数学专业英语(11)

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数学专业英语

举一个简单的例子，当常微分方程满足f‟(x) = f(x) 的关系时，最特殊的情况是指数函数 f(x) = ex
We shall see presently that every solution of (9.1) f‟(x) = f(x) must be of the form f(x) = Cex , where C may be any constant.
The study of differential equations is one part of mathematics that, perhaps more than any other , has been directly inspired by mechanics, astronomy, and mathematical physics .Its history began in the 17th century when Newton, Leibniz, and the Bernoullis solved some simple differential equations arising from problems in geometry and mechanics .
displacement Bernoulli
n.位移
n. (人名) 伯努利
The Bernoullis 伯努利(家族) mathematical physics 数学物理
A large variety of scientific problems arise in which one tries to determine something from its rate of change.
这些方程叫做微分方程，他们的研究方式是最难的数学分ations are classified under two main headings: ordinary and partial, depending on whether the unknown is a function of just one variable or of two or more variables. classified 分类 variable 变量

数学专业英语(Doc版).Word5

数学专业英语－Differential CalculusHistorical IntroductionNewton and Leibniz,quite independently of one another,were largely responsible for developing the ideas of integral calculus to the point where hitherto insur mountable problems could be solved by more or less routine methods.The succ essful accomplishments of these men were primarily due to the fact that they were able to fuse together the integral calculus with the second main branch o f calculus,differential calculus.The central idea of differential calculus is the notion of derivative.Like the inte gral,the derivative originated from a problem in geometry—the problem of find ing the tangent line at a point of a curve.Unlile the integral,however,the deriva tive evolved very late in the history of mathematics.The concept was not form ulated until early in the 17th century when the French mathematician Pierre de Fermat,attempted to determine the maxima and minima of certain special func tions.Fermat’s idea,basically very simple,can be understood if we refer to a curve a nd assume that at each of its points this curve has a definite direction that ca n be described by a tangent line.Fermat noticed that at certain points where th e curve has a maximum or minimum,the tangent line must be horizontal.Thus t he problem of locating such extreme values is seen to depend on the solution of another problem,that of locating the horizontal tangents.This raises the more general question of determining the direction of the tange nt line at an arbitrary point of the curve.It was the attempt to solve this gener al problem that led Fermat to discover some of the rudimentary ideas underlyi ng the notion of derivative.At first sight there seems to be no connection whatever between the problem of finding the area of a region lying under a curve and the problem of findin g the tangent line at a point of a curve.The first person to realize that these t wo seemingly remote ideas are,in fact, rather intimately related appears to have been Newton’s teacher,Isaac Barrow(1630-1677).However,Newton and Leibniz were the first to understand the real importance of this relation and they explo ited it to the fullest,thus inaugurating an unprecedented era in the development of mathematics.Although the derivative was originally formulated to study the problem of tang ents,it was soon found that it also provides a way to calculate velocity and,mo re generally,the rate of change of a function.In the next section we shall consi der a special problem involving the calculation of a velocity.The solution of this problem contains all the essential fcatures of the derivative concept and may help to motivate the general definition of derivative which is given below.A Problem Involving VelocitySuppose a projectile is fired straight up from the ground with initial velocity o f 144 feet persecond.Neglect friction,and assume the projectile is influenced onl y by gravity so that it moves up and back along a straight line.Let f(t) denote the height in feet that the projectile attains t seconds after firing.If the force of gravity were not acting on it,the projectile would continue to move upward with a constant velocity,traveling a distance of 144 feet every second,and at ti me t we woule have f(t)=144 t.In actual practice,gravity causes the projectile t o slow down until its velocity decreases to zero and then it drops back to eart h.Physical experiments suggest that as the projectile is aloft,its height f(t) is gi ven by the formula(1)f(t)=144t –16 t2The term –16t2is due to the influence of gravity.Note that f(t)=0 when t=0 a nd when t=9.This means that the projectile returns to earth after 9 seconds and it is to be understood that formula (1) is valid only for 0<t<9.The problem we wish to consider is this:To determine the velocity of the proj ectile at each instant of its motion.Before we can understand this problem,we must decide on what is meant by the velocity at each instant.To do this,we int roduce first the notion of average velocity during a time interval,say from time t to time t+h.This is defined to be the quotient.Change in distance during time interval =f(t+h)-f(t)/hThis quotient,called a difference quotient,is a number which may be calculated whenever both t and t+h are in the interval[0,9].The number h may be positiv e or negative,but not zero.We shall keep t fixed and see what happens to the difference quotient as we take values of h with smaller and smaller absolute v alue.The limit process by which v(t) is obtained from the difference quotient is wri tten symbolically as follows:V(t)=lim(h→0)[f(t+h)-f(t)]/hThe equation is used to define velocity not only for this particular example bu t,more generally,for any particle moving along a straight line,provided the position function f is such that the differerce quotient tends to a definite limit as h approaches zero.The example describe in the foregoing section points the way to the introducti on of the concept of derivative.We begin with a function f defined at least on some open interval(a,b) on the x axis.Then we choose a fixed point in this in terval and introduce the difference quotient[f(x+h)-f(x)]/hwhere the number h,which may be positive or negative(but not zero),is such th at x+h also lies in(a,b).The numerator of this quotient measures the change in the function when x changes from x to x+h.The quotient itself is referred to a s the average rate of change of f in the interval joining x to x+h.Now we let h approach zero and see what happens to this quotient.If the quot ient.If the quotient approaches some definite values as a limit(which implies th at the limit is the same whether h approaches zero through positive values or through negative values),then this limit is called the derivative of f at x and is denoted by the symbol f’(x) (read as “f prime of x”).Thus the formal defi nition of f’(x) may be stated as follows:Definition of derivative.The derivative f’(x)is defined by the equationf’(x)=lim(h→o)[f(x+h)-f(x)]/hprovided the limit exists.The number f’(x) is also called the rate of change of f at x.In general,the limit process which produces f’(x) from f(x) gives a way of ob taining a new function f’from a given function f.This process is called differ entiation,and f’is called the first derivative of f.If f’,in turn,is defined on an interval,we can try to compute its first derivative,denoted by f’’,and is calle d the second derivative of f.Similarly,the nth derivative of f denoted by f^(n),is defined to be the first derivative of f^(n-1).We make the convention that f^(0) =f,that is,the zeroth derivative is the function itself.Vocabularydifferential calculus微积分differentiable可微的intergral calculus 积分学differentiate 求微分hither to 迄今 integration 积分法insurmountable 不能超越 integral 积分routine 惯常的integrable 可积的fuse 融合integrate 求积分originate 起源于sign-preserving保号evolve 发展，引出 axis 轴（单数）tangent line 切线 axes 轴（复数）direction 方向 contradict 矛盾horizontal 水平的contradiction 矛盾vertical 垂直的 contrary 相反的rudimentary 初步的，未成熟的composite function 合成函数，复合函数area 面积composition 复合函数intimately 紧密地interior 内部exploit 开拓，开发 interior point 内点inaugurate 开始 imply 推出，蕴含projectile 弹丸 aloft 高入云霄friction摩擦initial 初始的gravity 引力 instant 瞬时rate of change 变化率integration by parts分部积分attain 达到definite integral 定积分defferential 微分indefinite integral 不定积分differentiation 微分法 average 平均Notes1. Newton and Leibniz,quite independently of one another,were largely responsible for developing…by more or less routine methods.意思是：在很大程度上是牛顿和莱伯尼，他们相互独立地把积分学的思想发展到这样一种程度，使得迄今一些难于超越的问题可以或多或少地用通常的方法加以解决。

《数学专业英语》常用英文表达

7
max, min maximum value, minimum value Eample: max f ( x) Maximum value of f(x)
max(a1 ,an ) Maximum value of the series
a1 to an Powers and roots Example: x 2 x squared
10
Function f
2 Example: f ( x ) ax bx c , a 0. The function of x
equals a times the square of x plus b times x plus c, where a is not equal to zero.
Imaginary number and two common irrational numbers
, ratio of the circumference of a circle to its
diameter,approximate value 3.1415926
9
1 x i 1, e lim(1 ) x x
Example:
f ( x ) f double-prime x, f double-dashed x f ( x ) f triple-prime x, f triple-dashed x (4) f ( x ) f four x
8
xn x 1
Example:
3
x x
4 n
x x
fourth root (of) x
nth root (of) x
Example: 24 16 Two to the fourth power is sixteen

