数学专业英语(1)
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 equation2.命题proposition，公理axiom，公设postulate，定义definition，定理theorem，引理lemma，推论deduction3.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chart4.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 equation5.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 deduction6.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。
数学专业英语词汇英汉对照
1 概率论与数理统计词汇英汉对照表A absolute value 绝对值accept 接受acceptable region 接受域additivity 可加性adjusted 调整的alternative hypothesis 对立假设analysis 分析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 假设assumption checking 假设检验availability 有效度average 均值B balanced 平衡的band 带宽bar chart 条形图beta-distribution 贝塔分布between groups 组间的bias 偏倚binomial distribution 二项分布binomial test 二项检验C calculate 计算case 个案category 类别center of gravity 重心central tendency 中心趋势chi-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column 列compare 比较comparison 对照components 构成，分量compound 复合的confidence interval 置信区间consistency 一致性constant 常数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crosstab 列联表cubic 三次的，立方的cubic term 三次项cumulative distribution function 累加分布函数curve estimation 曲线估计D data 数据default 默认的definition 定义deleted residual 剔除残差density function 密度函数dependent variable 因变量description 描述design of experiment 试验设计deviations 差异df.（degree of freedom）自由度diagnostic 诊断dimension 维discrete variable 离散变量discriminant function 判别函数discriminatory analysis 判别分析distance 距离distribution 分布D-optimal design D-优化设计E eaqual 相等effects of interaction 交互效应efficiency 有效性eigenvalue 特征值equal size 等含量equation 方程error 误差estimate 估计estimation of parameters 参数估计estimations 估计量evaluate 衡量exact value 精确值expectation 期望expected value 期望值exponential 指数的exponential distributon 指数分布extreme value 极值F factor 因素，因子factor analysis 因子分析factor score 因子得分factorial designs 析因设计factorial experiment 析因试验fit 拟合fitted line 拟合线fitted value 拟合值fixed model 固定模型fixed variable 固定变量fractional factorial design 部分析因设计frequency 频数F-test F检验full factorial design 完全析因设计function 函数G gamma distribution 伽玛分布geometric mean 几何均值group 组H harmomic mean 调和均值heterogeneity 不齐性histogram 直方图homogeneity 齐性homogeneity of variance 方差齐性hypothesis 假设hypothesis test 假设检验I independence 独立independent variable 自变量independent-samples 独立样本index 指数index of correlation 相关指数interaction 交互作用interclass correlation 组内相关interval estimate 区间估计intraclass correlation 组间相关inverse 倒数的iterate 迭代K kernal 核Kolmogorov-Smirnov test柯尔莫哥洛夫-斯米诺夫检验kurtosis 峰度L large sample problem 大样本问题layer 层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 水平level of significance 显著性水平leverage value 中心化杠杆值life 寿命life test 寿命试验likelihood function 似然函数likelihood ratio test 似然比检验linear 线性的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logistic 逻辑的lost function 损失函数M 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model 模型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N negative relationship 负相关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O 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 排序order statistics 次序统计量origin 原点orthogonal 正交的outliers 异常值P paired observations 成对观测数据paired-sample 成对样本parameter 参数parameter estimation 参数估计partial correlation 偏相关partial correlation coefficient 偏相关系数partial regression coefficient 偏回归系数percent 百分数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predict 预测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probit analysis 概率分析proportion 比例Q qadratic 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，度量的quartiles 四分位数R random 随机的random number 随机数random number 随机数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 秩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reject 拒绝rejection region 拒绝域relationship 关系reliability 可靠性repeated 重复的report 报告，报表residual 残差residual sum of squares 剩余平方和response 响应risk function 风险函数robustness 稳健性root mean square 标准差row 行run 游程run test 游程检验S sample 样本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separately 单独地sets 集合sign test 符号检验significance 显著性significance level 显著性水平significance testing 显著性检验significant 显著的，有效的significant digits 有效数字skewed distribution 偏态分布skewness 偏度small sample problem 小样本问题smooth 平滑sort 排序soruces of variation 方差来源space 空间spread 扩展square 平方standard deviation 标准离差standard error of mean 均值的标准误差standardization 标准化standardize 标准化statistic 统计量statistical quality control 统计质量控制std. residual 标准残差stepwise regression analysis 逐步回归stimulus 刺激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 和sum of squares 平方和summary 概括，综述T table 表t-distribution t分布test 检验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total 总共，和transformation 转换treatment 处理trimmed mean 截尾均值true value 真值t-test t检验two-tailed test 双侧检验U unbalanced 不平衡的unbiased estimation 无偏估计unbiasedness 无偏性uniform distribution 均匀分布V value of estimator 估计值variable 变量variance 方差variance components 方差分量variance ratio 方差比various 不同的vector 向量W weight 加权，权重weighted average 加权平均值within groups 组内的Z Z score Z分数2. 