数学专业英语

数学专业英语
数学专业英语

MATHS ENGLISH

absolute value 绝对值 acceptable region 接受域 additivity 可加性alternative hypothesis 对立假设 analysis of covariance 协方差分析analysis of variance 方差分析 arithmetic mean 算术平均值 association 相关性 assumption checking 假设检验 availability 有效度 band 带宽bar chart 条形图 beta-distribution 贝塔分布 between groups 组间的binomial distribution 二项分布binomial test 二项检验center of gravity 重心 central tendency 中心趋势 hi-square distribution 卡方分布 chi-square test 卡方检验 classify 分类 cluster analysis 聚类分析coefficient 系数 coefficient of correlation 相关系数 collinearity 共线性 components 构成,分量 compound 复合的 confidence interval 置信区间consistency 一致性continuous variable 连续变量control charts 控制图 correlation 相关 covariance 协方差 covariance matrix 协方差矩阵 critical point 临界点 critical value 临界值 cross tab 列联表 cubic term 三次项 cumulative distribution function 累加分布函数curve estimation 曲线估计 default 默认的 deleted residual 剔除残差density function 密度函数dependent variable 因变量design of experiment 试验设计 df.(degree of freedom) 自由度 diagnostic 诊断discrete variable 离散变量discriminant function 判别函数discriminatory analysis 判别分析 D-optimal design D-优化设计 effects of interaction 交互效应eigenvalue 特征值equal size 等含量estimation of parameters 参数估计 estimations 估计量 exact value 精确值 expected value 期望值 exponential指数的 exponential distribution 指数分布 extreme value 极值 factor analysis 因子分析 factor score 因子得分 factorial designs 析因设计 factorial experiment 析因试验fitted line 拟合线fitted value 拟合值fixed variable 固定变量fractional factorial design 部分析因设计 F-test F检验 full factorial design 完全析因设计 gamma distribution 伽玛分布 geometric mean 几何均值 harmonic mean 调和均值 heterogeneity 不齐性 histogram 直方图homogeneity 齐性homogeneity of variance 方差齐性 hypothesis test 假设检验independence独立independent variable 自变量independent-samples 独立样本index of correlation 相关指数interclass correlation 组内相关 interval estimate 区间估计inverse 倒数的iterate 迭代kurtosis 峰度large sample problem 大样本问题least-significant difference 最小显著差数 least-square estimation 最小二乘估计 least-square method 最小二乘法 level of significance 显著性水平 leverage value 中心化杠杆值 life test 寿命试验likelihood function 似然函数 likelihood ratio test 似然比检验 linear estimator 线性估计linear model 线性模型 linear regression 线性回归 linear relation 线性关系 linear term 线性项 logarithmic 对数的 logarithms 对数 lost function 损失函数 main effect 主效应matrix 矩阵 maximum 最大值maximum likelihood estimation 极大似然估计mean squared deviation(MSD) 均方差 mean sum of square 均方和 measure 衡量 media

中位数M-estimator M估计minimum 最小值missing values 缺失值mixed model 混合模型mode 众数 Monte Carle method 蒙特卡罗法 moving average移动平均值 multicollinearity 多元共线性 multiple comparison 多重比较multiple correlation 多重相关multiple correlation coefficient 复相关系数 multiple correlation coefficient 多元相关系数multiple regression analysis 多元回归分析 multiple regression equation 多元回归方程 multiple response 多响应 multivariate analysis 多元分析negative nonadditively 不可加性 nonlinear 非线性 nonlinear regression 非线性回归 noparametric tests 非参数检验 normal distribution 正态分布null hypothesis 零假设number of cases 个案数one-sample 单样本one-tailed test 单侧检验one-way ANOVA 单向方差分析one-way classification 单向分类 optimal 优化的 optimum allocation 最优配制order statistics 次序统计量 origin 原点 orthogonal 正交的 outliers 异常值paired observations 成对观测数据paired-sample 成对样本parameter estimation 参数估计partial correlation 偏相关partial correlation coefficient 偏相关系数 partial regression coefficient 偏回归系 percentiles 百分位数 pie chart 饼图 point estimate 点估计poisson distribution 泊松分布 polynomial curve 多项式曲线 polynomial regression 多项式回归 polynomials 多项式 positive relationship 正相关 power 幂 P-P plot P-P概率图 predicted value 预测值prediction intervals 预测区间principal component analysis 主成分分析proability 概率 probability density function 概率密度函数 quadratic 二次的 Q-Q plot Q-Q概率图 quadratic term 二次项 quality control 质量控制 quantitative 数量的,度量quartiles 四分位数 random sampling 随机取样random seed 随机数种子random variable 随机变量randomization 随机化range 极差rank correlation 秩相关rank statistic 秩统计量regression analysis 回归分析regression coefficient 回归系数 regression line 回归线rejection region 拒绝域residual 残差 residual sum of squares 剩余平方和 risk function 风险函数 robustness 稳健性 root mean square 标准差 row 行 run test 游程检验sample size 样本容量 sample space 样本空间 sampling 取样sampling inspection 抽样检验 scatter chart 散点图 S-curve S形曲线sets 集合sign test 符号检验significance level 显著性水平significance testing 显著性检验significant digits 有效数字skewed distribution 偏态分布 small sample problem 小样本问题 sort 排序sources of variation 方差来源 ion 标准离差 standard error of mean 均值的标准误差 statistical quality control 统计质量控制 std. residual 标准残差 stepwise regression analysis 逐步回归 strong assumption 强假设 stud. deleted residual 学生化剔除残差 stud. residual 学生化残差subsamples 次级样本 sufficient statistic 充分统计量 sum of squares 平方和t-distribution t分布test criterion 检验判据test for linearity 线性检验test of goodness of fit 拟合优度检验test of homogeneity 齐性检验 test of independence 独立性检验 test rules 检验法则test statistics 检验统计量 testing function 检验函数 time

series 时间序列 tolerance limits 容许限 trimmed mean 截尾均值 true value 真值 t-test t检验 two-tailed test 双侧检验unbiased estimation 无偏估计 unbiasedness 无偏性 uniform distribution 均匀分布 value of estimator 估计值variance 方差 variance components 方差分量 variance ratio 方差比weighted average 加权平均值 within groups 组内的 Z score Z分数 active constraint 活动约束 active set method 活动集法 analytic gradient 解析梯度 approximate 近似 arbitrary 强制性的 argument 变量attainment factor 达到因子 bandwidth 带宽 be equivalent to 等价于best-fit 最佳拟合 coefficient 系数 complex-value 复数值 component 分量constrained 有约束的 constraint function 约束函数 converge 收敛cubic polynomial interpolation method 三次多项式插值法 curve-fitting 曲线拟合 data-fitting 数据拟diagonal 对角的 direct search method 直接搜索法direction of search 搜索方向eigenvalue 特征值empty matrix 空矩阵exceeded 溢出的feasible solution 可行解finite-difference 有限差分 first-order 一阶 Gauss-Newton method 高斯-牛顿法 goal attainment problem 目标达到问题 gradient method 梯度法 handle 句柄 Hessian matrix 海色矩阵 independent variables 独立变量inequality 不等式infeasibility 不可行性initial feasible solution 初始可行解 initialize 初始化 invoke 激活 iteration 迭代Jacobian 雅可比矩阵 Lagrange multiplier 拉格朗日乘子 large-scale 大型的least square 最小二乘least squares sense 最小二乘意义上的Levenberg-Marquardt method 列文伯格-马夸尔特法 line search 一维搜索linear equality constraints 线性等式约束 linear programming problem 线性规划问题local solution 局部解 medium-scale 中型的 mixed quadratic and cubic polynomial interpolation and extrapolation method 混合二次、三次多项式内插、外插法 multi objective 多目标的 norm 范数 observed data 测量数据optimization routine 优化过程optimizer 求解器over-determined system 超定系统 partial derivatives 偏导数polynomial interpolation method 多项式插值法quadrati二次的quadratic interpolation method 二次内插法quadratic programming 二次规划real-value 实数值 residuals 残差robust 稳健的robustness 稳健性,鲁棒性scalar 标量semi-infinitely problem 半无限问题Sequential Quadratic Programming method 序列二次规划法 simplex search method 单纯形法sparse matrix 稀疏矩阵 sparsity pattern 稀疏模式 sparsity structure 稀疏结构 starting point 初始点 step length 步长 subspace trust region method 子空间置信域法symmetric matrix 对称矩阵termination message 终止信息 termination tolerance 终止容限 the exit condition 退出条件 the method of steepest descent 最速下降法 transpose 转置unconstrained 无约束的under-determined system 负定系统weighting matrix 加权矩阵approximation 逼近a spline in b-form/b-spline b样条 a spline of polynomial piece /ppform spline 分段多项式样条bivariate spline function 二元样条函数break/breaks 断点coefficient/coefficients 系数cubic interpolation 三次插值/三次内插cubic polynomial 三次多项式cubic smoothing spline 三次平滑样条