数学专业英语

数学专业英语Lesson 1Mathematics as a Language of Scienceassert vt. 断言；坚持主张；维护表明qualitative adj. 性质的；定性的quantitative adj. 量的；数量的；定量的；与数量有关的astronomy n. 天文学postulate n. 假定, 基本条件, 基本原理 vt. 要求, 假定 vi. 要求hypothetical adj. 假设的, 假定的,爱猜想的Lesson 2deduction n. 减除, 扣除, 减除额, 推论, 演绎induction n. 归纳；归纳法；归纳所得之结论verification n. 验证；证实correlate vt. 使相互关联 vi. 和...相关discard vt. 丢弃, 抛弃 v. 放弃discredit n. 不信任；失信consistent adj. 一致的, 调和的, 坚固的, [数、统]相容的inadequacy n. 不充分 ,不适当,不适合,不足额conic, conical adj 圆锥的；圆锥形的ellipse n. 椭圆, 椭圆形 ellipt (n.)hyperbolic adj. 双曲线的 hyperbola (n.)parabolic adj. 用寓言表达的: 抛物线的，像抛物线的 parabola (n.) algebraic adj. 代数的, 关于代数学的mineralogy n. 矿物学refraction n. 折光, 折射stimulus n. 刺激物, 促进因素, 刺激, 刺激impetus n. 冲力推动力；刺激Lesson 3Axioms, definitions and Theoremsaxiom n. [数]公理definition n. 阐明；确定定义；界说extravagant adj. 奢侈的, 浪费的, 过分的, 放纵的collinear adj. 在同一直线上的, 同线的convex adj. 凸出的；凸面的segment n. 部分；片段；节, 弓形；圆缺；弧形, 线段conswquently adv. 从而, 因此in terms of adv. 根据, 按照, 用...的话, 在...方面pretense n. 主张, 要求, 伪称, 借口, 自称Lesson 4Geometry and Geometrical termsterm n. 学期, 期限, 期间, 条款, 条件, 术语triangle n. [数]三角形, 三人一组, 三角关系parallelogram n. 平行四边形straight angle n. [数]平角right angle n. 直角acute angle n. 锐角obtuse angle n. 钝角reflex angle n. 优角rectilinear adj 直线的；由直线组成的；循直线进行的isosceles triangle n. 等腰三角形equilateral triangle n. 等边三角形right triangle n. 直角三角形obtuse triangle n. 钝角三角形acute triangle n. 锐角三角形equiangular triangle n. 正三角形,等角三角形hypotenuse n. （直角三角形的）斜边circle 圆center 中心；中央；圆心diameter n. 直径radius n. 半径, 范围, 辐射光线, 有效航程, 范围, 界限circumference n. 圆周, 周围Lesson 5The Method of Limitslimit n. 限度,极限,极点infinite adj. 无限的；无穷的infinitesimal adj. 无穷小的, 极小的, 无限小的calculus n. 微积分学, 结石exemplify vt. 例证, 例示, 作为...例子inscribe v. 记下polygon n. [数]多角形, 多边形diminish v. (使)减少, (使)变小curvilinear adj 曲线的, 由曲线组成的intuition n. 直觉, 直觉的知识integral n. [数学] 积分, 完整, 部分defective adj. 有缺陷的, (智商或行为有)欠缺的differential coefficient 微分系数arithmetical adj. 算术的, 算术上的convergence n. 集中, 收敛criterion n. (批评判断的)标准, 准据, 规范sequence n. 次序, 顺序, 序列irrational numbers n. [数]无理数domain ，定义域contradiction 矛盾reversal n. 颠倒, 反转, 反向, 逆转, 撤销Lesson 6Functioncontinuous variable 连续变量;［连续变数］variation 变分, 变化interval 区间independent variable 自变量dependent variable 应变量rectangular coordinate 直角坐标abscissa n. 〈数〉横坐标ordinate n. [数]纵线, 纵座标gradient adj. 倾斜的n. 梯度, 倾斜度, 坡度slope n. 斜坡, 斜面, 倾斜 v. (使)顺斜Lesson 7Differential and Integral calculusdifferential adj. 微分的n. 微分 (differentiation)Integral n. [数学] 积分, 完整, 部分 (integration)calculus n. 微积分学, 结石interrelation n. 相互关系trigonometry n. 三角法exponential adj. 指数的, 幂数的logarithm n. [数] 对数derivative n. 导数；微商tangent n. 切线, [数]正切counterclockwise adj. 反时针方向的adv. 反时针方向 (clockwise) definite integral 定积分approximation n. 接近, 走近, [数]近似值culminate v. 达到顶点mean n. 平均数, 中间, 中庸differential equation 微分方程extreme value n. 极值multiple integral 多重积分double integralline integralfunctional analysis 泛函分析Lesson 8 The Concept of Cardinal Number (I)cardinal number n. 基数（如： 1, 2, 3, ... 有别于序数）denumerable adj. 可数的aggregate n. 合计, 总计, 集合体adj. 合计的, 集合的, 聚合的v. 聚集, 集合, 合计purport n. 主旨 v. 声称fancier n. 空想家, 培育动物(或植物)的行家, 爱好者sniff v. 用力吸, 嗅, 闻到, 发觉, 轻视, 用力吸气n. 吸, 闻, 吸气声, 嗤之以鼻scheme n. 安排, 配置, 计划, 阴谋, 方案, 图解, 摘要v. 计划, 设计, 图谋, 策划, * n.（计算数学）方法，格式superior n. 长者, 高手, 上级adj. 较高的, 上级的, 上好的, 出众的, 高傲的cumbersome adj. 讨厌的, 麻烦的, 笨重的instruction n. 指示, 用法说明(书), 教育, 指导, 指令drastically adv. 激烈地, 彻底地conservation 守衡律quadrature n. 求积, 求积分interpolation n. 插值extrapolation n. [数]外推法, 推断internal point 内点identical adj. 同一的, 同样的generalized solution 广义解functional 泛函hydrodynamics 流体力学，水动力学divergence 发散（性），梯度，发散量play an important (fundamental ... ) role 起着重要的（...）作用integro-interpolation method 积分插值法Variational method 变分方法comparatively adv. 比较地, 相当地deficiency n. 缺乏, 不足fictive adj. 虚构的, 想象上的, 虚伪的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 n. 使者, 传令官, 通报者, 先驱, 预兆vt. 预报, 宣布, 传达, 欢呼advection n. 水平对流phenomenological adj. 现象学的, 现象的fluctuation n. 波动, 起伏optimism n. 乐观, 乐观主义pessimism n. 悲观, 悲观主义unjustified adj 未被证明其正确的mean-square 均方dispersion n. [数] 离差, 差量Polynomial n adj. [数]多项式的interpolation 插值arithmetic n. 算术, 算法rounding errors 舍入误差multiple n. 倍数, 若干subjective adj. 主观的, 个人的objective adj. 客观的,outcome n. 结果, 成果pattern n. 样品toss v. 投, 掷exhaust vt. 用尽, 耗尽, 抽完, 使精疲力尽divisible adj. 可分的dice, die n. 骰子assign vt. 分配, 指派attach vt. 缚上, 系上, 贴上v. 配属, 隶属于pitfall n. 缺陷chairperson 主席mechanics n. (用作单数)机械学、力学, (用作复数)技巧, 结构statics n. [物]静力学dynamics n. 动力学adequately adv. 充分地celestial adj. 天上的macroscopic adj. 肉眼可见的, 巨观的classical field theory 经典场理论rigit adj. 刚硬的, 刚性的, 严格的elastic adj. 弹性的plastic n. 可塑的,塑性的,塑料的quantum n. 量, 额, [物] 量子, 量子论inception n. 起初, 获得学位pertain v. 适合, 属于gravitation n. 地心吸力, 引力作用tide n. 潮, 潮汐, 潮流, 趋势monumental adj. 纪念碑的, 纪念物的, 不朽的, 非常的encompass v. 包围, 环绕, 包含或包括某事物ingredient n. 成分, 因素acquainted adj. 有知识的, 知晓的synonymous adj. 同义的configuration n. 构造, 结构, 配置, 外形reference n. 提及, 涉及, 参考, 参考书目inertia n. 惯性, 惯量attribute 特性momentum n. 动量proportional adj. 比例的, 成比例的, 相称的, 均衡的designate 指明negligible adj. 可以忽略的, 不予重视的projectile n. 射弹 adj. 发射的ballistics n. 弹道学, 发射学intractable adj. 难处理的{Mechanics of a Particlein consequence of adv. 由于的...缘故exert vt. 尽(力), 施加(压力等), 努力v. 发挥, 竭尽全力, 尽galaxy n. 星系, 银河, 一群显赫的人, 一系列光彩夺目的东furnish vt. 供应, 提供, 装备, 布置v. 供给torque n. 扭矩, 转矩moment 力矩的friction 摩擦dissipation n. 消散, 分散, 挥霍, 浪费, 消遣, 放荡, 狂饮infer v. 推断Hooke s Law and Its Consequenceselasticity n. 弹力, 弹性constitutive adj. 构成的, 制定的atomistic adj. 原子论的crack n. 裂缝, 噼啪声v. (使)破裂, 裂纹, (使)爆裂continuum mechanics n. 连续介质力学superposition n. 重叠, 重合, 叠合strain n. 过度的疲劳, 紧张, 张力, 应变vt. 扭伤, 损伤v. 拉紧, 扯紧, (使)紧张, 尽力thermodynamics n. [物] 热力学reckon vt. 计算, 总计, 估计, 猜想vi. 数, 计算, 估计, 依赖, 料想lesson 20strength 强度load 载荷empirical 以经验为依据的member 构件isolated 孤立的segment 部分、段、节stress 应力strain 应变tension 拉伸shear 剪切bend 弯曲torsion 扭转、扭力insofar 在……范围cohesive 内聚性的tensile 拉力、张力stiffness 硬度furnish 供给Lesson 23 Fluid Mechanicseruption 喷发、爆发turbulent 湍流laminar 层流isothermal 等温isotropic 各向同性prevalent 普遍的、流行的tornado 旋风、飓风eddy 旋涡viscosity 粘性、粘度nonviscous 无粘性的rotation 旋转adiabatic 绝热的reversible 可逆的isentropic 等熵的instant 瞬时的streamline 流线stream tube 流管tangential 切线的incompressible 不可压缩的resultant 合成的,组合的downstream 下游的,顺流的elbow 弯管,肘similitude 相似性hydraulic 水力的,水力学的predominante 占主导地位spillway (河或水坝的)放水道,泄洪道prototype 原型,样板Lesson 24 Mechanical Vibration repetitive 重复的,反复的periodic 周期的,定期的tidal 潮的,像潮的stationary 固定的,不动的vibratory 振动的,摆动的propagation 传播couple v .连接,连合acoustic 听觉的,声学的annoyance 烦恼,困惑adjacent 接近的,邻近的damp 阻尼,衰减restore 复职,归还neutral 平衡exciting force 激励力resonant adj. 共振的,谐振的stiffness 刚度,刚性proportionality 成比例地inclusion 包含,包括magnitude 数值,大小substantially adv. 实质上的perturb 干扰,扰乱resonance n. 共振vibratory adj. 振动的, 可知的perceptible 可见的,可知的adudible 听得见的,可闻的foregoing 前述的impulsive 冲击的shock 冲击Fourier series 傅里叶级数excitation 激发,激励discrete 分离,离散的contend with 向…作斗争compressor 压气机fatigue 疲劳perceptible 可见的,可知觉的shredder 切菜器disposal 处理urban 都市的metropolitan 大都市的at-grade 在同一水平面上elevated 高架的guideway 导轨Lesson 25 A prefect to the Continuum Mechanics preface 序言continuum连续 pl. continuua rigid body 刚体contemporary 当代的,同时期的widespread 分布广的, 普及的accommodate 容纳,使适应medium 介质plasticity 塑性residual 剩余的,残留的creep 蠕变,爬行,塑性变形aging 老化polymeric聚合(物)的sandy 沙的,沙质的aubterranean 地下的,隐藏的essence 精髓,本质thermodynamics 热力学self-similar 自相似expedient 方便的sonsolidate 把…联合为一体,统一justify 证明…有理radically 根本地,本质上deliberate 从容不迫的,深思熟虑Lesson 33 what is a computer Attribute v. 赋予medieval 中世纪的astronomer 天文学家Mars 火星resemble vt. 像,相似tedious adj. 冗长乏味的pulp 浆状物,果肉filter vt.过滤underlying adj. 潜在的, 基本的ore n. 矿沙,矿石perceive v. 察觉,看见intervention n. 干涉,插入intelligent adj. 有智力的,聪明的Lesson 34 A computer system manipulate vt. 操纵,使用chip n. 芯片etch vt. 蚀刻,蚀镂fingernail 指甲mount vt. 安装,安置assemble vt. 集合,聚集cabinet 橱柜execute vt. 执行,实现paycheck n.支付薪金的支票bar chart 直方图joystick 游戏杆encounter vt. 遇到,遇上Mathematical Modelingindustry n. 工业, 产业, 行业, 勤奋commerce n. 商业complexity n. 复杂(性), 复杂的事物, 复杂性career n. (原意:道路, 轨道)事业, 生涯, 速度outset n. 开端, 开始essence n. 基本, [哲]本质, 香精advocation n. (=advocacy)拥护支持provision n. 供应, (一批)供应品, 预备, 防备, 规定publicize v. 宣扬roundabout adj. 迂回的, 转弯抹角的n. 道路交叉处的环形路, 迂回路线, 兜圈子的话trial-error vt. n. 试制, 试生产maneuverability n. 可操作性, 机动性vehicle n. 交通工具, 车辆, 媒介物, 传达手段junction n. 连接, 接合, 交叉点, 汇合处ponder v. 