最优化方法词汇英汉对照表A 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B bandwidth 带宽be equivalent to 等价于best-fit 最佳拟合bound 边界C coefficient 系数complex-value 复数值component 分量constant 常数constrained 有约束的constraint 约束constraint function 约束函数continuous 连续的converge 收敛cubic polynomial interpolation method 三次多项式插值法curve-fitting 曲线拟合D data-fitting 数据拟合default 默认的，默认的define 定义diagonal 对角的direct search method 直接搜索法direction of search 搜索方向discontinuous 不连续E eigenvalue 特征值empty matrix 空矩阵equality 等式exceeded 溢出的F feasible 可行的feasible solution 可行解finite-difference 有限差分first-order 一阶G Gauss-Newton method 高斯-牛顿法goal attainment problem 目标达到问题gradient 梯度gradient method 梯度法Hhandle 句柄Hessian matrix 海色矩阵I independent variables 独立变量inequality 不等式infeasibility 不可行性infeasible 不可行的initial feasible solution 初始可行解initialize 初始化inverse 逆invoke 激活iteration 迭代iteration 迭代J Jacobian 雅可比矩阵L 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 线性的linear equality constraints 线性等式约束linear programming problem 线性规划问题local solution 局部解M medium-scale 中型的minimize 最小化mixed quadratic and cubic polynomial interpolation and extrapolation method 混合二次、三次多项式内插、外插法multiobjective 多目标的N nonlinear 非线性的norm 范数O objective function 目标函数observed data 测量数据optimization routine 优化过程optimize 优化optimizer 求解器over-determined system 超定系统P parameter 参数partial derivatives 偏导数polynomial interpolation method多项式插值法Q quadratic 二次的quadratic interpolation method 二次内插法quadratic programming 二次规划R real-value 实数值residuals 残差robust 稳健的robustness 稳健性，鲁棒性S 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solution 解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sum-of-squares 平方和symmetric matrix 对称矩阵T 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U unconstrained 无约束的under-determined system 负定系统V variable 变量vector 矢量W weighting matrix 加权矩阵3 样条词汇英汉对照表A approximation 逼近array 数组a spline in b-form/b-spline b样条a spline of polynomial piece /ppform spline 分段多项式样条B bivariate spline function 二元样条函数break/breaks 断点C 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D degree of freedom 自由度dimension 维数E end conditions 约束条件I input argument 输入参数interpolation 插值/内插interval 取值区间K knot/knots 节点L least-squares approximation 最小二乘拟合M multiplicity 重次multivariate function 多元函数O optional argument 可选参数order 阶次output argument 输出参数P point/points 数据点R rational spline 有理样条rounding error 舍入误差（相对误差）S scalar 标量sequence 数列（数组）spline 样条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T tolerance 允许精度U univariate function 一元函数V vector 向量W weight/weights 权重4 偏微分方程数值解词汇英汉对照表A absolute error 绝对误差absolute tolerance 绝对容限adaptive mesh 适应性网格B boundary condition 边界条件C contour plot 等值线图converge 收敛coordinate 坐标系D decomposed 分解的decomposed geometry matrix 分解几何矩阵diagonal matrix 对角矩阵Dirichlet boundary conditionsDirichlet边界条件E eigenvalue 特征值elliptic 椭圆形的error estimate 误差估计exact solution 精确解G generalized Neumann boundary condition 推广的Neumann边界条件geometry 几何形状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H hyperbolic 双曲线的I initial mesh 初始网格J jiggle 微调L Lagrange multipliers 拉格朗日乘子Laplace equation 拉普拉斯方程linear interpolation 线性插值loop 循环M machine precision 机器精度mixed boundary condition 混合边界条件N 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P 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Q quality 质量R refined triangular mesh 加密的三角形网格relative tolerance 相对容限relative tolerance 相对容限residual 残差residual norm 残差范数S singular 奇异的。
数学专业英语
vt.表明，标示，指示; 象征，暗示，预 示; [医]显示需要做…的治疗;
numerical[英][nju:ˈmerɪkl][美][nu:ˈmerɪkl]
adj.数字的，用数字表示的，数值的;
root[英][ru:t][美][rut, rʊt]
n.根，根源; 原因，本质; 祖先; [乐]和弦基音; vt.使生根; 使固定; 根源在于; 欢呼，喝彩; vi.生根; 根除;
n.身份; [逻]同一性; 个性; [数]恒等（式）;
arithmetic[英][əˈrɪθmətɪk][美][əˈrɪθmɪtɪk]
n.算术，计算; 算法;
algebraic[英][ˌældʒɪ'breɪɪk][美][ˌældʒəˈbreɪk]
adj.代数的，关于代数学的;
indicate[英][ˈɪndɪkeɪt][美][ˈɪndɪˌket]
你拿这个或那个都可以。
1. either…or…连接两个成分作主语时，谓语动 词通常与其靠近的主语保持一致。如： Either you or I am to go. 你或我必须有人去。 但在非正式文体中，有时也会一律用复数谓 语。如：If either David or Janet come, they will want a drink.
