypothesis proposition: 假言命题
column:n. 列;column count:列计算;column rank: 列秩;column sum of matrix: 矩阵的列和;column vector: 列向量
row : n. 行;row vector:行向量;raw rank:行秩;raw sum of matrix: 矩阵的行和
simultaneous: 同时的,即时的;simultaneous approximiately:联合逼近;simultaneous equations:联立方程;simultaneous linear equations:联立线性方程;
consistent:a. 相容的,无矛盾的;consistent axioms: 相容性公理;consistent equations: 相容性方程
Ordered: a. 有序的;ordered basis: 有序基;ordered pair:有序对
Transformation: n. 变换;linear transformation: 线性变换;transformation group: 变换群;transformation matrix:变换矩阵;trasformation of coordinate: 坐标系变换
Isomorphism n. 同构;isomorphism class: 同构族;isomorphism of algebra:代数的同构;isomorphism of groups: 群的同构;
Isomorphic: adj. 同构的;isomorphic group:同构群;isomorphic relation:同构关系
Call: call the matrix of cofficients A.
Make: make sth effective: 使得…有效
Lead: lead to 导致
We may assume i=1 without loss of generality. 不失一般性,我们可以假设i=1
This is contradictory to the hypothesis that … 与。。。假设矛盾
八、函数的概念和演变
Function: n. 函数;function of first degree: 一次函数;function of one variable: 一元函数;function of serveral variables: 多元函数;function of real variable: 实变函数;function of complex variable: 复变函数;function theory: 函数论
Functional: a. 函数的;n. 泛函;functional analysis:泛函分析
Domain: n. 区域、定义域; domain axiom:域公理;domain of convergence: 收敛域;domain of integration:积分区域;
range:n.值域,范围;range of definition:定义范围;range of function:函数值域;range of integration: 积分区域;
Mapping: n. 映射. One-one mapping:一一映射;
Injection: n. 单射;surjection: n. 满射; bijection:双射
Map: v. 映射;map into: 映入;map onto:映上
Image: n.像,像点;inverse image: 逆像;image identification: 图像识别;image processing:图像处理
statistical: a. 统计的;statistical analysis: 统计分析;statistic chart:统计图表;statistic data:统计数据;statistic table: 统计表;statistic estimation method: 统计估计方法;statistic hypothesis: 统计假设;statistic inference:统计推断。
Measurable: 可测的;measurable function: 可测函数; measurable set:可测集;measurable space:可测空间;measurable transformation: 可测变换;
Measure: n. 测度,测量
Meausrement: vt. 测量
Characteristic a. 特征的;characteristic function: 特征函数;characteristic matrix: 特征矩阵;characteristic vector: 特征向量;characteristic polynomial:特征多项式;characteristic root:特征根;characteristic solution:特征解;characteristic value: 特征值.
exclude:vt. 排除. Exclude … From …
Proportional: 成正比例的,常与to+名词,与…成正比
九、变量的极限
Sequence: n. 序列; sequence of number:实数序列;sequence of points: 点序列; infinite sequence: 无穷序列;finite sequence: 有限序列;convergence sequence:收敛序列
Limit: v. 限制; n.极限,界限;limit condition:极限条件;limit of function: 函数的极限;left limit: 左极限;right limit: 右极限
Limiting: 极限的; limiting point of a sequence: 极限点;limitng value:极限值
Limited: 有限的,局限的;limited variation:有界变差
Converge: v. 收敛;converge almost everywhere: 几乎处处收敛;converge criterion: 收敛判断式;converge domain: 收敛域;converge in measure: 依测度收敛;converge in mean: 平均收敛;converge property: 收敛性质;converge uniformly: 一致收敛
Convergent: a. 收敛的;convergence: n. 收敛性
Diverge: v. 发散;diverge infinite series: 发散无穷级数;diverge integrals: 发散积分;diverge series: 发散级数
Divergence: n. 发散性;divergent:a.发散的.