沉思, 考虑contrive v. 发明, 设计, 图谋snooker n. (=snooker pool)彩色台球, 桌球context n. 上下文, 文章的前后关系deviation n. 背离数学专业英语－Groups and RingsDuring the present century modern abstract algebra has become more and more important as a tool for research not only in other branches of mathematics bu t even in other sciences .Many discoveries in abstract algebra itself have been made during the past years and the spirit of algebraic research has definitely t ended toward more abstraction and rigor so as to obtain a theory of greatest p ossible generality. In particular, the concepts of group ,ring,integral domain and field have been emphasized.The notion of an abstract group is fundamental in all sciences ,and it is certai nly proper to begin our subject with this concept. Commutative additive groupsare made into rings by assuming closure with respect to a second operation h aving some of the properties of ordinary multiplication. Integral domains and fi elds are rings restricted in special ways and may be fundamental concepts and their more elementary properties are the basis for modern algebra.GroupsDEFINITION A non-empty set G of elements a,b,…is said to form a group with respect to 0 if:I.G is closed with respect to 0II.The associative law holds in G, that isaо(bоc)=(aоb)оcfor every a, b, c of GⅢ. For every a and b of G there exist solutions χand Уin G of the equ ationsaοχ=b yοa=bA group is thus a system consisting of a set of elements and operation οwit h respect to which G forms a group. We shall generally designate the entire s ystem by the set G of its elements and shall call G a group. The notation use d for the operation is generally unimportant and may be taken in as convenien t a way as possible.DEFINITION A group G is called commutative or abelian ifaοb=bοaFor every a and b of G.An elementary physical example of an abelian group is a certain rotation grou p. We let G consist of the rotations of the spoke of a wheel through multiples of 90ºand aοb be the result of the rotation a followed by the rotation b. T he reader will easily verify that G forms a group with respect to οand that aοb=bοa. There is no loss of generality when restrict our attention to multipl icative groups, that is, write ab in stead of aοb.EQUIVALENCEIn any study of mathematical systems the concept of equivalence of systems of the same kind always arises. Equivalent systems are logically distinct but weusually can replace any one by any other in a mathematical discussion with no loss of generality. For groups this notion is given by the definition: let G an d G´be groups with respective operations o and o´,and let there be a1-1 corr espondenceS : a a´ (a in G and a´in G´)between G and G´such that(aοb)´=a´οb´for all a, b of G. then we call G and G´equivalent(or simply, isomorphic)grou ps.The relation of equivalence is an equivalence relation in the technical sense in the set of all groups. We again emphasize that while equivalent groups may be logically distinct they have identical properties.The groups G and G´of the above definition need not be distinct of course a nd o´may be o. when this is the case the self-equivalence S of G is called a n automorphism.I: a aOf G, but other automorphisms may also exist.RingsA ring is an additive abelian groupB such thatI.the set B is closed with respect to a second operation designated by multiplication; that is , every a and b of B define a unique element ab of B. II.multiplication is associative; that isa (bc) = (ab)cfor every a, b, c of B.Ⅲ. The distributive lawsa (b+c) = ab +ac (b+c) a=ba +cahold for every a, b, c of B.The concept of equivalence again arises. We shall writeB ≌B′to mean that B and B′are equivalent.VocabularyGroup 群rigor 严格ring 环 generalization 推广integral domain 整环Abelian group 阿贝尔群commutative additive group 可交换加法群 rotation 旋转automorphism 自同构数学专业英语－Historical introduction of CalculusThe Two Basic Concepts of CalculusThe remarkable progress that has been made in science and technology during the last century is due in large part to the development of mathematics. That branch of mathematics known as integral and differential calculus serves as a natural and powerful tool for attacking a variety of problems that arise in phys ics,engineering,chemistry,geology,biology, and other fields including,rather recentl y,some of the social sciences.To give the reader an idea of the many different types of problems that can b e treatedby the methods of calculus,we list here a few sample questions.With what speed should a rocket be fired upward so that it never returns to e arth? What is the radius of the smallest circular disk that can cover every isosceles triangle of a given perimeter Ｌ? What volume of material is removed fr om a solid sphere of radius 2 r if a hole of redius r is drilled through the ce nter? If a strain of bacteria grows at a rate proportional to the amount present and if the population doubles in one hour,by how much will it increase at th e end of two hours? If a ten-pound force stretches an elastic spring one inch,h ow much work is required to stretch the spring one foot?These examples,chosen from various fields,illustrate some of the technical quest ions that can be answered by more or less routine applications of calculus.Calculus is more than a technical tool－it is a collection of fascinating and ex eiting idea that have interested thinking men for centuries.These ideas have to do with speed,area,volume,rate of growth,continuity,tangent line,and otherconcept s from a varicty of fields.Calculus forces us to stop and think carefully about the meanings of these concepts. Another remarkable feature of the subject is it s unifying power.Most of these ideas can be formulated so that they revolve a round two rather specialized problems of a geometric nature.We turn now to a brief description of these problems.Consider a cruve C which lies above a horizontal base line such as that show n in Fig.1. We assume this curve has the property that every vertical line inter sects it once at most.The shaded portion of the figure consists of those pointe which lie below the curve C , above the horizontal base,and between two para llel vertical segments joining C to the base.The first fundamental problem of c alculus is this: To assign a number which measures the area of this shaded re gion.Consider next a line drawn tangent to the curve,as shown in Fig.1. The second fundamental problem may be stated as follows:To assign a number which me asures the steepness of this line.Basically,calculus has to do with the precise formulation and solution of these two special problems.It enables us to define the concepts of area and tangent l ine and to calculate the area of a given region or the steepness of a given an gent line. Integral calculus deals with the problem of area while differential cal culus deals with the problem of tangents.Historical BackgroundThe birth of integral calculus occurred more than 2000 years ago when the Gr eeks attempted to determine areas by a procees which they called the method of exhaustion.The essential ideas of this ,method are very simple and can be d escribed briefly as follows:Given a region whose area is to be determined,we inscribe in it a polygonal region which approximates the given region and whos e area we can easily compute.Then we choose another polygonal region which gives a better approximation,and we continue the process,taking polygons with more and more sides in an attempt to exhaust the given region.The method is illustrated for a scmicircular region in Fig.2. It was used successfully by Arch imedes(287－212 B.C.) to find exact formulas for the area of a circle and a fe w other special figures.The development of the method of exhaustion beyond the point to which Ar chimcdcs carried it had to wait nearly eighteen centuries until the use of algeb raic symbols and techniques became a standard part of mathematics. The eleme ntary algebra that is familiar to most high-school students today was completel y unknown in Archimedes’time,and it would have been next to impossible to extend his method to any general