prep.在...的附近; 在...的周围
解方程意味着求未知项的值，为了求未知项的值，当 然，我们必须移项，直到未知项单独在方程的一边， 令其等于方程的另一边，求得未知项的值，这样我们 就解决了问题。
on one side…on the other side…一方面……另一方面……
脑筋急转弯：
Two little brother,One lives on one side,The other on the other side,They hear what you say But they do not see each other,Who are they?
数学专业英语1
数学专业英语1学专业英语－How to Write Mathematics?How to Write Mathematics?------ Honesty is the Best PolicyThe 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 comp utation.”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 expositor y 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 thenonimplication 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, a nd 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 tion?) the obvious answers to these rhetorical questions are among the rules th at should control the use of “obvious”. There is the most frequent source o f mathematical error: make that the “obvious”is true.It should go without saying that you are not setting out to hide facts from the reader: you are writing to uncover them. What I am saying now is that you should not hide the status of your statements and your attitude toward them eit her. Whenever you tell him something, tell him where it stands: this has been proved, that hasn’t, this will be proved, that won’t. Emphasize the importan t and minimize the trivial. The reason saying that they are obvious is to put t hem in proper perspecti e for the uninitiated. Even if your saying so makes an occasional readerangry at you, a good purpose is served by your telling him how you view the matter. But, of course, you must obey the rules. Don’t le t the reader down; he wants to believe in you. Pretentiousness, bluff, and conc ealment may not get caught out immediately, but most readers will soon sense that there is something wrong, and they will blame neither the facts nor them selves, but quite properly, the author. Complete honesty makes for greatest clar ity.---------Paul R.Haqlmosvocabularyflashy 一闪的 counter-example 反例unobtrusiveness 谦虚dictum 断言；格言forestall 阻止，先下手deride嘲弄anticipate 预见 subside沉静pedantry 迂腐；卖弄学问 mutter出怨言，喃喃自语fuss 小题大做 intimidation威下reconcilable 使一致的 rhetorical合符修辞学的gloss 掩饰 pretentiousness自命不凡alleviate 减轻，缓和bluff 欺骗implication 包含，含意concealment隐匿notes1. 本课文选自美国数学学会出版的小册子How to write mathematics 中Paul R.Halmos. 的文章第9节2. The purpose is smooth the reader’way, to anticipates his difficulties and to forestall them. Clarit y is what’s wanted, not pedantry; understanding, not fuss.意思是：目的是为读者扫清阅读上的障碍，即预先设想读者会遇到什么困难，并力求避免出现这类困难。
数学专业英语第一章
特点二：科学内容的完整性与表达形式的精 炼性要求
1、长句较多 2、非限定动词使用频率高
Eg1: By introducing a new smoothing function, the problem is approximated by a family of parameterized optimization problems with twice continuously differentiable objective functions.
3、能用英语书写文章摘要、学术会议通知、 学术交流信件等。同时培养简单的英语会 话能力。 4、为部分优秀学生攻读研究生奠定数学专 业英语的基础，同时让大部分同学了解数 学专业英语与生活英语的区别，为今后走 上工作岗位，特别是服务于IT业或外资企 业有独当一面的能力。
本课程分四部分讲解：
精选课文：1、理解数学专业文章和一般英语文章写作的不同；
对于学习数学的学生和准备从事数学研究的人员在掌握了公共英语的基本知识的基础上如果希望较快地掌握阅读英文版数学教程和科研资料的基本方法进一步学习数学专业英语是必须的
数学专业英语 第一讲
为什么要学习数学专业英语？
❖ 数学学科发展需要：20世纪90年代计算机科学技术 的迅速发展宣告了人类信息时代的到来。数学，这 个古老而又优雅的学科获得了新的发展动力和发挥 作用的舞台。
Eg2: A right angle is a 90 angle. 见P31
2. 被动语态出现频率高，应用范围广
Eg1:The Fermat Conjecture has been proved to be true.