Bound n.界,限;v. 界定;upper bound: 上界;lower bound: 下界;least upper boudn: 上确界;greates lower bound:下确界
bounded: a. 有界的; bounded function: 有界函数; bounded sequence: 有界序列;bounded set: 有界集
Unbounded: a. 无界的;unbounded domain: 无界域;unbounded solution: 无界解;unbounded function: 无界函数
Continous: 连续的;continous function: 连续函数;continous mapping:连续映射;continous on the left: 左连续的;continous on the right: 右连续的;continous as point x0 在x0点连续
Definite: n. 定的,确定的;definite integral: 定积分;definite quadratic form: 定二次型 ;definite quantity: 定量
Increasing: a. 递增的;increasing function: 增函数;increasing sequence:递增序列;increasing series: 递增级数
Decreasing a. 递减的;decreasing sequence: 递减序列;decreasing sequence of sets: 递减集序列
Monotonic: n. 单调的;monotonic function: 单调函数;monotonic sequence: 单调序列
Successive: a. 逐次的,累次的;successive term: 逐项,邻项;successive integration: 逐次积分
ϵ − δ \epsilon-\delta ϵ − δ language: ϵ − δ \epsilon-\delta ϵ − δ 语言(描述函数的极限)
Converge v. 收敛; converge to 0: 收敛到0.
Approach: vt. 接近,趋近;to approach closer and closer some number: 越来越趋近于某某.
Contradict: vt. 与…矛盾;this conclusion contradicts the hypothesis: 这个结论与假设矛盾
Illustrate: vt. 说明,阐明,给…加插图. As illustrated: 正如阐述的
十、导数、微分和不定积分
Derivative: n. 导数,微商;derivative of first order: 一阶导数;derivative of higher order: 高阶导数;derivative on the left: 左导数;derivative on the right: 右导数;partial derivative: 偏导数;total derivative: 全导数,全微商;directional derivative: 方向导数
Differential: n. 微分,a. 微分的;differential calculus: 微分学,微分;differential equation: 微分方程;differential quotient: 微商;differential of a function 函数的微分;differential value: 微分值.
Interval: n. 区间;open interval: 开区间;closed interval: 闭区间;finite interval: 有限区间;infinite interval: 无限区间;interval estimation:区间估计;interval of convergence: 收敛区间.
Integral: adj. 积分的,整数的;n. 积分,整体;integral calculus: 积分学;definite integral: 定积分;indefinite integral: 不定积分;integral curve: 积分曲线;integral constant:积分常数;integral muliple: 整数倍;intergral rational expression: 有理整式
Integration: 积分;integration by parts: 分布积分法; integration by substitution(置换): 换元积分法; successive integration: 累次积分
Constant: n. 常数,常项;constant coefficient: 常数系数;constant curvature: 常曲率;constant function: 常值函数;constant mapping: 常值映射;constant multiple: 常数倍;constant of integration: 积分常数;constant of quantity: 常量;constant term: 常数项
Independent: a. 独立的,无关的;independent equation: 独立方程;independent event: 独立事件;independent increment: 独立增量;independent solutions:无关解;independent set:无关集;independent variables: 自变量
Independence: n. 无关性;linear independence: 线性无关
Approximate: a. 近似; v. 逼近; approximate analysis: 近似分析; approximate computation: 近似计算; approximate evaluation: 近似估计; approximate number:近似数; approximate value: 近似值.
Directed: 有向的;directed angle:有向角;directed distance: 有向距离;directed graph: 有向图;directed line:有向直线;directed number: 有向数。
Concern: vt. (事情)与…有关,使有关
Resolve: vt. 下决心,作决议,解决; resolve problem: 解决问题
Construct: vt. 建立,构成; construct a new function: 构造一个函数
name: vt. 给…命名,把…命名为…; Here C is an arbitrary constant named integral constant.
As is usually the case: 和通常的情形一样
When and only when: 当且仅当
available: a. 有用的,有效的;be available for : 对…有效的
whereas: adj. 然而,却,反之.