class of regions without some convenient w ay of expressing rather lengthy calculations in a compact and simpolified form.A slow but revolutionary change in the development of mathematical notations began in the 16th century A.D. The cumbersome system of Roman numerals was gradually displaced by the Hindu-Arabic characters used today,the symbol s “+”and “-”were introduced for the forst time,and the advantages of the decimal notation began to be recognized.During this same period,the brilliant su ccesse of the Italian mathematicians Tartaglia,Cardano and Ferrari in finding al gebraic solutions of cubic and quadratic equations stimulated a great deal of ac tivity in mathematics and encouraged the growth and acceptance of a new and superior algebraic language. With the wide spread introduction of well-chosen algebraic symbols,interest was revived in the ancient method of exhaustion an d a large number of fragmentary results were discovered in the 16 th century by such pioneers as Cavalieri, Toricelli, Roberval, Fermat, Pascal, and Wallis.Fig.2. The method of exhaustion applied to a semicircular region.Gradually the method of exhaustion was transformed into the subject now calle d integral calculus,a new and powerful discipline with a large variety of applic ations, not only to geometrical problems concerned with areas and volumes but also to jproblems in other sciences. This branch of mathematics, which retaine d some of the original features of the method of exhaustion,received its bigges t impetus in the 17 th century, largely due to the efforts of Isaac Newion (16 42—1727) and Gottfried Leibniz (1646—1716), and its development continued well into the 19 th century before the subject was put on a firm mathematical basis by such men as Augustin-Louis Cauchy (1789-1857) and Bernhard Riem ann (1826-1866).Further refinements and extensions of the theory are still being carried o ut in contemporary mathematicsVocabularygeology 地质学decimal 小数，十进小数biology 生物学discipline 学科social sciences 社会科学 contemporary 现代的disk (disc) 圆盘bacteria 细菌isosceles triangle 等腰三角形 elastic 弹性的perimeter 周长 impetus 动力volume 体积 proportional to 与…成比例center 中心 inscribe 内接steepness 斜度 solid sphere 实心球method of exhaustion 穷举法 refinement 精炼，提炼polygon 多边形，多角形 cumbersome 笨重的，麻烦的polygonal 多角形fragmentary 碎片的，不完全的approximation 近似，逼近 background 背景学专业英语－How to Organize a paper (For Beginers)?The usual journal article is aimed at experts and near-experts, who are the peo ple most likely to read it. Your purpose should be say quickly what you have done is good, and why it works. Avoid lengthy summaries of known results, and minimize the preliminaries to the statements of your main results. There ar e many good ways of organizing a paper which can be learned by studying pa pers of the better expositors. The following suggestions describe a standard acc eptable style.Choose a title which helps the reader place in the body of mathematics. A use less title: Concerning some applications of a theorem of J. Doe. A. good titlecontains several well-known key words, e. g. Algebraic solutions of linear parti al differential equations. Make the title as informative as possible; but avoid re dundancy, and eschew the medieval practice of letting the title serve as an infl ated advertisement. A title of more than ten or twelve words is likely to be m iscopied, misquoted, distorted, and cursed.The first paragraph of the introduction should be comprehensible to any mathe matician, and it should pinpoint the location of the subject matter. The main p urpose of the introduction is to present a rough statement of the principal resul ts; include this statement as soon as it is feasible to do so, although it is som etimes well to set the stage with a preliminary paragraph. The remainder of th e introduction can discuss the connections with other results.It is sometimes useful to follow the introduction with a brief section that estab lishes notation and refers to standard sources for basic concepts and results. N ormally this section should be less than a page in length. Some authors weave this information unobtrusively into their introductions, avoiding thereby a dull section.The section following the introduction should contain the statement of one or more principal results. The rule that the statement of a theorem should precede its proof a triviality. A reader wants to know the objective of the paper, as well as the relevance of each section, as it is being read. In the case of a ma jor theorem whose proof is long, its statement can be followed by an outline of proof with references to subsequent sections for proofs of the various parts.Strive for proofs that are conceptual rather than computational. For an example of the difference, see A Mathematician’s Miscellany by J.E.Littlewood, in wh ich the contrast between barbaric and civilized proofs is beautifully and amusin gly portrayed. To achieve conceptual proofs, it is often helpful for an author t o adopt an initial attitude such as one would take when communicating mathe matics orally (as when walking with a friend). Decide how to state results wit h a minimum of symbols and how to express the ideas of the proof without c omputations. Then add to this framework the details needed to clinch the resul ts.Omit any computation which is routine (i.e. does not depend on unexpected tri cks). Merely indicate the starting point, describe the procedure, and state the o utcome.It is good research practice to analyze an argument by breaking it into a succe ssion of lemmas, each stated with maximum generality. It is usually bad practi ce to try to publish such an analysis, since it is likely to be long and unintere sting. The reader wants to see the path-not examine it with a microscope. A part of the argument is worth isolating as a lemma if it is used at least twice l ater on.The rudiments of grammar are important. The few lines written on the blackbo ard during an hour’s lecture are augmented by spoken commentary, and aat t he end of the day they are washed away by a merciful janitor. Since the publ ished paper will forever speak for its author without benefit of the cleansing s ponge, careful attention to sentence structure is worthwhile. Each author must develop a suitable individual style; a few general suggestions are nevertheless a ppropriate.The barbarism called the dangling participle has recently become more prevalen t, but not less loathsome. “Differentiating both sides with respect to x, the eq uation becomes---”is wrong, because “the equation”cannot be the subject th at does the differentiation. Write instead “differentiating both sides with respec t to x, we get the equation---,”or “Differentiation of both sides with respect to x leads to the equation---”Although the notion has gained some currency, it is absurd to claim that infor mal “we”has no proper place in mathematical exposition. Strict formality is appropriate in the statement of a theorem, and casual chatting should indeed b e banished from those parts of a paper which will be printed in italics. But fif teen consecutive pages of formality are altogether foreign to the spirit of the t wentieth century, and nearly all authors who try to sustain an impersonal digni fied text of such length succeed merely in erecting elaborate monuments to slu msiness.A sentence of the form “if P,Q”can be understood. However “if P,Q,R,S,T”is not so good, even if it can be deduced from the context that the third co mma is the one that serves the role of “then.”The reader is looking at the paper to learn something, not with a desire for mental calisthenics.Vocabularypreliminary 序,小引(名)开端的,最初的(形)eschew 避免medieval 中古的，中世纪的inflated 夸张的comprehensible 可领悟的，可了解的pinpoint 准确指出（位置）weave 插入，嵌入unobtrusivcly 无妨碍地triviality 平凡琐事barbarism 野蛮，未开化portray 写真，描写clinch 使终结rudiment 初步，基础commentary 注解，说明janitor 看守房屋者sponge 海绵dangling participle 不连结分词prevalent 流行的，盛行loathsome 可恶地absurd 荒谬的banish 排除sustain 维持，继续slumsiness 粗俗，笨拙monument 纪念碑calisthenics 柔软体操，健美体操notes1. 本课文选自美国数学会出版的小册子A mamual for authors of mathematical paper的一节，本文对准备投寄英文稿件的读者值得一读。