Eg2: The function idea may be illustrated schematically in many ways. 见P54
1-1 数学专业英语的基本特点
译文： 因为 h(x) 在某个邻域 B(a, r) 内调和 , 故 h( x ) d ( x ) h( a ) 。
B
这里“we have”并不强调“我们有”什么，而是说明“可以得出” 什么结论，可以换为“one has”或者省略而不影响原意。
特点二：科学内容的完整性与表达形式的精练性要求 • 数学结论的成立都是有条件的，推导都有充分根
完成时。
7
如：
Definition. Let y = f(x) be a function and suppose that a is in the domain of f. A line L containing (a, f(a)) is a tangent line to f at x = a if the slope of L is the limit
well as the domain over which the integration is performed has been generalized. 19世纪初，出现了一些更复杂的积分概念，这些概念是通过推
广被积函数和积分区域而得到。
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In general, the integrand may be a function of more than one
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例：Now we investigate whether the functions are integrable and why they are integrable or not. 现在，我们来研究这些函数是否可积及它们可积或不可积的原因 改：Now we investigate the integrability of the function. 名词化结构integrability of the functions代替了whether和why 引起的从句，不仅使句子简洁，而且显得专业性更强。 例： Television is the transmission and reception of images of moving objects by radio waves. 电视通过无线电波发射和接受活动物体的图象。 the transmission and reception of images of moving objects by radio waves 名词化结构
数学专业英语(Doc版).15
数学专业英语－Notations and Abbreviations (I) Learn to understand N set of natural numbersZ set of integersR set of real numbersC set of complex numbers+ plus; positive－minus; negative×multiplied by; times÷divided by＝equals; is equal to≡identically equal to≈,≌approximately equal to＞greater than≥greater than or equal to＜less than≤less than or equal to》much greater than《much less thansquare rootcube rootnth root│a│ absolute value of an! n factoriala to the power n ; the nth power of a[a] the greatest integer≤athe reciprocal of aLet A, B be sets∈ belongs to ; be a member ofnot belongs tox∈A x os amember of A∪ unionA∪B A union B∩ intersectionA∩B A intersection BA B A is a subset of B;A is contained in B A B A contains Bcomplement of Athe closure of Aempty set( ) i=1,2,…,r j=1,2,…,s r-by-s（r×s）matrix││I,j=1,2,…,n determinant of order ndet( ) the determinant of the matrix ( )vector Fx=( , ,…, ) x is an n-tuple of‖‖the norm of …‖ parallel to┴ perpendicular tothe exponential function of xlin x the logarithmic function of xsie sinecos cosinetan tangentsinh hyperbolic sinecosh hyperbolic cosinethe inverse of ff is the composite or the composition of u and vthe limit of …as n approaches ∞(as x approaches )x a x approaches a, the differential coefficient of y; the 1st derivative of y , the nth derivative of ythe partial derivative of f with respect to xthe partial derivative of f with respect to ythe indefinite integral of fthe definite integral of f between a and b (from a to b) the increment of xdifferential xsummation of …the sum of the terms indicated∏the product of the terms indicated=> impliesis equivalent to（）round brackets; parantheses[ ] square brackets{ } braces。
数学专业英语词汇（L）
数学专业英语词汇（L）l distribution l分布l function l函数l integral 勒贝格积分l measurable function 勒贝格可测函数l null set l零集l'hospital rule 洛必达规则labeled graph 标号图labile 不稳定的laboratory system of coordinates 实验室坐标系labyrinth 迷宫lacation principle 介值定理lacunarity 缺项性lacunary series 间隙级数lacunary space 缺项空间lag 延迟lag correlation 滞后相关lag correlation coefficient 滞后相关系数lag covariance 落后协方差lag of phase 相位滞后lag regression 落后回归lagrange bracket 拉格朗日括号lagrange equation of motion 拉格朗日运动方程lagrange interpolation formula 拉格朗日插置公式lagrange interpolation polynomial 拉格郎日插值多项式lagrange multiplier 拉格朗日乘子lagrange problem 拉格朗日问题lagrange remainder term 拉格朗日剩余项lagrange residual term 拉格朗日剩余项lagrange theorem 拉格朗日定理lagrangian 拉格朗日算子thermocouple pyrometer 热电偶高温计lagrangian function 拉格朗日算子lagrangian operator 拉格朗日算符laguerre differential equation 拉盖尔微分方程laguerre function 拉盖尔函数laguerre polynomial 拉盖尔多项式lambert series 兰伯特级数lame equation 拉梅方程lame function 拉梅函数laminar 薄层的laminar flow 层流片流landau symbol 兰道记号landen transformation 兰登变换language of formula 公式语言laplace beltrami operator 拉普拉斯贝尔特拉米算子laplace distribution 拉普拉斯分布laplace equation 拉普拉斯方程laplace expansion 拉普拉斯展开laplace expansion theorem 