cubic spline 三次样条 cubic spline interpolation 三次样条插值/三次样条内插 curve 曲线 degree of freedom 自由度 end conditions 约束条件input argument 输入参数 interpolation 插值/内插 interval 取值区间knot/knots 节点least-squares approximation 最小二乘拟合 multiplicity 重次 multivariate function 多元函数 optional argument 可选参数 output argument 输出参数point/points 数据点rational spline 有理样条rounding error 舍入误差(相对误差)sequence 数列(数组spline approximation 样条逼近/样条拟合spline function 样条函数spline curve 样条曲线 spline interpolation 样条插值/样条内插 spline surface 样条曲面 smoothing spline 平滑样条 tolerance 允许精度univariate function 一元函数 absolute error 绝对误差 absolute tolerance 绝对容限adaptive mesh 适应性网格 boundary condition 边界条件 contour plot 等值线图coordinate 坐标系decomposed geometry matrix 分解几何矩阵diagonal matrix 对角矩阵Dirichlet boundary conditions 边界条件eigenvalue 特征值 elliptic 椭圆形的 error estimate 误差估计exact solution 精确解 generalized Neumann boundary condition 推广的Neumann 边界条件geometry description matrix 几何描述矩阵 geometry matrix 几何矩阵 graphical user interface(GUI)图形用户界面 hyperbolic 双曲线的 initial mesh 初始网格 jiggle 微调Lagrange multipliers 拉格朗日乘子 Laplace equation 拉普拉斯方程 linear interpolation 线性插值machine precision 机器精度mixed boundary condition 混合边界条件Neuman boundary condition Neuman边界条件 node point 节点 nonlinear solver 非线性求解器normal vector 法向量Parabolic 抛物线型的partial differential equation 偏微分方程plane strain 平面应变 plane stress 平面应力 Poisson's equation 泊松方程 polygon 多边形positive definite 正定refined triangular mesh 加密的三角形网格relative tolerance 相对容限 relative tolerance 相对容限 residual norm 残差范数 singular 奇异的postulate假定, 基本条件, 基本原理,要求, 假定,要求conic, conical圆锥的;圆锥形的ellipse椭圆, 椭圆形ellipt hyperbolic 双曲线的parabolic用寓言表达的: 抛物线的,像抛物线的algebraic代数的, 关于代数学的mineralogy 矿物学axiom公理collinear在同一直线上的同线的convex 凸出的;凸面的triangle三角形, 三人一组, 三角关系parallelogram平行四边形straight angle平角right angle 直角acute angle锐角obtuse angle钝角reflex angle优角rectilinear直线的;由直线组成的;循直线进行的isosceles triangle等腰三角形equilateral triangle等边三角形right triangle n. 直角三角形obtuse triangle钝角三角形acute triangle锐角三角形equiangular triangle正三角形,等角三角形hypotenuse(直角三角形的)斜边infinitesimal 无穷小的, 极小的, 无限小的calculus 微积分学, 结石inscribe 记下polygon多角形, 多边形curvilinear曲线的, 由曲线组成的intuition 直觉, 直觉的知识integral积分, 完整, 部分defective有缺陷的, (智商或行为有)欠缺的differential coefficient 微分系数irrational numbers无理数domain 定义域contradiction 矛盾continuous variable 连续变量;[连续变数]variation 变分, 变化

independent variable 自变量dependent variable 应变量rectangular coordinate 直角坐标abscissa〈数〉横坐标ordinate纵线, 纵座标differential 微分的,微分(differentiation)Integral 积分, 完整, 部分(integration) trigonometry 三角法exponential 指数的, 幂数的logarithm 对数derivative导数;微商tangent 切线正切definite integral 定积分culminate 达到顶点differential equation 微分方程extreme value 极值multiple integral 多重积分functional analysis 泛函分析cardinal number 基数(如:1, 2, 3, ... 有别于序数)denumerable可数的aggregate 合计, 总计, 集合体,合计的, 集合的, 聚合的,聚集, 集合, 合计purport主旨,声称superior 长者, 高手, 上级,较高的, 上级的, 上好的, 出众的, 高傲的cumbersome 讨厌的, 麻烦的, 笨重的drastically 激烈地, 彻底地conservation 守衡律quadrature求积, 求积分interpolation插值extrapolation外推法, 推断internal point 内点generalized solution 广义解hydrodynamics 流体力学,水动力学divergence 发散(性),梯度,发散integro-interpolation method 积分插值法Variational method 变分方法comparatively 比较地, 相当地self-adjoint (nonself-adjoint) 自治的,自伴的,自共轭的finite element method 有限元法spline approximation 样条逼近Particles-in-the-Cell 网格质点法herald 使者, 传令官, 通报者, 先驱, 预兆,预报, 宣布, 传达, 欢呼advection水平对流fluctuation波动, 起伏mean-square 均方dispersion离差, 差量nterpolation 插值divisible 可分的dice, die 骰子pitfall 缺陷celestial天上的macroscopic肉眼可见的, 巨观的classical field theory 经典场理论rigit 刚硬的, 刚性的, 严格的quantum量, 额, [物] 量子, 量子论inception 起初, 获得学位pertain 适合, 属于encompass 包围, 环绕, 包含或包括某事物ingredient 成分, 因素acquainted有知识的, 知晓的 synonymous同义的configuration 构造, 结构, 配置, 外形inertia 惯性, 惯量attribute 特性momentum动量designate 指明projectile 射弹,发射的ballistics 弹道学, 发射学intractable 难处理的furnish 供应, 提供, 装备, 布置torque n. 扭矩, 转矩moment 力矩的dissipation 消散, 分散, 挥霍, 浪费, 消遣, 放荡, 狂饮constitutive构成的, 制定的continuum mechanics 连续介质力学superposition重叠, 重合, 叠合reckon 计算, 总计, 估计, 猜想,数, 计算, 估计, 依赖, 料想strength 强度load 载荷empirical 以经验为依据的insofar 在……范围cohesive 内聚性的stiffness 硬度furnish 供给turbulent 湍流laminar 层流isothermal 等温isotropic 各向同性eddy 旋涡viscosity 粘性、粘度adiabatic 绝热的reversible 可逆的 isentropic 等熵的stream tube 流管 tangential 切线的incompressible 不可压缩的similitude 相似性hydraulic 水力的,水力学的spillway (河或水坝的)放水道,泄洪道prototype 原型,样板vibratory 振动的,摆动的propagation 传播acoustic 听觉的,声学的damp 阻尼,衰减restore 复职,归还neutral 平衡 exciting force 激励力resonant共振的,谐振的stiffness 刚度,刚性magnitude 数值,大小substantially实质上的perturb 干扰,扰乱Fourier series 傅里叶级数shredder 切菜器

metropolitan 大都市的at-grade 在同一水平面上elevated 高架的guide way 导轨rigid body 刚体medium 介质aging 老化polymeric聚合(物)的consolidate 把…联合为一体,统一radically 根