数学专业英语(Doc版).11

数学专业英语－Linear AlgebraFor the definition that follows we assume that we are given a particular field K. The scalars to be used are to be elements of K.DEFINITION. A vector space is a set V of elements called vectors satisfyi ng the following axioms.(A) To every pair, x and y ,of vectors in V corresponds a vector x+y,call ed the sum of x and y, in such a way that.(1) addition is commutative, x + y = y + x.(2) addition is associative, x + ( y + z ) = ( x + y ) + z.(3) there exists in V a unique vector 0 (called the origin ) such that x + 0 = x for every vector x , and(4) to every vector x in V there corresponds a unique vector - x such that x + ( - x ) = 0.(B) To every pair,αand x , where αis a scalar and x is a vector in V ,the re corresponds a vector αx in V , called the product of αand x , in such a way that(1) multiplication by scalars is associative,α(βx ) = (αβ) x(2) 1 x = x for every vector x.(C) (1) multiplication by scalars is distributive with respect to vector addition,α( x + y ) = αx+βy , and(2)multiplication by vectors is distributive with respect to scalar addition,(α+β) x = αx + βx .The relation between a vector space V and the underlying field K is usually d escribed by saying that V is a vector space over K . The associated field of s calars is usually either the real numbers R or the complex numbers C . If V i s linear space and M真包含于V , and if αu -v belong to M for every u an d v in M and every α∈ K , then M is linear subspace of V . If U = { u 1,u 2,…} is a collection of points in a linear space V , then the (linear) span of the set U is the set of all points o the form ∑c i u i, where c i∈ K ,and all but a finite number of the scalars c i are 0.The span of U is al ways a linear subspace of V.A key concept in linear algebra is independence. A finite set { u 1,u 2,…, u} is said to be linearly independent in V if the only way to write 0 = ∑kc i u i is by choosing all the c i= 0 . An infinite set is linearly independent if every finite set is independent . If a set is not independent, it is linearlyd ependent, and in this case, some point in the set can be written as a linear co mbination of other points in the set. A basis for a linear space M is an indep endent set that spans M . A space M is finite-dimensional if it can be spanne d by a finite set; it can then be shown that every spanning set contains a basi s, and every basis for M has the same number of points in it. This common number is called the dimension of M .Another key concept is that of linear transformation. If V and W are linear sp aces with the same scalar field K , a mapping L from V into W is called lin ear if L (u + v ) = L( u ) + L ( v ) and L ( αu ) = αL ( u ) for ever y u and v in V and αin K . With any I , are associated two special linear spaces:ker ( L ) = null space of L = L-1 (0)= { all x ∈V such that L ( X ) = 0 }Im ( L ) = image of L = L( V ) = { all L( x ) for x∈V }.Then r = dimension of Im ( L ) is called the rank of L. If W also has dime nsion n, then the following useful criterion results: L is 1-to-1 if and only if L is onto.In particular, if L is a linear map of V into itself, and the only solu tion of L( x ) = 0 is 0, then L IS onto and is therefore an isomorphism of V onto V , and has an inverse L -1. Such a transformation V is also said to b e nonsingular.Suppose now that L is a linear transformation from V into W where dim ( V ) = n and dim ( W ) = m . Choose a basis {υ 1 ,υ 2 ,…,υn} for V and a basis {w 1 ,w2 ,…,w m} for W . Then these define isomorphisms of V onto K n and W onto K m, respectively, and these in turn induce a linear transfor mation A between these. Any linear transformation ( such as A ) between K n and K m is described by means of a matrix ( a), according to the formula Aij( x ) = y , where x = { x1, x 2,…, x n} y = { y1, y 2,…, y m} and Y j =Σn j=i a ij x i I=1,2,…,m.The matrix A is said to represent the transformation L and to be the represent ation induced by the particular basis chosen for V and W .If S and T are linear transformations of V into itself, so is the compositic tra nsformation ST . If we choose a basis in V , and use this to obtain matrix re presentations for these, with A representing S and B representing T , then ST must have a matrix representation C . This is defined to be the product AB o f the matrixes A and B , and leads to the standard formula for matrix multipli cation.The least satisfactory aspect of linear algebra is still the theory of determinants even though this is the most ancient portion of the theory, dating back to Lei bniz if not to early China. One standard approach to determinants is to regard an n -by- n matrix as an ordered array of vectors( u 1 , u 2,…, u n) and t hen its determinant det ( A ) as a function F( u 1 , u 2 ,…, u n) of these n vectors which obeys certain rules.The determinant of such an array A turns out to be a convenient criterion for characterizing the nonsingularity of the associated linear transformation, since d et ( A ) = F ( u 1, u 2,…, u n) = 0 if and only if the set of vectors u i ar e linearly dependent. There are many other useful and elegant properties of det erminants, most of which will be found in any classic book on linear algebra. Thus, det ( AB ) = det ( A ) det ( B ), and det ( A ) = det ( A') ,where A' is the transpose of A , obtained by the formula A' =( a ji ), thereby rotating the array about the main diagonal. If a square matrix is triangular, meaning th at all its entries above the main diagonal are 0,then det ( A ) turns out to be exactly the product of the diagonal entries.Another useful concept is that of eigenvalue. A scalar is said to be an eigenva lue for a transformation T if there is a nonzero vector υwith T (υ) λυ. It is then clear that the eigenvalues will be those numbers λ∈ K such that T -λI is a singular transformation. Any vector in the null space of T -λI is called an eigenvector of T associated with eigenvalue λ, and their span the eigenspace, E λ. It is invariant under the action of T , meaning that T carrie s Eλinto itself. The eigenvalues of T are then exactly the set of roots of the polynomial p(λ) =det ( T -λI ).If A is a matrix representing T ,then one h as p (λ) det ( A -λI ), which permits one to find the eigenvalues of T easil y if the dimension of V is not too large, or if the matrix A is simple enough. The eigenvalues and eigenspaces of T provide a means by which the nature and structure of the linear transformation T can be examined in detail.Vocabularylinear algebra 线性代数non-singular 非奇异field 域isomorphism 同构vector 向量isomorphic 同构scalar 纯量,无向量 matrix 矩阵(单数)vector space 向量空间matrices 矩阵(多数)span 生成,长成determinant 行列式independence 无关(性),独立(性) array 阵列dependence 有关(性) diagonal 对角线linear combination 线性组合 triangular 三角形的basis 基(单数) entry 表值,元素basis 基(多数) eigenvalue 特征值,本征值dimension 维eigenvector 特征向量linear transformation 线性变换 invariant 不变,不变量null space 零空间 row 行rank 秩 column 列singular 奇异 system of equations 方程组homogeneous 齐次Notes1. If U = { u 1, u 2,…}is a collection of points in a linearspace V , then the (linear) span of the set U is the set of all points of the form ∑c i u i , w where c i ∈K ,and all but a finite number of scalars c I are 0.意思是:如果U = { u 1, u 2,…}是线性空间V 的点集,那么集 U 的(线性)生成是所有形如∑c i u i的点集,这里c i ∈ K ,且除了有限个c i外均为0.2. A finite set { u 1, u 2,…, u k}is said to be linearly independent if the only way to write 0 = ∑c i u I is by choosing all the c i= 0.这一句可以用更典型的句子表达如下: A finite set { u 1, u 2,…, u k} is said to be linearly independen t in V if ∑c i u i is by choosing all the c i= 0.这里independent 是形容词,故用linearly修饰它. 试比较F(x) is a continuous periodic function.这里periodi c 是形容词但它前面的词却用continuous 而不用continuously,这是因为continuous 这个词不是修饰periodi c而是修饰作为整体的名词periodic function.3. Then these define isomorphisms of V onto K n and W onto K M respectively, and these in turn inducea linear transformation A between these.这里第一个these代表前句的两个基(basis);第二个these代表isomorphisms;第三个these代表什么留给读者自己分析.4. The least satisfactory aspect of linear algebra is still the theory of determinants-意思是:线性代数最令人不满意的方面仍是有关行列式的理论.least satisfactory 意思是:最令人不满意.5. If a square matrix is triangular, meaning that all its entries above the main diagonal are 0,then det ( A ) turns out to be exactly the product of the diagonal entries.意思是:如果方阵是三角形的,即所有在主对角线上方的元素均为零,那末det( A ) 刚好就是对角线元素的乘积.这里meaning that 可用that is to say 代替,turns out to be解为”结果是”.ExerciseI. Answer the following questions:1. How can we define the linear independence of an infinite set?2. Let T be a linear transformation (T: V →W ) whose associated matrix is A.Give a criterion for the non-singularity of the transformation T.3. Where is the entry a45of a m -by- n matrix( m>4; n>5) located ?4. Let A , B be two rectangular matrices.Under what condition is the product matrix well-defined ?II.Translate the following two examples and their proofs into Chinese:1.Example1. Let u k= t k ,k=0,1,2,... and t real. Show that the set ｛u 0,u1,u2,…｝is independent.Proof: By the definition of independence of an infinite set, it suffices to show that for each n ,the n+ 1 polynomials u0,u1,...,u n are independent.A relation of the form ∑n k=0c k u k=0 means ∑n k=0c k t k=0 for all t.When t=0,this gives c0=0.Differentiating both sides of ∑n k=0c k t k=0 and setting t=0,we fi nd that c1=0.Repeating the process,we find that each cocfficient is zero2. Example 2. Let V be afinite dimensional linear space, Then every finite basis for V has the same nu mber of elements.Proof: Let S and T be two finite bases for V. Suppose S consists of k elemnts and T consists of m e lements.Since S is independent and spans V ,every set of k+1 elements in V is dependent.Therefore eve ry set of more than k elements in V is dependent. Since T is an independent set , we must have m<k. The same argument with S and T interchanged shows that k<m. Hence k=m.III.Translate the following sentences into English:1.设 A 是一矩阵。