拉普拉斯展开定理laplace integral 拉普拉斯积分laplace linear equation 拉普拉斯线性方程laplace transform 拉普拉斯变换laplacian 拉普拉斯算子laplacian equation 拉普拉斯方程large sample analysis 大样本分析large sample test 大样本检验last multiplier 最后乘子last term 末项latency 潜在latent 潜在的lateral 横的lateral area 侧面积lateral surface 侧面latin cube 拉丁立方latin rectangle 拉丁矩形latin square 拉丁方latitude 纬度lattice 格子;格lattice constant 点阵常数lattice design 格子设计lattice distribution 格分布lattice function 点阵函数lattice isomorphism 格同构lattice matrix 点阵矩阵lattice of sets 集格lattice operation 格运算lattice ordered group 格序群lattice point at the boundary 边界格点lattice theoretic 格论的lattice theory 格论latticehomomorphism 格同态latus rectum 通径laue's equations 劳卮方程laurent series 罗郎级数law 法则law of commutation 交换律law of composition 合成律law of cosines 余弦定律law of deduction 演绎定律law of double negation 双重否定律law of errors 误差律law of excluded middle 排中律law of exponentiation 指数定律law of inertia 惯性律law of iterated logarithm 迭对数定律law of large numbers 大数定律law of similarity transformation 相似变换律law of sines 正弦定律law of small numbers 小数定律law of tangents 正切定律laws of integral exponents 整指数定律leading coefficient 首项系数leading diagonal 衷角线leading ideal 猪想leading term 知项leaf 叶least common denominator 最小公分母least common left multiple 左最小公倍数least common multiple 最小公倍数least common right multiple 右最小公倍数least significant digit 最小有效数字least squares approximation 最小二乘逼近least squares estimator 最小二乘估计量least upper bound 最小上界lebesgue area 勒贝格面积lebesgue decomposition 勒贝格分解lebesgue integrable 勒贝格可积的lebesgue integral 勒贝格积分lebesgue measurable 勒贝格可测的lebesgue measure 勒贝格测度lebesgue number 勒贝格数lebesgue space 勒贝格空间lebesgue stieltjes integral 勒贝格斯蒂尔吉斯积分left adjoint 左伴随的left adjoint homomorphism 左伴随同态left almost periodic function 左殆周期函数left alternative division ring 左交错可除环left alternative law 左交错律left alternative ring 左交错环left annihilator 左零化子left artinian ring 左阿廷环left associated element 左相伴元素left balanced functor 左平衡函子left closed object 在闭对象left completion 左完备化left continuous 左方连续的left continuous function 左连续函数left coset 左陪集left coset space 左傍系空间left derivative 左导数left derived functor 左导函子left differential 左微分left direct product 左直积left directed quasiorder 逆有向拟序left distributive 左分配的left distributive law 左分配律left divisor 左因子left end point 左端点left exact functor 左正合函子left exactness 左正合性left faithful functor 左一一的函子left hand differentiable function 左可微函数left hand lower dini derivative 左下狄尼导数left hand side 左边left hand symmetrizable kernel 左方可对称化核left hand upper dini derivative 左上狄尼导数left handed co ordinate system 左手坐标系left handed curve 左旋曲线left handed system 左手坐标系left hereditary ring 左遗传环left homotopy inverse 左同伦逆元left ideal 左理想left identity element 左幺元left injective dimension 左内射维数left inner product 左内积left invariant mean 左不变平均值left invariant measure 左不变测度left inverse 左逆的left inverse element 左逆元left inverse matrix 左逆阵left inverse operator 左逆算子left invertible element 左可逆元left invertible mapping 左可逆映射left isolated point 左孤立点left kernel 左核left length 左长left limit value 左极限值left linear topology 左线性拓扑left localization 左局部化left mean 左平均left module 左模left monotonicity 左单翟left multiplication ring 左乘环left noetherian semigroup 左诺特半群left non zerodivisor 左非零因子left operator 左算子left order 左整环left periodic group 左周期群left primitive ideal 左本原理想left primitive ring 左本原环left projective space 左射影空间left quasi inverse 左拟逆元left quasi regularity 左拟正则性left quasi simple ring 左拟单环left quasigroup 左拟群left quotient 左商left quotient field 左商域left quotient ring 左商环left radical 左根基left regular element 左正则元素left regular representation 左正则表示left regularity 左正则性left remainder 左剩余left representation 左表示left resolution 左分解left satellite 左卫星函子left semihereditary ring 左半遗传环left semilinear mapping 左半线性映射left side contiuous function 左连续函数left side derivative 左导数left side half open interval 左半开区间left side limit value 左极限值left sided decomposition 左分解left simple groupoid 左单广群left simple semigroup 左单半群left tensor product 左张量乘积left topology 左拓扑left translation 左平移left zero divisor 左零因子leg of a right triangle 直角三角形的侧边legendre function 勒让德函数legendre polynomial 勒让德多项式legendre