Clockwise and counterclockwise: 顺时针和逆时针
十一、定积分的性质和应用
Strict: adj. 严格的;strict inequality: 严格不等式;strict implication: 严格蕴涵
Strictly: adv. 严格地;strictly convex: 严格凸的;strictly increasing: 严格递增的;strictly monotone: 严格单调的;strictly decreasing: 严格递减的;strictly speaking: 严格来说
Invariance: n. 不变性. Invariance of differential forms: 微分形式不变性;invariance principle: 不变原理
Definite: a. 定的,确定的;definite integral: 定积分;definite operator: 有定算子;definite quadratic form: 定二次型;
Indefinite: a. 不定的,不确定的;indefinite integral: 不定积分;
Step: n. 阶段,级,步骤,步长; step-by-step integration: 逐步积分;step curve: 阶梯曲线;step function: 阶梯函数.
Cylindrical: a. 圆柱形的;cylindrical coordinate: 圆柱坐标系
Integrable: 可积的;integrable function: 可积函数;integrable representation 可积表示;
Subinterval: n. 子区间;
Additivity: n. 可加性;additivity of measure 测度的可加性;additivity of probability: 概率的可加性
Congruent: a. 全等的. Congruent triangles: 全等三角形;congruent figures: 相似形;congruent with: 全等于
Cross-sectional: a. 截面的; cross-sectional area: 截面面积
convex: 凸的;convex set: 凸集;convex space: 凸空空;convex linear combination: 凸线性组合
Extent: vi. 扩展,extent … To: 把…扩展到
deduce: vt. 推论,演绎;deduce A from B: 从B推出A
Evalute: vt. 评价,估计,计算;对应名词evaluation: n. 赋值,计算: evaluation of determinants: 行列式的求值;
Revolve: vt. 使旋转;vi. 旋转;同义词rotate. Revolve about the x-axis: 沿着x轴旋转=roate about the x-axis.
Imply: vt. 蕴含,推出
By … We mean:解释上文出现过的一个概念. By a right cylindrical solid we mean a set congruent to a set S of the form …
十二、函数项序列与级数
Test: n. 测试,判别法;Weierstrass M- test: Weierstrass M判别法;comparision test: 比较判别法;ratio comparision: 比率判别法;root comparision: 根式判别法
Term: n. 项,术语;general term: 通项;the first n terms: 前n项;consecutive terms: 相继项;term-by-term: 逐项;term-by-term integration: 逐项积分.
Series: n. 级数,串. Geometric series: 几何级数;power series: 幂级数; function series: 函数项级数
Boundary: n. 边界;boundary point: 边界点;boundary of a domain: 区域的边界;
Bound: n.界
Bounded: a. 有界的;bounded function: 有界函数;bounded above: 上有界;bounded lower: 下有界
Empty: adj. 空的; empty set:空集; nonempty: a. 非空的;empty set: 非空界;empty closed set: 非空闭集
Behavior: n. 性质,性状,作用
conclude: vt.推导出,结束;we conclude that …
Dominate: vt. 控制;be dominated by: 由…控制
manpulate: vt. 操作;进行运算
Justify: vt. 判断,判别
Consecutive: a. 相邻的;consecutive number: 相邻数;consecutive even numbers: 相邻偶数;consecutive terms: 相邻项
Absolutely: adv. 绝对地;converge absolutely: 绝对收敛;absolutely convergent: 绝对收敛的
Uniformly: adv. 一致地;converge uniformly: 一致收敛;uniformly convergent: 一致收敛的
Say for. 例如
十三、常微分方程
Equation: n. 方程;equation of plane: 平面方程;equation of curve: 曲面方程;equation of straight line: 直线方程;equation of higher degree: 高次方程;equation of nth order: n次方程;equation with constant coefficient: 常系数方程;ordinary differential: 常微分方程;partial differential: 偏微分方程;quadratic equation: 二次方程
Homogeneous: a. 齐次的;homogeneous equation: 齐次方程;homogeneous polynomial: 齐次多项式
non-homogeneous equation:非齐次方程;non-homogeneous problem:非齐次问题
Initial: a. 初始的;initial condition: 初始条件;initial distribution: 初始分布;initial function: 初始函数
Solution: n. 解,解法;complementary solution: 补充解;general solution: 通解;particular solution: 特解;solution curve: 解曲线;solution of differential equation: 微分方程的解;linearly independent solution: 线性无关解;
Uniqueness: n. 唯一性;uniqueness theorem: 唯一性定理;uniqueness of solution: 解的唯一性.