本地,本质上deliberate 从容不迫的,深思熟虑Attribute赋予medieval 中世纪的etch 蚀刻,蚀镂fingernail 指甲bar chart 直方

图joystick 游戏杆trial-error 试制, 试生产junction n. 连接, 接合, 交叉点, 汇合处contrive v. 发明, 设计, 图谋snooker (=snooker pool)彩色台球, 桌球****公理 axiom 命题 proposition 被加数augend , summand 加数addend 被减数minuend 减数subtrahend 差remainder 被乘数multiplicand, faciend 乘数multiplicator 积 product 被除数 dividend 除数 divisor 商 quotient 大于等于 is equal or greater than 小于等于 is equal or lesser than 运

算符operator 算术平均数geometric mean n个数之积的n次方

根(reciprocal) x的倒数为1/x 有理数 rational number 无理数irrational number 整数 integer小数点 decimal point分数 fraction 分

子 numerator 分母 denominator 比 ratio 十进制 decimal system 二进制binary system 十六进制 hexadecimal system 权 weight, significance 截尾 truncation 四舍五入 round 下舍入 round down 上舍入 round up 有效数字significant digit 无效数字 insignificant digit 代数 algebra 单项式monomial 多项式polynomial, multinomial 系数coefficient 未知数 unknown, x-factor, y-factor, z-factor 等式,方程式 equation 一次方程simple equation 二次方程quadratic equation 三次方程cubic equation 四次方程 quartic equation 阶乘 factorial 对数logarithm 指数,幂 exponent 乘方 power 二次方,平方 square 三次方,立方 cube 四次方 the power of four, the fourth power n次方 the power of n, the nth power 开方 evolution, extraction 二次方根,平

方根 square root 三次方根,立方根 cube root 四次方根 the root of four, the fourth root n次方根 the root of n, the nth root 坐标系coordinates 坐标轴 x-axis, y-axis, z-axis 横坐标 x-coordinate 纵坐

标y-coordinate 原点origin 象限quadrant 截距(有正负之分)intercede (方程的)解solution 线段 segment 射线 radial 平行parallel 相交intersect 角度degree 弧度radian 钝角obtuse angle 平角 straight angle 周角 perigon 底 base 锐角三角形 acute triangle 直角边 leg 斜边 hypotenuse 勾股定理 Pythagorean theorem 钝角三角形 obtuse triangle 不等边三角形 scalene triangle 等腰三角

形isosceles triangle 等边三角形equilateral triangle 四边形quadrilateral 平行四边形parallelogram 周长perimeter 全等congruent 三角 trigonometry 正弦 sine 余弦 cosine 正切 tangent 余切 cotangent 正割 secant 余割 cosecant 反正弦 arc sine 反余

弦 arc cosine 反正切 arc tangent 反余切 arc cotangent 反正割arc secant 反余割 arc cosecant 集合aggregate 空集 void 子集subset 交集intersection 并集union 补集complement 映射mapping 定义域 domain, field of definition 值域 range 单调性monotonicity 图象 image 数列,级数 series 导数 derivative 无穷

小infinitesimal 复数complex number 矩阵matrix 行列式determinant 半圆 semicircle 扇形 sector 环 ring 椭圆 ellipse 圆周 circumference 轨迹 locus, loca(pl.) 平行六面体 parallelepiped 立方体 cube 七面体 heptahedron 八面体 octahedron 九面体 enneahedron 十面体 decahedron 十一面体 hendecahedron 十二面体 dodecahedron 二

十面体 icosahedron 多面体 polyhedron 四面体 tetrahedron 五面体pentahedron 六面体hexahedron 菱形rhomb, rhombus, rhombi(pl.), diamond 正方形 square 梯形 trapezoid 直角梯形 right trapezoid 等腰梯形 isosceles trapezoid 五边形 pentagon 六边形 hexagon 七边形heptagon 八边形 octagon 九边形 enneagon 十边形 decagon 十一边

形hendecagon 十二边形dodecagon 多边形polygon 正多边形equilateral polygon 相位 phase 振幅 amplitude 内心 incentre(BrE), incenter(AmE) 外心 excentre(BrE), excenter(AmE) 旁心 escentre(BrE), escenter(AmE) 垂心orthocentre(BrE), orthocenter(AmE) 重心barycentre(BrE), barycenter(AmE) 内切圆 inscribed circle 外切圆circumcircle 方差variance 标准差root-mean-square deviation, standard deviation 百分点 percentage 百分位数 percentile 排列permutation 分布 distribution 正态分布 normal distribution 非正

态分布abnormal distribution 条形统计图bar graph 柱形统计图histogram 折线统计图 broken line graph 曲线统计图 curve diagram 扇形统计图pie diagram**** mutually disjoint events 互不相交事件mutually disjoint subsets 互不相交子集 mutually independent events 互

相独立事件

myria 万 myriad 无数的 multiplicity 重数 mid square method 平方取

中法 midperpendicular 中垂线 minor 子式 minor arc 劣弧 mixed number 带分数 regular convergence 正则收敛 relative discriminant 相对判别式relative error 相对误差 relative extremum 局部极值 ricci equatoin 李

奇恒等式ricci identity 李奇恒等式riemann function 黎曼函数riemann integral 黎曼积分 right direct product 右直积 right endpoint 右端点 right inner product 右内积 ring of integers 整数环 ring of matrices 矩阵环 root mean square error 均方根差 root of equation 方

程式的根 rotation of axes 坐标轴的旋转 rotation of co ordinate system 坐标轴的旋转 round off error 舍入规则 round up error 舍入规则 runge kutta method 龙格库塔法 n disk n维圆盘 nth member 第n项 nth partial quotient 第n偏商 nth power operation n次幂运算 nth root n

次根 nth term 第n项 n times continuously differentiable n次连续可

微的natural injection 自然单射natural isomorphism 自然等necessary and sufficient conditions 必要充分的条件necessary and sufficient statistic 必要充分统计量 neutral element 零元素 neutral line 中线 nonhomogeneous linear boundary value problem 非齐次线性边值

问题 nonhomogeneous linear differential equation 非齐次线性微分方程nonhomogeneous linear system of differential equations 非齐次线性微分