11数学专业英语词汇A2

11数学专业英语词汇A2 4.1Cauchy Mean Value Theorem 柯西中值定理mathematical analysis 数学分析sequence limit 数列极限determinant 行列式monotonic increasing 单调递增4.2二次型quadratic form凸函数convex function凹函数concave function标准型standard form规范型normal form拐点breaking point非退化线性替换nonsingular linear replacement4.3generated subspace 生成子空间linear subspace 线性子空间quadratic matrix 二次型矩阵4.4inertia theorem 惯性定理contract relationship 合同关系positive definite matrix 正定矩阵mapping 映射linear space 线性空间Taylor theorem 泰勒定理4.5will power 意志力indefinite integral 不定积分Taylor’s formula 泰勒公式subspace 子空间4.6subspace and straight 子空间的直和indefinite integral 不定积分identity mapping 恒等映射4.7• theorem of nested interval区间套定理•the Euler transform 欧拉变换•changing integral 换元积分•the subsection integral 分部积分4.8变限积分：variable limit integral微积分学基本定理：calculus basic theorem积分型余项：integral type of more than柯西型余项：Cauchy type of more than定积分：definite integral牛顿-莱布尼茨公式：formula of Newton-Lebniz 对角矩阵：diagonal matrix线性变换：linear transformation。

数学专业英语

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

数学专业英语词汇摘要数学是一门广泛的学科，涉及到各种概念、理论和方法。

为了有效地学习和交流数学，我们需要掌握一些基本的数学专业英语词汇。

本文根据不同的数学分支，列出了一些常见的数学术语及其中英文对照，包括算术、代数、几何、三角学、微积分、概率论和统计学等。

本文旨在帮助数学专业的考研复试者和其他对数学感兴趣的人士提高英语水平，增强数学素养。

算术（Arithmetic）算术是数学的基础，主要研究数字和基本运算。

以下是一些常用的算术术语及其中英文对照：中文英文数字number整数integer自然数natural number偶数even number奇数odd number质数prime number合数composite number分数fraction小数decimal有理数rational number无理数irrational number实数real number复数complex number运算operation加法addition减法subtraction乘法multiplication除法division指数exponentiation对数logarithm四则运算arithmetic operations平方根square root立方根cube root四次根fourth rootn次根nth root代数（Algebra）代数是研究符号和规则的一门数学分支，主要用于解决方程和不等式。

以下是一些常用的代数术语及其中英文对照：中文英文符号symbol变量variable常量constant系数coefficient项term表达式expression方程equation不等式inequality解solution根root一元方程equation in one variable二元方程equation in two variables多元方程equation in more than two variables一次方程linear equation二次方程quadratic equation高次方程higher degree equation方程组system of equations代数式algebraic expression多项式polynomial单项式monomial二项式binomial几何（Geometry）几何是研究形状、大小和位置的一门数学分支，主要用于描述空间中的对象。

数学专业英语

专业英语1/2 ：a half 或one half1/4：a quarter(fourth)或one quarter(fourth) 1/1234：one over a thousand two hundred and thirty-four4/5：four fifths 或four over five113/300：one hundred and thirteen over three Hundred872：two and seven over eight 或two andseven eighths20o ：wenty degrees 6’ ：six minutes; six feet 10” ：ten seconds; ten inches 2% ：two percent 5‰：five per millea ＋b a plus b; (positive)a －b a minus b; (negative) a±b a plus or minus b a×b a multiplied by b; (times) a÷b a divided by b;a:b the ratio of a to ba=b a is equal to b; a equals to b a ≠b a is not equal to b; a is not b a ＞b a is greater than ba ＜b a is less than ba ≣b a is greater than or equal to b a ≢b a is less than or equal to ba ≡b a is identically equal to b; a is of identity to ba ba is approximately equal to bsquare root of an th root of aa the absolute value of aalgebra 代数学 geometrical 几何的algebraic 代数的 identity 恒等式arithmetic 算术, 算术的 measure 测量，测度axiom 公理numerical 数值的, 数字的conception 概念，观点 operation 运算 constant 常数 postulate 公设logical deduction 逻辑推理 proposition 命题division 除，除法 subtraction 减，减法 formula 公式term 项，术语trigonometry 三角学 variable 变化的，变量angle 角 cube 立方体arc 弧 curved line 曲线major arc 优弧 cylinder 柱体minor arc 劣弧 diameter 直径architect 建筑师 dimention 维数，大小breadth 宽度 endpoint 端点chord 弦 equidistant 等距离的circumference 周长 line segment 直线段cone 圆锥 radius 半径critical 临界的 pyramid 棱锥 ray 射线 sphere 球，球面semicircle 半圆 surface 面，曲面solid 立体的，立体 thickness 厚度brace 大括号 roster 名册consequence 结论，推论roster notation 枚举法designate 标记，指定rule out 排除，否决diagram 图形，图解subset 子集distinct 互不相同的the underlying set 基础集distinguish 区别，辨别universal set 全集divisible 可被除尽的validity 有效性dummy 哑的，哑变量visual 可视的even integer 偶数visualize 可视化irrelevant 无关紧要的void set(empty set) 空集conversely 反之geometric interpretation 几何意义correspond 对应induction 归纳法deducible 可推导的proof by induction 归纳证明difference 差inductive set 归纳集distinguished 著名的inequality 不等式entirely complete 完整的integer 整数Euclid 欧几里得interchangeably 可互相交换的Euclidean 欧式的intuitive直观的the field axiom 域公理irrational 无理的irrational number 无理数rational 有理的the order axiom 序公理rational number 有理数ordered 有序的reasoning 推理product 积scale 尺度，刻度quotient 商sum 和abscissa 横坐标horizontal 水平的analytic geometry 解析几何hypotenuse 斜边arbitrary 任意的integral 整数的,积分的,积分Cartesian 笛卡儿的intersect 相交Rene Descartes 笛卡儿intertwine 融合，结合circular 圆的，圆周的leg 侧边，直角边coordinate 坐标ordinate 纵坐标the origin 坐标原点segment 线段parabolic 抛物线的three-dimensional 三维的perpendicular 垂直的triangle 三角形polygonal 多边形的the unit distance 单位长度quadrant 象限vector 向量, 矢量reduce 归结，化简vertical 竖直的课后答案2-1（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。