Existence: n. 存在性; existence theorem: 存在性定理;existence of solution: 解的存在性
Input: n. 输入. Input function: 输入函数;input data: 输入数据
Output: n.输出. Output function: 输出函数.
Range: vi. 变化;n. 范围,值域;range … From … To …
substitution of ϕ ( t ) \phi(t) ϕ ( t ) and the appropriate derivatives of ϕ \phi ϕ in the given equation yields the desired equality: 用 ϕ ( t ) \phi(t) ϕ ( t ) 和 ϕ \phi ϕ 的导数代入该方程时,能够使它成为所要的等式。
十四、期望、方差与中心极限定理
Distribution: 分布;probability distribution: 概率分布
Expectation: 数学期望;expectation value: 期望值;
Variance: 方差;variance analysis: 方差分析;variance estimation: 方差估计;variance of random variable: 随机变量的方差
Deviation: n. 偏差,离差,变差;standard deviation: 标准差;deviation from mean: 平均偏差
Dispersion: n. 离差;dispersion analysis: 离差分析;dispersion method: 离差法
Mass: n.质量,大量,块: center of mass: 质心
Random: a. 随机的. Random variable: 随机变量;random measure: 随机测度;
Moment: n. 矩; second moment: 二阶矩
Discrete: a. 离散的;discrete random variable: 离散随机变量;discrete mathematics: 离散数学
Individual: a. 个别的,个体的;n.个体;individual element: 个体元素;
Game: n. 博弈
Generalize: 推广,使一般化
十五、数理逻辑入门
Propositional: a. 命题的; propositional calculus: 命题演算;propositional connectives: 命题连词
statement:语句;
Compound: n. 复合,合成;adj. 复合的,合成的
Proof: n. 证明. Proof by consistency: 一致性证明;proof by contradiction: 反证法;proof by induction: 归纳证明;proof of theorem: 定理证明;direct proof: 直接证明;indirect proof: 间接证明
Inference: n. 推理,推论; inference formula: 推理公式
Translation: n. 平移,翻译;translation formula: 平移公式;translation invariant: 平移不变性;translation principle: 平移准则;translation transformation: 平移变换;
Logical: a. 逻辑的;logical calculus: 逻辑演算
十六、组合分析与数值分析
Enumeration: n. 枚举,计数;enumeration algorithm: 枚举算法;enumeration problem: 计数问题;
Algorithm: 算法;algorithm algebra: 算法代数;algorithm approach: 算法逼近;
Approximation: n. 逼近,近似,近似法,近似值. Approximation in mean:均值逼近;
Interpolation: n. 插值,插值法;interpolation formula: 插值公式;interpolation condition: 插值条件;interpolation by proportional parts: 比例插值法;interpolation knot: 插值节点
Polynomial: n. 多项式;polynomial equation: 多项式方程; polynomial expansion: 多项式展开;polynomial of degree n: n阶多项式
As asserted: 正如上面断言的
As is obvious: 显然。
十七、补充词汇
Harmonic function: 调和函数
nontrivial solutions: 非平凡解
By A we understand B: 我们把A理解成B
Capitals: 大写;lower case letters: 小写字母。
Cartesian product: 笛卡尔积;Descartes: 笛卡尔。
Regular polygon: 正多边形;regular triangle: 正三角形;
Incidence: 关联
If S=(x_a) is a family indexed by a set A. 如果S是一个以A为指标集的族
Stand in the relation w to y: 依关系w与y关联
Immaterial: 不重要的
主句A whenever B: 只要B就A
Cauchy-Schwarz inequality
Calculus: 微积分
Volume: 体积
在数学中,up to后面接一个表示某种意义下的等价关系的术语,例如equivalence(等价),isomorophism(同构)等,常译为“按照…的意义“
十八、句子
英文摘要:we consider/ is concerned with/ the scope of the research covers …/ The aim … Is to … This research aims to …/
常用动词: analyze( 分析);characterize(刻画);clarify(阐明);construct(构造);describe(描述);determine(确定);establish(建立);estimate(估计);evaluate(计算);examine(考察);identify(建立);report(报告)
介绍已有成果:Inspired by ; It is well-known that …; it has been reported that …; An important tool of these investigations is … ; The main new technique for proving this theorem is …; by using the method of … We…
介绍研究成果:It is found that …; xxx are proved; was perfected; was proved; was obtained; we obtain that; we show that; it is suggested that… ;
定理和定义的表达:
定理的表达。
简单句子表达。
用单个条件从句的复句叙述的定理,If … , then …; … When … If function f(x) is continuous on [a,b], then there exists a point c in [a,b] such that f(x)<=f© for all x in [a,b] A quadratic equation ax^2+bx+c=0 has two different real roots when the discriminant b^2-4ac is greater than 0.