方程组interval algebra 区间代数 interval analysis 区间分析 interval closed at the right 右闭区间 interval estimation 区域估计 interval

function 区间函数 interval graph 区间图 interval of convergence 收敛区间 interval of definition 定义区间 interval topology 区间拓扑irreducible set 不可约集 irreducible r module 不可约r模 periodical decimal fraction 循环十进小数 pentad 拼五小组 pentadecagon 十五边形pentagon 五角形 pentagonal number 五角数 pentagonal pyramid 五角锥pentagram 五角星 pentahedron 五面体 pentaspherical coordinates 五球坐标 penalty method 补偿法 pascal distribution 帕斯卡分布 partition function 分折函数 partial differential equation of elliptic type 椭圆型偏微分方程 partial differential equation of first order 一阶偏微分方程 partial differential equation of hyperbolic type 双曲型偏微分方程 partial differential equation of mixed type 混合型偏微分方程partial differential equation of parabolic type 抛物型偏微分方程partial differential operator 偏微分算子parametric test 参数检验particular solution 特解parallelogram axiom 平行四边形公理orthogonality relation 正交关系 ordinary differential equation 常微分方程optimal value function 最优值函数opposite angles 对角opposite category 对偶范畴 one to one mapping 一一映射 onto mapping 满射 open mapping theorem 开映射定理 one to many mapping 一对多映射one sided limit 单侧极限 numerical solution of linear equations 线性方程组的数值解法 null set 空集 null solution 零解 third boundary condition 第三边界条件two sided neighborhood 双侧邻域unbiased estimating equation 无偏估计方程unbounded function 无界函数unbounded quantifier 无界量词uncertainty principle 测不准原理uncorrelated random variables 不相关随机变量 undetermined coefficient 末定系数 velocity distribution 速度分布 velocity optimal 速度最优的weak approximation theorem 弱逼近定理 weak completeness 弱完备性weak continuity 弱连续性 weak convergence 弱收敛 wiener measure 维纳测度word group 自由群 sample correlation coefficient 样本相关系数sample covariance 样本协方差schwarz inequality 施瓦尔兹不等式second boundary condition 诺伊曼边界条件second comparison test 第二比较检验second limit theorem 第二极限定理 self adjoint differential equation 自伴微分方程 semimajor axis 半长轴semiminor axis 半短轴 sentential calculus 命题演算 set of measure zero 零测度集 set topology 集论拓扑simple connectedness 单连通性slope function 斜率函数 solution curve 积分曲线 solution domain 解域solution set of equation 方程的解集spatial co ordinate 空间坐标specific address 绝对地址spherical bessel function 球贝塞耳函数 spherical cap 球冠 spherical coordinates 球极坐标 spherical curvature 球面曲率 spherical shell 球壳 spherical zone 球带spline function 样条函数spline interpolation 样条内插stability conditions 稳定条件 statistical hypothesis testing 统计假设检验strict inequality 严格不等式strict isotonicity 严格保序性strict isotony 严格保序性strict increasing 严格递增system of partial differential equations 偏微分方程组system of ordinary differential equations 常微分方程组system of linear homogeneous

equations 线性齐次方程组 system of linear inhomogeneous equations 线

性非齐次方程组system of inequalities 联立不等式system of polar

coordinates 极坐标系system of variational equations 变分方程组system with concentrated parameters 集中参数系统system with distributed

parameters 分布参数系统 t1topological space t1拓扑空间 t2topological

space t2拓扑空间 t3topological space 分离空间 t4topological space 正

则拓扑空间 t5 topological space 正规空间 t6topological space 遗传正

规空间 tangent cone 切线锥面 telegraph equation 电报方程 theorem for damping 阻尼定理****充分条件sufficient condition必要条件

necessary condition 充要条件sufficient and necessary condition……的

充要条件是……… if and only if …****abscissa 横坐标 alternating

series 交错级数 angle of the sector 扇形角 arbitrary constant 任意常

数 augmented matrix 增广矩阵 axis of parabola 拋物线的轴 axis of revolution 旋转轴 axis of rotation 旋转轴 binomial series 二项级数

binomial theorem 二项式定理 binomial distribution 二项分布 bisection

method 分半法;分半方法 bounded above 有上界的;上有界的 bounded

below 有下界的;下有界的bounded function 有界函数bounded

sequence 有界序列brace 大括号bracket 括号Cartesian coordinates 笛卡儿坐标 certain event 必然事件 circumcentre 外心;外

接圆心 circumcircle 外接圆 classical theory of probability 古典概率

论 cofactor 余因子; 余因式 common denominator 同分母;公分母 common

difference 公差 common divisor 公约数;公约 common logarithm 常用对

数 common multiple 公位数;公倍 common ratio 公比 commutative law 交换律 compasses 圆规 Cauchy-Schwarz inequality 柯西 - 许瓦尔兹不等式

central limit theorem 中心极限定理 centripedal acceleration 向心加速

度concave downward 凹向下的concurrent 共点concyclic 共圆

concyclic points 共圆点Euclidean geometry 欧几里德几何Euler's

formula 尤拉公式;欧拉公式 even function 偶函数 even number 偶数(2)博奕 Gaussian distribution 高斯分布 greatest term 最game (1)对策;

大项 greatest value 最大值 harmonic mean (1) 调和平均数; (2) 调和中

项 harmonic progression 调和级数 higher order derivative 高阶导数

improper fraction 假分数improper integral 广义积分; 非正常积分

implicit function 隐函数 incircle 内切圆 inclined plane 斜 included angle 夹角 indefinite integral 不定积分 initial condition 原始条件;初值条件 initial-value problem 初值问题 interior angles on the same side of the transversal 同旁内角interior opposite angle 内对角isosceles triangle 等腰三角形 iterate (1)迭代值; (2)迭代 Lagrange interpolating polynomial 拉格朗日插值多项代Laplace expansion 拉普拉斯展式 lemniscate 双纽线 left hand limit 左方极限 limiting case 极限情况limiting position 极限位置line of best-fit 最佳拟合line segment 线段 logarithmic equation 对数方程 mathematical analysis 数学分析mathematical induction 数学归纳法monotonic decreasing function 单调递减函数 monotonic convergence 单调收敛性 monotonic increasing function 单调递增函数multiple-angle formula 倍角公式

multiple root 多重根 mutually disjoint 互不相交 mutually exclusive events 互斥事件mutually independent 独立; 互相独立mutually perpendicular lines 互相垂直 numerical method 计算方法;数值法oblique cone 斜圆锥 orthogonal circles 正交圆 orthogonality 正交性oscillatory convergence 振动收敛性 ordinary differential equation 常微分方程pairwise mutually exclusive events 两两互斥事件place holder 补位数字 point of inflection (inflexion) 拐点; 转折点Pisson distribution 泊松分布point-slope form 点斜式polar coordinate plane 极坐标平面polynomial equation 多项式方程posterior probability 后验概率; 事后概率premultiply 前乘; 自左乘prime factor 质因子;质因素 prime number 素数;质数 principal angle 主角principal axis 主轴 principal value 主值 prior probability 先验概率; 事先概率 probability density function 概率密度函数 product and sum formula 和积互变公式 product sample space 积样本空间 product to sum formula 积化和差公式 proof by contradiction 反证法; 归谬法 proper fraction 真分数proper integral 正常积分proper subset 真子集propositional calculus 命题演算propositional inference 命题推演protractor 量角器Pythagoras' theorem 勾股定理Pythagorean triplet 毕氏三元数组 quadratic convergence 二阶收敛性 quadrature 求积法 quotient set 商集 radial component 沿径分量 radical axis 根轴range 值域;区域;范围;极差;分布域 rationalization 有理化 raw data 原始数据 rectifiable 可求长的 reciprocal 倒数 rectangular coordinate plane 直角坐标平面 recurrence formula 递推公式 reducibility 可约性; 可化简性 reflexive relation 自反关系 reference angle 参考 reference line 基准线 reflex angle 优角;反角 region of acceptance 接受区域region of convergency 收敛区域 region of rejection 否定区域 right circular cone 直立圆锥(体) resolution of vector 向量分解; 矢量分解right hand limit 右方极限 right prism 直立棱柱;直立角柱(体) right pyramid 直立棱锥;直立角锥(体) right-angled triangle 直角二角形scalene triangle 不等边三角形;不规则三角形 scatter diagram 散点图scientific notation 科学记数法semi-conjugate axis 半共轭轴semi-transverse axis 半贯轴semi-vertical angle 半顶角separable differential equation 可分微分方程septic equation 七次方程set square 三角尺;三角板 shaded portion 有阴影部分 significance level 显著性水平 significant figure 有效数字 similar triangles 相似三角形simple iteration method 简单迭代法simple pendulum 单摆Simpson's integral 森逊积分 standard deviation 标准差;标准偏离 standard normal distribution 标准正态分布; 标准常态分布 stationary point 平稳点; 逗留点; 驻点 strictly monotonic 严格单调 statistical chart 统计分析submultiple angle formula 半角公式subsidiary angle 辅助角substitution 代入; 代入法successive approximation 逐次逼近法successive derivative 逐次导数 successive differentiation 逐次微分法suffix 下标 sum to infinity 无限项之和 sum to product formula 和化积公式 superimposing 迭合 supplementary angle 补角 surjection 满射