relation 勒让德关系legendre symbol 勒让德记号legendre transform 勒让德变换leibniz series 莱布尼兹级数leibniz theorem 莱布尼兹定理lemma 引理lemniscate 双纽线lemniscate function 双纽线函数lemniscate of bernoulli 伯努利双纽线length 长度length of arc 弧长length of curve 曲线的长length of normal 法线的长length of queue 队列长度length of tangent 切线的长length of vector 向量的长length unit 长度单位lens 透镜lens space 透镜空间leptokurtic distribution 尖峰态分布less than or equal 小于或等于letter 文字level 水准level curve 阶层曲线level line 等高线level plane 水准面level surface 等位面lever 杠杆levi decomposition 列维分解levi problem 列维问题lexicographic 词典的lexicographic order 字典顺序liapunov function 李雅普诺夫函数library 厍library subroutine 库存子程序lie algebra 李代数lie continuous group 李连续群lie derivative 李导数lie group 李群lie homomorphism 李同态lie ring 李环lie series 李级数lie subring 李子环life insurance 寿命保险life table 死亡率表life time 生存时间lifting 提升lifting map 提升映射lifting theorem 提升定理like term 同类项likelihood 似然likelihood function 似然函数likelihood ratio 似然比likelihood ratio test 似然比值检验limacon of pascal 帕斯卡蚶线limes inferior 下极限limes superior 上极限limit 极限limit case 极限情况limit circle 极限圆limit circle type 极限圆型limit cycle 极限环limit distribution 极限分布limit element 极限元limit function 极限函数limit in the sense of pointwise convergence 点态收敛极限limit of efficiency 有效极限limit of error 误差限度limit of integration 积分极限limit of proportionality 比例极限limit on the left 左极限limit on the right 右极限limit ordinal number 极限序数limit point 极限点limit point type 极限点型limit relation 极限关系limit theorem 极限定理limit theorem in probability theory 概率论极限定理limit value 极限值limitation 限制limited 有界的limited function 有界函数limiting cone 极限锥limiting distribution 极限分布limiting point 极限点limiting position 极限位置limitless 无界的limits of integration 积分限line 线line at infinity 无穷远线line bundle 线丛line coordinates 线坐标line critical graph 线临界图line element 线素line graph 线图line integral 线积分line of curvature 曲率线line of discontinuity 不连续线line of horizon 水平线line of intersection 交线line of nodes 交点线line of steepest descent 最速下降线line of vector 向量线line segment 线段linear 线的linear acceleration 线性加速度linear algebra 线性代数linear approximation 线性近似linear approximation problem 线性逼近问题linear associative algebra 线性结合代数linear closure 线性闭包linear combination 线性组合linear convergence 线性收敛linear density 线密度linear dependence 线性关系linear difference equation 线性差分方程linear differential equation 线性微分方程linear differential equation with constant coefficients 常系数线性微分方程linear dimension 线性维数linear eigenvalue problem 线性特盏问题linear equation 线性方程linear extrapolation 线性外插linear form 线性形式linear fractional function 单应函数linear fractional transformation 线性分式变换linear function 线性函数linear functional 线性泛函linear genus 线性狂linear group 线性群linear homogeneous equation 线性齐次方程linear hull 线性闭包linear independence 线性无关linear integral equation 线性积分方程linear integral equation of the third kind 第三种线性积分方程linear interpolation 线性插值linear isomorphism 线性同构linear manifold 线性廖linear map 线性映射linear measure 线性测度linear operator 线性算子linear optimization 线性最优化linear optimization problem 线性最优化问题linear order 线性有序类linear orderedness 线性次序linear ordinary differential equation 线性常微分方程linear pencil 线性束linear programming 线性规划linear quotient optimization 线性商最优化linear regression 线性回归linear relationship 线性关系linear space 线性空间linear subspace 线性子空间linear subsystem 线性子系linear system 线性系linear system of curves 线性曲线系linear system of differential equations 线性微分方程系linear transformation 线性变换linear vector function 线性向量函数linear velocity 线速度linearity 线性linearization 线性化linearly dependent set 线性相关集linearly dependent system 线性相关集linearly independent set 线性无关系linearly independent system 线性无关系linearly ordered class 线性有序类linearly ordered set 线性有序集link group 连接群liouville number 刘维尔数liouville theorem 刘维尔定理lipschitz condition 李普希茨条件lipschitz constant 李普希茨常数lipschitz continuity 李普希茨连续性lipschitz continuous function 李普希茨连续函数lipschitz space 李普希茨空间listing knot 8字纽结liter 升literal constant 文字常数literal expression 文字式litre 升lituus 连锁螺线load 载荷load curve 载荷曲线lobachevski space 双曲空间lobachevskian geometry 双曲几何学local arcwise connectedness 局部弧连通性local base 局部基local betti group 局部贝蒂群local borel set 局部波莱尔集local class field theory 