(抱佛脚必备)数学专业英语重点词汇

【Mathematical analysis】1 、上确界(supremum value) 下确界(infimum value)2 、极限(limit) 导数(derivative) 一阶导数(firstderivative) 二阶导数(second derivate)偏导数(partialderivative)方向导数(directional derivative)3 、泰勒展式(Taylor’s expansion) 洛必达法则(L’Hopital’srule) 链式法则(chain rule)连续可微(continuouslydifferentiable)4、微积分 (calculus)微分(differential)级数(series)积分(integral)原函数 (antiderivative)不定积分(indefinite integral)定积分(definite integral)5 、调和级数(harmonic series)马克劳林级数(Maclaurin series)交错级数 (alternating series)傅里叶级数(Fourier series)6 、二重积分(double integral)三重积分(triple integral)多重积分(multiple integral) 格林公式(Green’s formula)斯托克斯定理(Stokes’ theorem)7、收敛(convergence)发散(divergence)一致收敛(uniformly convergent)绝对收敛(absolutely convergent)条件收敛(conditionally convergent) 连续(continuity) 一致连续(uniformly continuous)8 、指数函数(exponential function)对数函数(logarithmicfunction)幂函数(power function)初等函数(elementary function)三角函数(trigonometric function) 调和函数(harmonic function) 周期函数(periodic function) 可微函数(differential function)单调函数(monotonefunction)9 、素数(prime number) 正数(positive number) 负数(negative number) 相反数(opposite number) 自然数(natural number) 有理数(rational number)无理数(irrational number)实数(real number)虚数(imaginarynumber)复数(complex number) 10、等式(equality)不等式(inequality)三角不等式(triangle inequality)勾股定理(Pythagorean theorem)无穷大(infinity)无穷小(infinitesimal)【Linear algebra】1、向量(vector)秩(rank)行列式(determinant)线性方程(linear equation)2 、奇异矩阵(singular matrix)可逆矩阵(invertible matrix)逆矩阵(inverse matrix) 转置矩阵(transposed matrix)酉矩阵(unitary matrix)对称矩阵(symmetric matrix)正定矩阵(positive definite matrix)负定矩阵(negative definitematrix) 雅克比矩阵(Jacobian matrix)3 、迹(trace)主子式(principle minor)代数余子式(algebraic cofactor)4 、二次型(quadratic form)标准型(normal form)最小多项式(minimal polynomial) 特征多项式(characteristicpolynomial)约当块(Jordan block)5 、特征值(eigenvalue)特征向量(eigenvector)约当标准型(Jordan canonical form)6 、几何重数(geometric multiplicity)可对角矩阵(diagonalizable matrix) 【Analytic Geometry】1 、平面几何(plane geometry) 立体几何(solid geometry)射影几何(projective geometry)代数几何(algebraicgeometry)黎曼几何(Riemann geometry)微分几何(differential geometry)几何分析(geometryanalysis)分形几何(fractal geometry)2 、平行线(parallel line) 中线(median line) 直线(straightline) 垂直线(vertical line)水平线(horizontal line)切线(tangent line)法线(normal line)3 、抛物线(parabola)椭圆(ellipse)双曲线(hyperbola)斜率(slope) 【Complex analysis】1 、解析函数(holomorphic function) 留数定理(residualtheorem) 柯西积分公式 (Cauchy’s integral formula)2 、定义域(domain) 值域(range) 像(image) 中值定理(mean value theorem)3 、凸函数(convex function) 凸集(convex set) 变分不等式(variational inequality) 变分法(calculus of variation)线性规划(linear programming)【Real analysis】1 、测度(measure) 可测函数(measure function) 可积函数(integrable function) 平方可积函数(square integrablefunction)黎曼积分(Riemann integral) 勒贝格积分(Lebesgue integral)【Functional analysis】1 、内积(inner product) 向量积(cross product)范数(norm)2 、向量空间(vector space)距离空间(distance space)拓扑空间(topological space) 测度空间(measure space)线性空间(linear space)内积空间(inner product space) 希尔伯特空间(Hilbert space) 赋范空间(normed space) 巴拿赫空间(Banach space)完备空间(complete space)可分空间(separable space) 概率空间(probability space)3 、有穷维的(finite dimensional)无穷维的(infinitedimensional)基底(basis) 线性相关(linear dependence) 线性无关(linear independence) 最佳逼近(bestapproximation ) 最大值原理( maximum principle) 比较原理( comparison principle)最小二乘(least squares)4、泛函(functional)线性算子(linear operator)有界线性算子(bounded linear operator) 有界线性泛函(boundedlinear functional) 闭图像定理(closed graph theorem)一致有界定理(uniform boundedness principle)不动点定理(fixed point theorem)压缩映照定理(contraction mapping theorem)【Supplements】1 、引理(lemma)推论(corollary)公理(axiom)命题(proposition)猜想(conjecture) 数学归纳法(mathematical induction) 充分性(sufficiency) 必要性(necessity) 反例(counterexample)2、加法(addition)减法(subtraction)乘法(multiplication)除法(division)3、理想(ideal)环(ring)单位(unit)陪集(coset)群(group)域(field)置换群(permutation group)有限群(finite group)同态(homomorphism) 同构(isomorphism)维数(dimension)4 、抽象代数(abstract algebra) 广义函数论(theory of distribution) 弦理论(stringtheory) 随机变量(random variable) 动力系统(dynamical system) 偏微分方程(partial differentialequation)。

数学专业英语短语

2.1数学、方程与比例1.alike 一样2. bring out 产生，带来3.carry out 得出，完成4. come from sth 由···得到5.deal with sth 处理某事6.express change the term about 把这些项变形7.be equal to sth 等于某事8.bu full of sth ./sb 充满某物9.in turn 反之10.make sth equal to sth 取某式等于某事11.no matter 无论12.occupy 获得，占用13.occur 出现14.on the performance of sth 执行某事15.promote 促进16.resulting method 产生方法2.21.appreciation of(for) sth./sb. 对某物或某人的欣赏2.awareness of sth./sb. 某物或某人的意识3.blind acceptance of sth. 盲目接受某物4.change the terms about 变形5.be composed of sth./sb. 某物或某人组成6.be derived from sth. 起源于某事7.divide sth.into sth. 把某物分成···8.be equidistant from sth. 从···到···距离相等9.expect to do sth. 期望去做某事10.be familiar with sth./sb. 对某物或某人熟悉11.gain 获得，得到12.be led away from sth. 远离某物13.prerequisite to sth. 某事物的先决条件14.refer to sth./sb. as sth./sb. 把···称为15.treatment of sth. 处理某事，对···的处理16.work with sth. 与···一起工作，与···一起运用2.31.analogous to sth./sb. 类同于2.be concerned with sth./sb. 与··有关；关于3.consist of sth./sb. 由···组成4.be contained in sth. 包含于5.distinguish between sth./sb.and sth./sb. 把···和···区分开6.be divisible by sth. 可被···除尽7.be referred to as sth./sb. 被称为8.rely on sth./sb. 依赖9.be said to sth./sb. 被称为10.take the place of sth./sb. 代替11.think of sth./sb. as sth./sb. 把···看成12.vary from sth./sb. to sth./sb. 由···到···的变化2.41.be accepted as sth./sb. 被接受为2.clarify 阐明3.convenient method 简易方法4.depend on sth./sb. 取决于5.be familiar with sth./sb. 熟知6.as illustrated in Fig.1 如图1所示7.mean sth./sb.by sth./sb. 意思是8.by means of sth. 依靠9.more precise 更确切地10.motivate 激发11.be presented in sth. 存在于···中12.be shared by sth. 共享给13.a very worthwhile aid 非常有价值的14.without any reference to geometry 不借助几何2.51.arrive at 获得2.as mentioned earlier 如前述3.by no other 没有别的4.confine our attention to sth./sb. 把注意力限定在···5.a geometric figure 一个几何圆6.hypotenuse of a right triangle 直角三角形斜边7.be intimately intertwined 亲密缠绕8.locate the point 设定点的位置9.a little familiarity with 稍微熟知10.a much better way 好得当的方法11.mutually perpendicular planes 相当垂直的平面12.reduce sth. to sth. 使···简化为···13.the rudiments of calculus 微积分的入门14.three units to the right of the y-axis y轴右边的三个单位15.two units above the x-axis x轴上方的两个单位16.with appropriate regard for signs 相关合适的符号2.61.associate with sth./sb. 与···关联，对应于2.certain kinds of sth./sb. 固定类型的3.do with sth. 处理4.be expressed in the form 以···形式表示5.be familiar to sb. 熟知6.be fed into the machine 向机器投放7.independent of sth./sb. 不依靠8.be much too limited in 太过受限制于···中9.pair sth./sb. with sth./sb. 与···配对10.place no restriction on 不受限于···11.in a quantitative fashion 在一个定量模式中12.refer to sth./sb. 提出13.be referred to as sth./sb. 称为14.without counting 无须计算2.71.carry on 继续2.carries over to 转移到3.converge separately 分别收敛4.decompose into 分解为5.extend sth. to sth. 延伸至6.formulate the theorems 证明该定理7.be known as sth./sb. 被称为8.be labeled with 加上，贴上9.leave sth. For sb. to do 留···给···去做10.make the convention 约定，协定11.restrict x to take only integer values 限定x值只取整数值12.a set of instructions 指定集13.similar to sth./sb. 与···相似14.somewhat 某种，有点15.analogy between sth./sb. And sth./sb. 与···之间类似16.unless otherwise specified 除非另加申明2.81.approach sth. through sth. 通过···；超过···2.begin with 开始于pare with 与···相比4.happen to sth./sb. 恰好5.be interpreted geometrically 几何意义6.joint sth to sth 连接···与···7.make the convention 约定8.move along toward 继续向前9.the total decrease in velocity 速度总减少10.with respect to 关于···2.91.arise from(in) 由···产生2.be classified under 被分类为3.by is meant 指的是4.deduce from 从···得出结论5.do enable to do 让某人能做某事6.enter into 参与进来7.infinitely many 无穷多8.be inspired by 被···激发9.in term of 依据10.a knowledge of ···的知识11.a large variety of 多样的12.must be of the form of 一定是···的形式13.a prescribed value 一个规定值14.radioactive substance 发射性物质15.be required to do 需要去做16.at some particular instant 某个具体瞬间2.101.agree with 适合于；与···一致2.base on 在···基础上3.be identical to 同一的，和···相同4.by induction on n n归纳法5.it suffices to do 满足做某事6.reduce to 化简为7.relative to 与···相关8.be restricted to 被局限于···9.the same argument with 与···相同的讨论10.span the space 张成空间11.by subtraction form 从···中减去12.take in a given order 给定阶13.uniquely determine 惟一确定2.111.assert 主张2.be assigned to 赋予3.be encountered in some place 在某个地方相遇4.execute 执行5.be phrased in term of 以···语句表达6.produce from 从···获得7.specify 特定，指定8.universe of discourse 论域2.121.be acquired through 通过··取得2.closely similar 近似···3.coin tossing掷硬币plete body of ···完全体5.conceive 构思6.draw from 从···画出7.field trials 现场实验8.learn about 了解9.make inference 做推断10.originate from 源于11.particular to 特有的12.perform an experiment 做实验13.be subjected to 经受···14.sustain 维持15.the very definition 仅是概念。