symmetric relation 对称关系 tautology 恒真命题;恒真式 Taylor’s expansion 泰勒展开式 Taylor’s series 泰勒级数 Taylor’s theorem 泰勒定理 test criterion 检验标准 test of significance 显著性检验 to the nearest 至最接近之torque 转矩torus 环面transcendental function 超越函数 transformation of variable 变数转换 transitive 可传递的 transpose of matrix 倒置矩阵;转置矩阵 transversal 截 ;横截的 triangle law of addition 三角形加法 travel graph 行程图 tree diagram 树形图trapezoidal integral 梯形积分truncated Taylor’s series 截断泰勒级数 two-tailed test 双尾检验;只端检验 type I error I 型误差type II error II型误差unbiased estimator 无偏估计量undetermined coefficient 待定系数 unique solution 唯一解 vertical asymptote 垂直渐近线 vertically opposite angles 对顶角 without loss of generality 不失一般性****分子Numerator 分母Denominator 阿拉伯数字Hindu-Arabic numeral假分数Improper fraction 最大公因子Highest Common Factor (H.C.F.) 最小公倍数 Lowest Common Multiple (L.C.M.) 行列式 determinant****interval closed at the right 右闭区间 interval of convergence 收敛区间interval of definition 定义区间invariance theorem 不变性定理 invariant of an equation 方程的不变量 inverse circular function 反三角函数 inverse hyperbolic function 反双曲函数inversion formula 反演公式 isotonic injective mapping 保序单射映射jacobi identity 雅可比恒等式 jump point 跳跃点 law of double negation 双重否定律 law of inertia 惯性律law of large numbers 大数定律 leading ideal 猪想 liouville theorem 刘维尔定理 lipschitz condition 李普希茨条件 markov transform 马尔可夫变换 mathematical approximation 数学近似法 mathematical model 数学模型 maximum condition 极大条件 maximum deviation 最大偏差 mean square deviation 方差 mean square of error 误差的均方 meromorphic function 亚纯函数柱形统计图 histogram 折线统计图 broken line graph 曲线统计图 curve diagram 扇形统计图 pie diagram排列 permutatio内切圆 inscribed circle 外切圆 circumcircle正多边形 equilateral polygon metric space 度量空间 metric subspace 度量子空间method of runge kutta type 朗格库塔型的方法 method of steepest ascent 最速上升法 method of steepest descent 最速下降法method of finite elements 有限元法method of fractional steps 分步法method of exhaustion 穷竭法 method of approximation 近似法 method of artificial variables 人工变量法method of balayage 扫除法method of characteristic curves 特者法 method of comparison 比较法 method of conjugate gradients 共轭梯度法lateral area 侧面积 last multiplier 最后乘子large sample test 大样本检验lattice constant 点阵常数lattice design 格子设计method of difference 差分法method of elimination 消元法method of estimation 估计法meromorphic differential 亚纯微分 median 中位数 measuring rule 量尺 mean term 内项mean term 内项mean term 内项irreducibility criterion 不可约性判别准则irreducible polynomial 不可约多项式 irreducible generating set 不可约生成集 irregular divisor class 非正则因子类 irregular point 非正

则点irregular singular point 非正则奇点isometric circle 等距圆isometric embedding 等距嵌入isomorphic field 同构域isomorphic graph 同构图isomorphic group 同构群isomorphic image 同构象isothermal parameter 等温参数iterated function 叠函数iterated integral 累积分joint distribution 联合分布 jordan algebra 约当代数kernel of an integral equation 积分方程的核l'hospital rule 洛必达规则laboratory system of coordinates 实验室坐标系 labyrinth 迷宫lacation principle 介值定理lag correlation coefficient 滞后相关系数lag regression 落后回归laguerre differential equation 拉盖尔微分方程lame equation 拉梅方程language of formula 公式语言 laplace beltrami operator 拉普拉斯贝尔特拉米算子lateral area 侧面积 last multiplier 最后乘子large sample test 大样本检验lattice constant 点阵常数lattice design 格子设计 left adjoint 左伴随的 left derivative 左导数left differential 左微分 left direct product 左直积 left end point 左

端点 left length 左长 left limit value 左极限值left multiplication ring 左乘环length of curve 曲线的长 length of normal 法线的长 levi decomposition 列维分解 limes inferior 下极限 limes superior 上极限limit circle 极限圆 limit circle type 极限圆型logarithm to the base 10 常用对数logarithmic normal distribution 对数正态分布logic of relations 关系逻辑magic circle 幻圆magic cube 幻立方manifold without boundary 无边廖many valued mapping 多值映射marginal distribution density function 边缘分布密度函数 marginal distribution function 边缘分布函数mathematical programming 数学规划 mathematical random sample 数学随机样本 mathematical statistics 数理统计 maximum likelihood estimating function 极大似然估计量 independent variable 自

变量 dependent variable 应变量equiangular triangle 正三角形,等角

三角形命题proposition 差remainder 积product 除数divisor 商quotient 截尾truncation 未知数unknown, x-factor, y-factor, z-factor 阶乘 factorial 集合 aggregate 空集 void 子集 subset 交集 intersection 并集 union 补集 complement 映射 mapping 勾

股定理 Pythagorean theorem 菱形 rhomb, rhombus, rhombi(pl.), diamond 双曲线 hyperbola 抛物线 parabola topology of bounded convergence 有界收敛拓扑toroid 超环面 toroidal coordinates 圆环坐标trace of dyadic 并向量的迹transcendental integral function 超越整函数transformation formulas of the coordinates 坐标的变换公式 transformation to principal axes 轴变换 transversal lines 截线trapezoid method 梯形公式trefoil knot 三叶形纽结truth function 真值函项two sided test 双侧检定 two sided neighborhood 双侧邻域two sided surface 双侧曲面two termed expression 二项式ultrahyperbolic equation 超双曲型方程