用多个条件从句的复句叙述的定理; if … and if …, then If ABCD is a parallelogram, then it is a rectangle if one of its interior angles is right angle or is a rhombus if a pair of adjacent sides are equal.
用定理的前提或条件独立成句
把条件和结论各自独立成句。Suppose/Assume … Then …; Let … Then … Let u be an infinitesimal and v is a bounded quantity as x tends to a. Then the multiple uv is also an infinitesimal and the sum u+v is a bounded quantity as x tends to a.
把前提独立成句,后接条件复句。
多个前提依次罗列,后接条件复句,Let (大前提) …, and assume / suppose(小前提) … If …, then …
用充分必要条件 Then the sufficient and necessary condition for … is …; A 成立 if and only if …
数学定义的表达
数学术语的种类有:
作为数学对象或对象之间关系的名称:例如直线、曲线、线性无关
用于描述数学对象的属性和特征,多为形容词:收敛的,离散的,连续的
用于描述数学对象的行为或状态,多为动词或者动词词组,例如收敛,收敛于,相切于
用于描述数学对象之间的关系,多为词组或句子,例如P大于Q,x属于Q 叙述定义的常用动词及相关词组:call, say, define, refer
Define: We define B as A. 或 A is defined as B.
Call: We call A B. 或 A is called B.
Say: We say A to be B. 或 A is said to B.
Refer: We refer to A as B. 或 A is referred to as B. 少部分情况下用name, be named as, term, be termed as, mean, be meant,
数学推理与论证的英语表达
d1. 表达设定的句型:
一般型设定:
let/suppose/assume为动词的祈使句来表示; Let x be the length of the rectangle
Given a rectangle ABCD whose area is 54 cm^2.
简约化设定
指明多种情况可简化为其中一种: We can assume X>0, otherwise there is nothing to show.
We may assume that … without loss of generality.
For simplicity, we …
分层次设定:
Assume, First … , Then …, Finally …
反向性设定:
Assume the conclusion of the proposition is false under the given hypotheses.
符号设定:
Denoted by …
Set N={1,2,…}
任意性设定:
For any positive number ϵ \epsilon ϵ , there exists … Such that … for all …
d2. 表达理由和根据的句子和短语.
用状语从句表原因: Since + 状语从句,we have …
用介词短语表示根据和方法: by +公式:we obtain … By xx theorem.
用分词短语表示根据与方法: Based on … Theroem, …
d3. 表达具有某种性质的句子与短语:
用定语从句指明对象满足性质: which satisfies …
用such that连接的从句指明性质,such that … For all …, where…
用分词:satisfying …
用修饰名词的介词短语: Suppose D is an open set with its closure in G.
d4. 用于讨论和分析问题的句型
用条件复句进行讨论: if, when, as. 例如as t tends to infinty
用介词短语指明结论成立的范围: for n > 1 …
作充分性分析的句型: it is sufficient to prove …; It remains to do … (余下证明。。即可)
表示唯一性 Unique; uniquely; uniqueness.
d6. 表述推理行为的句型和词语:
表示A推出B的句型: A implies B.
表示由A产生或得到B的句型:From A follows B
表示A等价于B的句型: The sufficient and necessary condition is.
宣称得到某个结论: we obtain ; it is clear that …; xxx is proved …
先宣布某个结论,再补充证明,we cliam …
用副词带出进一步推导: hence, therefore, consequently, thus,
d7. 表述论证结束的句子
The proof of the theorem is complete.
We have completed the proof.
We conclude that …
反证法, This contradicts …; is contradictory to …\
转载自 blog.csdn.net/mathlxj/article/details/128930140