局部类域论local compactness 局部紧性local condition 局部条件local continuity 局部连续性local convergence 局部收敛local coordinate system 局部坐标系local degree 局部次数local degree of map 局部映射度local extremum 局部极值local group 局部群local isomorphism 局部同构local lie group 局部李群local limit theorem 局部极限定理local lipschitz condition 局部李普希茨条件local maximum 局部极大local minimum 局部极小local parameter 局部参数local property 局部性质local ring 局部环local ringed space 局部环式空间local uniformization 局部单值化local uniformizing 局部单值化localization 局部化localization principle 局部化原理localizing subcategory 局部化子范畴locally analytic function 局部解析函数locally arcwise connected space 局部弧连通空间locally bounded function 局部有界函数locally closed set 局部闭集locally compact mapping 局部紧映射locally compact space 局部紧空间locally connected continuum 局部连通连续统locally connected set 局部连通集locally connected space 局部连通空间locally constant function 局部常值函数locally constant sheaf 局部常数层locally contractible space 局部可缩空间locally convex algebra 局部凸代数locally convex space 局部凸空间locally convex topology 局部凸拓扑locally euclidean connection 局部欧几里得联通locally euclidean group 局部欧几里得群locally euclidean manifold 局部欧几里得廖locally euclidean space 局部欧几里得空间locally finite category 局部有限范畴locally finite complex 局部有限复形locally finite family of sets 局部有限集族locally finite graph 局部有限图locally finite sum 局部有限和locally flat 局部平坦的locally free sheaf 局部自由层locally homomorphic function 局部同态函数locally pathconnected space 局部道路连通空间locally regular confidence region 局部正则置信区域locally separable space 局部可分空间locally soluble group 局部可解群locally trivial embedding 局部平凡嵌入locally unbiased test 局部无偏检验locally uniformizing parameter 局部单值化参数locally uniformly convergent sequence 局部一致收敛序列locally zero function 局部零函数location 存储单元location parameter 位置参数location principle 介值locus 轨迹log curve 对数曲线log log paper 重对数坐标纸logarithm 对数logarithm table 对数表logarithm to the base 10 常用对数logarithm to the basese 讷代对数logarithmic 对数的logarithmic branchpoint 对数分歧点logarithmic convexity 对数凸性logarithmic coordinates 对数座标logarithmic curve 对数曲线logarithmic decrement 对数衰减logarithmic derivative 对数导数logarithmic distribution 对数分布logarithmic equation 对数方程logarithmic function 对数函数logarithmic integral 对数积分logarithmic normal distribution 对数正态分布logarithmic paper 对数坐标纸logarithmic potential 对数位势logarithmic residue 对数残数logarithmic scale 对数尺度logarithmic series 对数级数logarithmic singularity 对数奇点logarithmic slide rule 对数计算尺logarithmic spiral 对数螺线logarithmic table 对数表logic 逻辑logic calculus 逻辑学logic of pocket calculator 袖珍计算机的逻辑logic of relations 关系逻辑logic product 合取logic sum 析取logical 逻辑的logical circuit 逻辑电路logical comparison 逻辑比较logical diagram 逻辑图logical element 逻辑元件logical operation 逻辑运算logical paradox 逻辑悖论logical shift 逻辑移位logical symbol 逻辑符号logical variable 逻辑变量logically true proposition 逻辑地真命题logicism 逻辑皱logico mathematical model 逻辑数学模型logistic 暹辑斯谛logistic curve 逻辑斯谛曲线logistic system 形式系统lognormal distribution 对数正态分布longitude 经度longitudinal 经度的longitudinal axis 纵向轴loop 闭路loop of a curve 曲线的闭路loop space 圈空间lopology of the uniformity 一致拓扑lorentz group 洛伦茨群thermocouple pyrometer 热电偶高温计lorentz transformation 洛伦茨变换loss 损失loss function 损失函数loss system 损失系统lot 一批lot tolerance fraction defective 批容许废品率low of cosines 余弦定律lower approximate limit 下近似极限lower bound 下界lower central series 降中心列lower class 下类lower control limit 下控制界限lower darboux integral 达布下积分lower darboux sum 达布下和lower density 下密度lower dini derivative 狄尼下导数lower envelope 下包络lower half plane 下半平面lower integral 下积分lower limit 下限lower limit of integration 积分的下极限lower measure 内测度lower order 低位lower pure value 下方值lower quartile 第一四分位数lower semi modular lattice 下半模格lower semicontinuity 下半连续性lower semicontinuous decomposition 下半连续分解lower semicontinuous function 下半连续函数lower semilattice 下半格lower sum 下和lower triangular matrix 下三角形矩阵lower value 下方值lower variation 负变差lowest common denominator 最小公分母lowest common multiple 最低公倍数lowest term 最低项loxodrome 斜驶曲线loxodromic matrix 斜驶矩阵loxodromic spiral 斜驶曲线loxodromic transformation 斜驶变换lozenge diagram 菱形图形lune 弓形。
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Mathematical English 1: Mathematics, Equation and Ratio