数学专业英语

数学专业英语课后答案

2.1数学、方程与比例 词组翻译 1.数学分支branches of mathematics,算数arithmetics,几何学geometry,代数学algebra,三角学trigonometry,高等数学higher mathematics,初等数学elementary mathematics,高等代数higher algebra,数学分析mathematical analysis,函数论function theory,微分方程differential equation 2.命题proposition,公理axiom,公设postulate,定义definition,定理theorem,引理lemma,推论deduction 3.形form,数number,数字numeral,数值numerical value,图形figure,公式formula,符号notation(symbol),记法/记号sign,图表chart 4.概念conception,相等equality,成立/真true,不成立/不真untrue,等式equation,恒等式identity,条件等式equation of condition,项/术语term,集set,函数function,常数constant,方程equation,线性方程linear equation,二次方程quadratic equation 5.运算operation,加法addition,减法subtraction,乘法multiplication,除法division,证明proof,推理deduction,逻辑推理logical deduction 6.测量土地to measure land,推导定理to deduce theorems,指定的运算indicated operation,获得结论to obtain the conclusions,占据中心地位to occupy the centric place 汉译英 (1)数学来源于人类的社会实践,包括工农业的劳动,商业、军事和科学技术研究等活动。 Mathematics comes from man’s social practice, for example, industrial and agricultural production, commercial activities, military operations and scientific and technological researches. (2)如果没有运用数学,任何一个科学技术分支都不可能正常地发展。 No modern scientific and technological branches could be regularly developed without the application of mathematics. (3)符号在数学中起着非常重要的作用,它常用于表示概念和命题。 Notations are a special and powerful tool of mathematics and are used to express conceptions and propositions very often. (4)17 世纪之前,人们局限于初等数学,即几何、三角和代数,那时只考虑常数。Before 17th century, man confined himself to the elementary mathematics, i. e. , geometry, trigonometry and algebra, in which only the constants were considered. (5)方程与算数的等式不同在于它含有可以参加运算的未知量。 Equation is different from arithmetic identity in that it contains unknown quantity which can join operations. (6)方程又称为条件等式,因为其中的未知量通常只允许取某些特定的值。Equipment is called an equation of condition in that it is true only for certain values of unknown quantities in it. (7)方程很有用,可以用它来解决许多实际应用问题。

数学专业英语课文翻译(吴炯圻)第二章 2.

数学专业英语课文翻译(吴炯圻)第二 章 2. 数学专业英语3—A 符号指示集一组的概念如此广泛利用整个现代数学的认识是所需的所有大学生。集是通过集合中一种抽象方式的东西的数学家谈的一种手段。集,通常用大写字母:A、B、C、进程运行·、X、Y、Z ;小写字母指定元素:a、 b 的c、进程运行·,若x、y z.我们用特殊符号x∈S 意味着x 是S 的一个元素或属于美国的x如果x 不属于S,我们写xS.≠当方便时,我们应指定集的元素显示在括号内;例如,符号表示的积极甚至整数小于10 集{2,468} {2,,进程运行·} 作为显示的所有积极甚至整数集,而三个点等的发生。点的和等等的意思是清楚时,才使用。上市的大括号内的一组成员方法有时称为名册符号。涉及

到另一组的第一次基本概念是平等的集。DEFINITIONOFSETEQUALITY。两组A 和B,据说是平等的如果它们包含完全相同的元素,在这种情况下,我们写A = B。如果其中一套包含在另一个元素,我们说这些集是不平等,我们写 A = B。EXAMPLE1。根据对这一定义,于他们都是构成的这四个整数2,和8 两套{2,468} 和{2,864} 一律平等。因此,当我们用来描述一组的名册符号,元素的显示的顺序无关。动作。集{2,468} 和{2,2,4,4,6,8} 是平等的即使在第二组,每个元素 2 和 4 两次列出。这两组包含的四个要素2,468 和无他人;因此,定义要求我们称之为这些集平等。此示例显示了我们也不坚持名册符号中列出的对象是不同。类似的例子是一组在密西西比州,其值等于{M、我、s、p} 一组单词中的字母,组成四个不同字母M、我、s 和体育3 —B 子集S.从给定的集S,我们

数学专业英语第二版-课文翻译-converted

2.4 整数、有理数与实数 4-A Integers and rational numbers There exist certain subsets of R which are distinguished because they have special properties not shared by all real numbers. In this section we shall discuss such subsets, the integers and the rational numbers. 有一些R 的子集很著名,因为他们具有实数所不具备的特殊性质。在本节我们将讨论这样的子集,整数集和有理数集。 To introduce the positive integers we begin with the number 1, whose existence is guaranteed by Axiom 4. The number 1+1 is denoted by 2, the number 2+1 by 3, and so on. The numbers 1,2,3,…, obtained in this way by repeated addition of 1 are all positive, and they are called the positive integers. 我们从数字 1 开始介绍正整数,公理 4 保证了 1 的存在性。1+1 用2 表示,2+1 用3 表示,以此类推,由 1 重复累加的方式得到的数字 1,2,3,…都是正的,它们被叫做正整数。 Strictly speaking, this description of the positive integers is not entirely complete because we have not explained in detail what we mean by the expressions “and so on”, or “repeated addition of 1”. 严格地说,这种关于正整数的描述是不完整的,因为我们没有详细解释“等等”或者“1的重复累加”的含义。 Although the intuitive meaning of expressions may seem clear, in careful treatment of the real-number system it is necessary to give a more precise definition of the positive integers. There are many ways to do this. One convenient method is to introduce first the notion of an inductive set. 虽然这些说法的直观意思似乎是清楚的,但是在认真处理实数系统时必须给出一个更准确的关于正整数的定义。有很多种方式来给出这个定义,一个简便的方法是先引进归纳集的概念。 DEFINITION OF AN INDUCTIVE SET. A set of real number s is cal led an i n ductiv e set if it has the following two properties: (a) The number 1 is in the set. (b) For every x in the set, the number x+1 is also in the set. For example, R is an inductive set. So is the set . Now we shall define the positive integers to be those real numbers which belong to every inductive set. 现在我们来定义正整数,就是属于每一个归纳集的实数。 Let P d enote t he s et o f a ll p ositive i ntegers. T hen P i s i tself a n i nductive set b ecause (a) i t contains 1, a nd (b) i t c ontains x+1 w henever i t c ontains x. Since the m embers o f P b elong t o e very inductive s et, w e r efer t o P a s t he s mallest i nductive set. 用 P 表示所有正整数的集合。那么 P 本身是一个归纳集,因为其中含 1,满足(a);只要包含x 就包含x+1, 满足(b)。由于 P 中的元素属于每一个归纳集,因此 P 是最小的归纳集。 This property of P forms the logical basis for a type of reasoning that mathematicians call proof by induction, a detailed discussion of which is given in Part 4 of this introduction.