2023大学_数学专业英语试题及参考答案

2023数学专业英语试题及参考答案数学专业英语试题一、词汇及短语1. For a long period of the history of mathematics, the centric place of mathematical methods was occupied by the logical deductions “在数学史的很长的时期内，是逻辑推理一直占据数学方法的中心地位”2. An equation is a statement of the equality between two equal numbers or number symbols.equation ：“方程”“等式”等式是关于两个数或数的符号相等的'一种陈述3. In such an equation either the two members are alike, or become alike on performance of the indicated operation. 这种等式的两端要么一样，要么经过执行指定的运算后变成一样。

注“two members”表等号的两端alike 相同的一样的On the performance of …中的“on”引导一个介词短语做状语Either…or…4. is true “成立”5. to more and change the terms移次和变形without making the equation untrue 保持方程同解数学专业英语试题二、句型及典型翻译1. change 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。

数学专业英语

数学专业英语（1）、Given ε>0,there exists a number N >0 such that ε<-a a n for all N n ≥ 译文：对给定的ε>0，存在一个数N >0使得不等式ε<-a a n 对所有的N n ≥都成立。

（2）、The function )(x f approaches infinity as x tends to zero.译文：当x 趋于0时，函数)(x f 趋于∞。

（3）、Suppose D is an open set with its closure in G .译文：假定D 是一个开区间，且其闭包在G 中。

（4）、Suppose )(x f is a function on domain D such that M x f <)( for all x ∈D ,where M is a constant .译文：假定)(x f 是区域D 上的一个函数，使得对所有x ∈D ，不等式M x f <)(成立，其中M 是一个常数。

（可用“satisfying ”代替上述“such that ”。

）（5）、表示推理的根据常用“by 短语”，有时也用“according to ”。

By Lemma 2 we have x y ≥.译文：根据引理2可推出x y ≥。

（6）、有时用现在分词表示“经过……而得到……”（推论）。

Integrating the above inequality twice,we see that . log )(0t t c t y ≥译文：将上一不等式两次积分得到. log )(0t t c t y ≥。

（7）、表示充分必要条件The sufficient and necessary condition for the equality isα>0 and ≥p 3. 译文：该等式成立的充分必要条件是α>0 且≥p 3。

数学专业英语课后答案

数学专业英语课后答案1、He kept walking up and down, which was a sure（）that he was very worried. [单选题] *A. sign(正确答案)B. characterC. natureD. end2、20．Jerry is hard-working. It’s not ______ that he can pass the exam easily. [单选题] * A．surpriseB．surprising (正确答案)C．surprisedD．surprises3、--What’s the weather like today?--It’s _______. [单选题] *A. rainB. windy(正确答案)C. sunD. wind4、Many of my classmates are working _______volunteers. [单选题] *A. as(正确答案)B. toC. atD. like5、Mary is interested ______ hiking. [单选题] *A. onB. byC. in(正确答案)D. at6、We need a _______ when we travel around a new place. [单选题] *A. guide(正确答案)B. touristC. painterD. teacher7、While they were in discussion, their manager came in by chance. [单选题] *A. 抓住时机C. 碰巧(正确答案)D. 及时8、Our campus is _____ big that we need a bike to make it. [单选题] *A. veryB. so(正确答案)C. suchD. much9、57．Next week will be Lisa's birthday. I will send her a birthday present ________ post. [单选题] *A．withB．forC．by(正确答案)D．in10、The manager demanded that all employees _____ on time. [单选题] *A. be(正确答案)B. areC. to be11、He has two sisters but I have not _____. [单选题] *A. noneB. someC. onesD. any(正确答案)12、______! It’s not the end of the world. Let’s try it again.（）[单选题] *A. Put upB. Set upC. Cheer up(正确答案)D. Pick up13、My brother usually _______ his room after school. But now he _______ soccer. [单选题] *A. cleans; playsB. cleaning; playingC. cleans; is playing(正确答案)D. cleans; is playing the14、The museum is _______ in the northeast of Changsha. [单选题] *A. sitB. located(正确答案)C. liesD. stand15、______ my great joy, I met an old friend I haven' t seen for years ______ my way ______ town. [单选题] *A. To, in, forB. To, on, to(正确答案)C. With, in, toD. For, in, for16、In the closet（）a pair of trousers his parents bought for his birthday. [单选题] *A. lyingB. lies(正确答案)c. lieD. is lain17、44．—Hi, Lucy. You ________ very beautiful in the new dress today.—Thank you very much. [单选题] *A．look(正确答案)B．watchC．look atD．see18、They all choose me ______ our class monitor.（）[单选题] *A. as(正确答案)B. inC. withD. on19、My mother’s birthday is coming. I want to buy a new shirt ______ her.（）[单选题] *A. atB. for(正确答案)C. toD. with20、--Could you please tell me _______ to get to the nearest supermarket?--Sorry, I am a stranger here. [单选题] *A. whatB. how(正确答案)C. whenD. why21、?I am good at schoolwork. I often help my classmates _______ English. [单选题] *A. atB. toC. inD. with(正确答案)22、He was very excited to read the news _____ Mo Yan had won the Nobel Prize for literature [单选题] *A. whichB. whatC. howD. that(正确答案)23、Becky is having a great time ______ her aunt in Shanghai. （）[单选题] *A. to visitB. visitedC. visitsD. visiting(正确答案)24、In the future, people ______ a new kind of clothes that will be warm when they are cold, and cool when they’re hot.（）[单选题] *A. wearB. woreC. are wearingD. will wear(正确答案)25、This message is _______. We are all _______ at it. [单选题] *A. surprising; surprisingB. surprised; surprisedC. surprising; surprised(正确答案)D. surprised; surprising26、Your homework must_______ tomorrow. [单选题] *A. hand inB. is handed inC. hands inD. be handed in(正确答案)27、Since the war their country has taken many important steps to improve its economic situation. [单选题] *A. 制定B. 提出C. 讨论D. 采取(正确答案)28、How _______ Grace grows! She’s almost as tall as her mother now. [单选题] *A. cuteB. strongC. fast(正确答案)D. clever29、_____ is not known yet. [单选题] *A. Although he is serious about itB. No matter how we will do the taskC. Whether we will go outing or not(正确答案)D. Unless they come to see us30、You cannot see the doctor _____ you have made an appointment with him. [单选题] *A. exceptB.evenC. howeverD.unless(正确答案)。

数学专业英语短语

数学专业英语2-11C(精选5篇)

数学专业英语2-11C（精选5篇）第一篇：数学专业英语2-11C数学专业英语论文数学专业英语论文英文原文：2-12CSome basic principles of combinatorial analysisMany problems in probability theory and in other branches of mathematics can be reduced to problems on counting the number of elements in a finite set. Systematic methods for studying such problems form part of a mathematical discipline known ascombinatorial analysis. In this section we digress briefly to discuss some basic ideas in combinatorial analysis that are useful in analyzing some of the more complicated problems of probability theory.If all the elements of a finite set are displayed before us, there is usually no difficulty in counting their total number. More often than not, however, a set is described in a way that makes it impossible or undesirable to display all its elements. For example,we might ask for the total number of distinct bridge hands that can be dealt. Each player is dealt 13 cards from a 52-card deck. The number of possible distinct hands is the same as the number of different subsets of 13 elements that can be formed from a set of 52 elements.Since this number exceeds 635 billion, a direct enumeration of all the possibilities is clearly not the best way to attack this problem; however, it can readily be solved by combinatorial analysis.This problem is a special case of the more general problem of counting the number of distinct subsets of k elements that may be formed from a set of n elements (When we say that a set has n elements,we mean that it has n distinct elements.Such a set is sometimes called an n-element set.),where n k. Let us denote this number by f(n,k).It has long been known thatn(12.1)f(n,k)k,n where, as usual k denotes the binomial coefficient,n n!k k!(n k)!52In the problem of bridge hands we havef(52,13)13635,013,559,600different hands that a player can be dealt.There are many methods known for proving (12.1). A straightforward approach is to form each subset of k elements by choosing the elements one at a time. There are n possibilities for the first choice, n 1 possibilities for the second choice, and n(k1) possibilities for the kth choice. If we make all possible choices in this1manner we obtain a total ofn(n1)(n k1)n! (n k)!subsets of k elements. Of course, these subsets are not all distinct. For example, ifk3the six subsetsa,b,c,b,c,a,c,a,b,a,c,b,c,b,a, b,a,carc all equal. In general, this method of enumeration counts each k-element subset exactly k! times. Therefore we must divide the number n!/(n k)! by k! to n obtain f(n,k). This gives us f(n,k)k, as asserted.译文：组合分析的一些基本原则许多概率论和其他一些数学分支上的问题，都可以简化成基于计算有限集合中元素数量的问题。