trigonometry and algebra, in which only the constants were considered. The rapid development of industry in 17th century promoted the progress of economics and technology and required dealing with variable 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. Mathematicians study concepts and propositions. Axioms, postulates, definitions and theorems are all propositions. Notations are a special and powerful tool of mathematics and are used to express conceptions and propositions very often. Formulas figures and charts are full of different symbols. Some of the best know symbols of mathematics are the Arabic numerals 1, 2, 3, 4, 5, 6, 7, 8, 9, 0, and signs of addition “+”,
Dr. Xiaomin Zhang: Mathematics Department, School of Science, Ningbo Universitylish 1: Mathematics, Equation and Ratio
Notations
mathematical analysis The area of mathematics generally taken to include those topics that involve the use of limiting process. Thus differential calculus and integral calculus certainly come under this heading. Besides these, there are other topics, such as the summation of infinite series, which involve infinite processes of this sort. The term analysis has also come to be used to indicate a rather more rigorous approach to the topics of calculus, and to the foundations of the real number system. logical deductions The logico-deductive method, a system of inference where conclusions (new knowledge) follow from premises (old knowledge) through the application of sound arguments.
induction The process of deriving general principles from particular facts or instances.
axioms, postulates The basic assumptions underlying a given body of deductive knowledge. They are accepted without demonstration. All
Dr. Xiaomin Zhang: Mathematics Department, School of Science, Ningbo University
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Mathematical English 1: Mathematics, Equation and Ratio
other assertions (theorems, if we are talking about mathematics) must be proven with the aid of the basic assumptions. Axiom , in classical terminology, referred to a self-evident assumption common to many branches of science. At the foundation of the various sciences lay certain basic hypotheses that had to be accepted without proof. Such a hypothesis was termed a postulate . The postulates of each science were different. Their validity had to be established by means of real-world experience. The classical approach is well illustrated by Euclid's elements, where we see a list of axioms and postulates. A1 Things which are equal to the same thing are also equal to one another.
Mathematical English 1: Mathematics, Equation and Ratio
Mathematical English
Dr. Xiaomin Zhang Email: zhangxiaomin@
Dr. Xiaomin Zhang: Mathematics Department, School of Science, Ningbo University
A2 If equals be added to equals, the wholes are equal. A3 If equals be subtracted from equals, the remainders are equal. A4 Things which coincide with one another are equal to one another. A5 The whole is greater than the part. Dr. Xiaomin Zhang: Mathematics Department, School of Science, Ningbo University
Dr. Xiaomin Zhang: Mathematics Department, School of Science, Ningbo University
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Mathematical English 1: Mathematics, Equation and Ratio
subtraction “−”, multiplication “×”, division “÷” and equality “=”. The conclusions in mathematics are obtained mainly by logical deductions and computations. For a long period of the history of mathematics, the centric place of mathematics was occupied by the logical deductions. Now, since electronic computers are developed promptly and used widely, the role of computation becomes more and more important. In our times, computation is not only used to deal with a lot of information and data, but also to carry out some work that merely could be done earlier by logical deductions, for example, the proof of most of geometrical theorems.
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Mathematical English 1: Mathematics, Equation and Ratio