数学专业英语(Doc版).10

学专业英语-How to Write Mathematics? How to Write Mathematics? ------ Honesty is the Best Policy The purpose of using good mathematical language is, of course, to make the u nderstanding of the subject easy for the reader, and perhaps even pleasant. The style should be good not in the sense of flashy brilliance, but good in the se nse of perfect unobtrusiveness. The purpose is to smooth the reader’s wanted, not pedantry; understanding, not fuss. The emphasis in the preceding paragraph, while perhaps necessary, might see m to point in an undesirable direction, and I hasten to correct a possible misin terpretation. While avoiding pedantry and fuss, I do not want to avoid rigor an d precision; I believe that these aims are reconcilable. I do not mean to advise a young author to be very so slightly but very very cleverly dishonest and to gloss over difficulties. Sometimes, for instance, there may be no better way t o get a result than a cumbersome computation. In that case it is the author’s duty to carry it out, in public; the he can do to alleviate it is to extend his s ympathy to the reader by some phrase such as “unfortunately the only known proof is the following cumbersome computation.” Here is the sort of the thing I mean by less than complete honesty. At a certa in point, having proudly proved a proposition P, you feel moved to say: “Not e, however, that p does not imply q”, and then, thinking that you’ve done a good expository job, go happily on to other things. Your motives may be per fectly pure, but the reader may feel cheated just the same. If he knew all abo ut the subject, he wouldn’t be reading you; for him the nonimplication is, qui te likely, unsupported. Is it obvious? (Say so.) Will a counterexample be suppl ied later? (Promise it now.) Is it a standard present purposes irrelevant part of the literature? (Give a reference.) Or, horrible dictum, do you merely mean th at you have tried to derive q from p, you failed, and you don’t in fact know whether p implies q? (Confess immediately.) any event: take the reader into y our confidence. There is nothing wrong with often derided “obvious”and “easy to see”, b ut there are certain minimal rules to their use. Surely when you wrote that so mething was obvious, you thought it was. When, a month, or two months, or six months later, you picked up the manuscript and re-read it, did you still thi nk that something was obvious? (A few months’ripening always improves ma nuscripts.) When you explained it to a friend, or to a seminar, was the someth ing at issue accepted as obvious? (Or did someone question it and subside, mu ttering, when you reassured him? Did your assurance demonstration or intimida

数学专业英语第二版的课文翻译

1-A What is mathematics Mathematics comes from man’s social practice, for example, industrial and agricultural production, commercial activities, military operations and scientific and technological researches. And in turn, mathematics serves the practice and plays a great role in all fields. No modern scientific and technological branches could be regularly developed without the application of mathematics. 数学来源于人类的社会实践,比如工农业生产,商业活动,军事行动和科学技术研究。反过来,数学服务于实践,并在各个领域中起着非常重要的作用。没有应用数学,任何一个现在的科技的分支都不能正常发展。From the early need of man came the concepts of numbers and forms. Then, geometry developed out of problems of measuring land , and trigonometry came from problems of surveying . To deal with some more complex practical problems, man established and then solved equation with unknown numbers ,thus algebra occurred. Before 17th century, man confined himself to the elementary mathematics, . , geometry, trigonometry and algebra, in which only the constants are considered. 很早的时候,人类的需要产生了数和形式的概念,接着,测量土地的需要形成了几何,出于测量的需要产生了三角几何,为了处理更复杂的实际问题,人类建立和解决了带未知参数的方程,从而产生了代数学,17世纪前,人类局限于只考虑常数的初等数学,即几何,三角几何和代数。The rapid development of industry in 17th century promoted the progress of economics and technology and required dealing with variable quantities. The leap from constants to variable quantities brought about two new branches of mathematics----analytic geometry and calculus, which belong to the higher mathematics. Now there are many branches in higher mathematics, among which are mathematical analysis, higher algebra, differential equations, function theory and so on. 17世纪工业的快速发展推动了经济技术的进步,从而遇到需要处理变量的问题,从常数带变量的跳跃产生了两个新的数学分支-----解析几何和微积分,他们都属于高等数学,现在高等数学里面有很多分支,其中有数学分析,高等代数,微分方程,函数论等。Mathematicians study conceptions and propositions, Axioms, postulates, definitions and theorems are all propositions. Notations are a special and powerful

数学专业英语

第二章精读课文-- 入门必修 2.1 数学方程与比例 (Mathematics,Equation and Ratio) 一、词汇及短语: 1. Cha nge the terms about变形 2. full of :有许多的充满的 例The StreetS are full of people as on a holiday像假日一样,街上行人川流不息) 3. in groups of ten?? 4. match SOmething against sb. “匹配” 例Long ago ,when people had to Count many things ,they matChed them against their fingers. 古时候,当人们必须数东西时,在那些东西和自己的手指之间配对。 5. grow out of 源于由…引起 例Many close friendships grew out of common acquaintance 6. arrive at 得出(到达抵达达到达成) 例We both arrived at the Same COnclusion我们俩个得出了相同的结论) 7. stand for “表示,代表” 8. in turn “反过来,依次” 9. bring about 发生导致造成 10. arise out of 引起起源于 11. express by “用…表示” 12. occur 发生,产生 13. come from 来源于,起源于 14. resulting method 推论法 15. be equal to 等于的相等的

数学专业英语第二版2.2课文翻译

2.2 A 为什么要研究几何? 我们为什么研究几何?开始此文本研究的学生也许会问,"什么是几何。什么可以预料从这项研究获得?" 许多居于领导地位的学术机构承认,所有学习这个数学分支的人都将得到确实的收益,许多学校把几何的学习作为入学考试的先决条件,从这一点上可以证明。 几何学起源于很久以前巴比伦人和埃及人测量他们被尼罗河洪水淹没的土地,希腊语几何来源于geo ,意思是“土地”,和metron, 意思是"度量值"。早在公元前2000 年,我们发现这些民族的土地测量者利用几何知识重新确定消失了的土地标志和边界。 几何是研究由线所组成的图形的科学。几何的学习是成功工程师、科学家、建筑师和制图员培训的重要部分。木匠、机械师、采石者、艺术家和设计师在他们的职业中都应用几何的知识。在这门课程中,学生将学到大量几何图形,例如线条、角、三角形、圆和许多种设计和模式。 所得的几何研究的最重要的目标之一是使学生在他的听力、阅读和思维更审慎。学习几何他远离盲目接受语句和思想的实践领导和教想清楚与批判前形成的结论。学习几何使他被领导远离语句和思想的盲目接受的做法,教导形成结论之前,考虑清楚和审慎。(学生通过几何的学习而达到的最重要目标是:在听,读,和思考时变得更加审慎。在学习几何的过程中,他们不再盲目地接受一些陈述和思想,而是在得出结论之前学会了清楚和审慎的思考。) 学习几何的学生可以获得许多其他不太直接的利益。这些人当中必须包括训练英语的精确使用和分析新情况与新问题时直达基本要素,以及利用毅力、创意和逻辑推理来解决问题的能力。(这些人当中必须包括训练英语的精确使用和分析新情况与新问题时直达基本要素的能力,以及利用毅力、创意和逻辑推理来解决问题。)大自然的创作将作为一种几何研究的副产品。一种鉴赏能力属于几何形成的规律和审美在人们的作品中。学生也应该发展数学与我们的文化和文明数学家贡献的意识。 2.2B 一些几何术语 1.立体和平面。立体是一个三维图形。立体的常见示例是立方体、球体、柱体、圆锥和棱锥。立方体有光滑、平整的六个面。这些面被称为平面曲面,或简称平面。平面曲面是二维的,有长度和宽度。黑板或桌面的表面都是平面曲面的一个例子。 2、线条和线段。我们都很熟悉线,但很难定义这术语。一条线可由在一张纸上移动的钢笔或铅笔标记表示。一条线,可以被看做是一维的,即只有长度。尽管我们绘制一条直线时会赋予它宽度和厚度,但是当考虑线时,只考虑痕迹的长度。点没有长度、宽度和厚度,但标记了一个位置。我们熟悉铅笔尖,针尖这样的表达。我们可以用一个小圆点来表示一个点,在它旁边用打印体大写字母来命名,如图2-2-1中的点A。 直线用大写字母标志它上面的两个点或者旁边的一个小写字母来命名。图2-2-2 的直线是读"直线AB "或者“直线l"。直线向两个方向无限延伸,没有终点。线上两点间的部分被称为一条直线段。直线段用两个端点命名。因此,图2-2-2,我们称为AB 是线l 的一条直线段。当不引起混淆时,表达"直线段AB 通常被线段AB代替,或者简称直线AB。 有三种线:直线、折线和曲线。弯曲的线条或,简单地说,曲线是指其中没有任何部分是直的折线是由连起来的直线段构成,如图2-2-3的ABCDE。 3.圆的部分。平面上的闭曲线当其中每点到一个固定点的距离均相当时叫做圆。固定点称为圆心。图2-2-4,O 是ABC 中心,或简单的O.A连接圆心到圆周上点的直线段称为圆的半径。OA,OB,以及OC都是圆O的半径。经过圆心并且两个端点在圆周上的直线段被称为圆的直径。直径等于两个半径。连接圆周上两点的任意直线段被称为弦。图2-2-4 圆的弦是ED。 从这个定义很明显直径是弦。圆周的任何部分都是一条弧线,如弧AE,其中由AE 表示。

数学专业英语(Doc版).12

数学专业英语-Linear Programming Linear Programming is a relatively new branch of mathematics.The cornerstone of this exciting field was laid independently bu Leonid V. Kantorovich,a Russ ian mathematician,and by Tjalling C,Koopmans, a Yale economist,and George D. Dantzig,a Stanford mathematician. Kantorovich’s pioneering work was moti vated by a production-scheduling problem suggested by the Central Laboratory of the Leningrad Plywood Trust in the late 1930’s. The development in the U nited States was influenced by the scientific need in World War II to solve lo gistic military problems, such as deploying aircraft and submarines at strategic positions and airlifting supplies and personnel. The following is a typical linear programming problem: A manufacturing company makes two types of television sets: one is black and white and the other is color. The company has resources to make at most 30 0 sets a week. It takes $180 to make a black and white set and $270 to mak e a color set. The company does not want to spend more than $64,800 a wee k to make television sets. I f they make a profit of $170 per black and white set and $225 per color set, how many sets of each type should the company make to have a maximum profit? This problem is discussed in detail in Supplementary Reading Material Lesson 14. Since mathematical models in linear programming problems consist of linear in equalities, the next section is devoted to such inequalities. Recall that the linear equation lx+my+n=0represents a straight line in a plane. Every solution (x,y) of the equation lx+my+n=0is a point on this line, and vice versa. An inequality that is obtained from the linear equation lx+my+n=0by replacin g the equality sign “=”by an inequality sign < (less than), ≤(less than or equal to), > (greater than), or ≥(greater than or equal to) is called a linear i nequality in two variables x and y. Thus lx+my+n≤0, lx+my+n≥0are all lin ear liequalities. A solution of a linear inequality is an ordered pair (x,y) of nu mbers x and y for which the inequality is true. EXAMPLE 1 Graph the solution set of the pair of inequalities SOLUTION Let A be the solution set of the inequality x+y-7≤0 and B be th at of the inequality x-3y +6 ≥0 .Then A∩B is the solution set of the given pair of inequalities. Set A is represented by the region shaded with horizontal lines and set B by the region shaded with vertical lines in Fig.1. Therefore the

数学专业英语

MATHS ENGLISH absolute value 绝对值 acceptable region 接受域 additivity 可加性alternative hypothesis 对立假设 analysis of covariance 协方差分析analysis of variance 方差分析 arithmetic mean 算术平均值 association 相关性 assumption checking 假设检验 availability 有效度 band 带宽bar chart 条形图 beta-distribution 贝塔分布 between groups 组间的binomial distribution 二项分布binomial test 二项检验center of gravity 重心 central tendency 中心趋势 hi-square distribution 卡方分布 chi-square test 卡方检验 classify 分类 cluster analysis 聚类分析coefficient 系数 coefficient of correlation 相关系数 collinearity 共线性 components 构成,分量 compound 复合的 confidence interval 置信区间consistency 一致性continuous variable 连续变量control charts 控制图 correlation 相关 covariance 协方差 covariance matrix 协方差矩阵 critical point 临界点 critical value 临界值 cross tab 列联表 cubic term 三次项 cumulative distribution function 累加分布函数curve estimation 曲线估计 default 默认的 deleted residual 剔除残差density function 密度函数dependent variable 因变量design of experiment 试验设计 df.(degree of freedom) 自由度 diagnostic 诊断discrete variable 离散变量discriminant function 判别函数discriminatory analysis 判别分析 D-optimal design D-优化设计 effects of interaction 交互效应eigenvalue 特征值equal size 等含量estimation of parameters 参数估计 estimations 估计量 exact value 精确值 expected value 期望值 exponential指数的 exponential distribution 指数分布 extreme value 极值 factor analysis 因子分析 factor score 因子得分 factorial designs 析因设计 factorial experiment 析因试验fitted line 拟合线fitted value 拟合值fixed variable 固定变量fractional factorial design 部分析因设计 F-test F检验 full factorial design 完全析因设计 gamma distribution 伽玛分布 geometric mean 几何均值 harmonic mean 调和均值 heterogeneity 不齐性 histogram 直方图homogeneity 齐性homogeneity of variance 方差齐性 hypothesis test 假设检验independence独立independent variable 自变量independent-samples 独立样本index of correlation 相关指数interclass correlation 组内相关 interval estimate 区间估计inverse 倒数的iterate 迭代kurtosis 峰度large sample problem 大样本问题least-significant difference 最小显著差数 least-square estimation 最小二乘估计 least-square method 最小二乘法 level of significance 显著性水平 leverage value 中心化杠杆值 life test 寿命试验likelihood function 似然函数 likelihood ratio test 似然比检验 linear estimator 线性估计linear model 线性模型 linear regression 线性回归 linear relation 线性关系 linear term 线性项 logarithmic 对数的 logarithms 对数 lost function 损失函数 main effect 主效应matrix 矩阵 maximum 最大值maximum likelihood estimation 极大似然估计mean squared deviation(MSD) 均方差 mean sum of square 均方和 measure 衡量 media

数学专业英语

学号:10901040201 姓名:曹菁 lg LinearA ebra Non-trivial linear combination. This is a contradiction and proves 1).Part 2) follows from 1) because dim(V)=n. Exercise Let A=0110?? ?-?? ()2R ∈. Find an invertible 2C C ∈ such that 1 c AC - is diagonal. Show that C cannot be selected in 2R .Find the characteristic polynomial of A . Exercise Suppose V is a 3-dimensional vector space and :f V V → is an endomorphism with ()()3 f CP x x λ=-.Show that ()f I λ- has characteristic polynomial and is thus a nilpotent endomorphism. Show there is a basis for V so that the matrix representing is 001001λλλ?? ? ? ??? ,001000λλλ?? ? ? ???or.000000λλλ?? ? ? ??? . We could continue and finally give an ad hoc proof of the Jordan canonical form,but in this chapter we prefer to press on to inner product spaces.The Jordan form will be developed in Chapter 6 as of the general theory of finitely generated modules over Euclidean domains.The next section is included only as a convenient reference. This section should be just skimmed or omitted entirely.It is unnecessary for the rest of this chapter,and is not properly part of the flow of the chapter.The basic facts of Jordan form are summarized here simply for reference. The statement that a square matrix B over a field F is a Jordanblock means that F λ?∈ Such that B is a lower triangular matrix of the form 0101B λλ λ?? ? ? ?= ? ? ??? .B gives a homomorphism :m m g F F →with ()m m g e e λ= and ()1i i i e e e λ+=+ for 1i m ≤<.Note that ()()m B CP x x m =-and so λ is the only eigenvalue of B ,and B satisfies its characteristic polynomial,i.e.,()0B CP B =. Definition A matrix n D F ∈ is in Jordan if ?Jordan blocks i ni B F ∈ such that

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