数学专业英语
专业英语
1/2 ：a half 或one half
1/4：a quarter(fourth)或one quarter(fourth) 1/1234：one over a thousand two hundred and thirty-four
4/5：four fifths 或four over five
113/300：one hundred and thirteen over three Hundred
8
72：two and seven over eight 或two and
seven eighths
20o ：wenty degrees 6’ ：six minutes; six feet 10” ：ten seconds; ten inches 2% ：two percent 5‰：five per mille
a ＋
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 b
a=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 b
a ＜
b a is less than b
a ?
b a is greater than or equal to b a ?b a is less than or equal to b
a ≡
b a is identically equal to b; a is of identity to b
a b
a is approximately equal to b
square root of a
n th root of a
a the absolute value of a
algebra 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。
Mathematics comes from man’s social practice, for example, industrial and agricultural production, commercial activities, military operations and scientific and technological researches.
（3）符号在数学中起着非常重要的作用，它常用于表示概念和命题。
Notations are a special and powerful tool of mathematics and are used to express conceptions and propositions very often.
（5）方程与算数的等式不同在于它含有可以参加运算的未知量。
Equation is different from arithmetic identity in that it contains unknown quantity which can join operations.
（7）方程很有用，可以用它来解决许多实际应用问题。
Equations are of very great use. We can use equations in many mathematical problems.
2-2（1）许多专家都认为数学是学习其他科学技术的必备基础和先决条件。
Many experts recognize that mathematics is the necessary foundation and prerequisite of studying other science technology.
（3）几何的学习使学生在思考问题时更周密和审慎，他们将不会盲目接受任何结论。
In studying geometry, the student is taught to think clearly and critically and he is led away from the practice of blind acceptance of any conclusions.
（5）几何主要不是研究数，而是形，例如三角形，平行四边形和圆，虽然它也与数有关。Geometry mainly studies hot numbers but figures such as triangles, parallelograms and circles, though it is related with numbers.
（6）一个立体（图形）有长、宽和高；面（曲面或平面）有长和宽，但没有厚度；线（直线或曲线）有长度，但既没有宽度，也没有厚度；点只有位置，却没有大小。
A solid (figure) has length, width and height. A surface (curved surface or plane surface) has length and width, but no thickness. A line (straight line or curved line) has length, but no width and thickness. A point has position, but no dimension.
（7）射线从某个点出发无限延伸；两条从同一点出发的射线构成了角。这两条射线称为这个角的两边，当这两边位于同一直线上且方向相反时，所得的角是平角。
A ray starts from a point and extends infinitely far. Two rays starting from one point form an angle, which are called two edges of the angle. When two edges lie in the same line and have opposite direction named plane angle.
（8）平面上的闭曲线当其中每一点到一个固定点的距离均相等时叫做圆。这个固定点称为圆心，经过圆心且其两个端点在圆周上的线段称为这个圆的直径，直径的一半叫做半径，这条曲线的长度叫做周长。
A circle is a closed curve lying in one plane, all points of which are equidistant from a fixed point. The fixed point called the center. A diameter of a circle is a line segment through the center of the circle with endpoints on the circle. Half of the diameter is called radius. The length of the circle is called circumference.
2-3（未找到）
2-4 （1）严格说，这样描述整数是不完整的，因为我们并没有说明“依此类推”或“反复加1”的含义是什么。
Strictly speaking, this description of the positive integers is not entirely complete because we have not explained in detail what we mean by the expressions “and so on”, or “repeated addition of 1”.
2-5（1）计算图形的面积是积分的一种重要应用。
The calculation of figure area is the important application of the integral.
（4）选取两条互相垂直的直线，其中一条是水平的，另一条是竖立的，把它们的交点记作O，称为原点。
Two perpendicular reference lines are chosen, one horizontal, the other vertical. Their point of intersection, denoted by O, is called the origin.
数学专业英语
数学专业英语课后答案
2.1数学、方程与比例 词组翻译 1.数学分支branches of mathematics，算数arithmetics，几何学geometry，代数学algebra，三角学trigonometry，高等数学higher mathematics，初等数学elementary mathematics，高等代数higher algebra，数学分析mathematical analysis，函数论function theory，微分方程differential equation 2.命题proposition，公理axiom，公设postulate，定义definition，定理theorem，引理lemma，推论deduction 3.形form，数number，数字numeral，数值numerical value，图形figure，公式formula，符号notation(symbol)，记法/记号sign，图表chart 4.概念conception，相等equality，成立/真true，不成立/不真untrue，等式equation，恒等式identity，条件等式equation of condition，项/术语term，集set，函数function，常数constant，方程equation，线性方程linear equation，二次方程quadratic equation 5.运算operation，加法addition，减法subtraction，乘法multiplication，除法division，证明proof，推理deduction，逻辑推理logical deduction 6.测量土地to measure land，推导定理to deduce theorems，指定的运算indicated operation，获得结论to obtain the conclusions，占据中心地位to occupy the centric place 汉译英 （1）数学来源于人类的社会实践，包括工农业的劳动，商业、军事和科学技术研究等活动。 Mathematics comes from man’s social practice, for example, industrial and agricultural production, commercial activities, military operations and scientific and technological researches. （2）如果没有运用数学，任何一个科学技术分支都不可能正常地发展。 No modern scientific and technological branches could be regularly developed without the application of mathematics. （3）符号在数学中起着非常重要的作用，它常用于表示概念和命题。 Notations are a special and powerful tool of mathematics and are used to express conceptions and propositions very often. （4）17 世纪之前，人们局限于初等数学，即几何、三角和代数，那时只考虑常数。Before 17th century, man confined himself to the elementary mathematics, i. e. , geometry, trigonometry and algebra, in which only the constants were considered. （5）方程与算数的等式不同在于它含有可以参加运算的未知量。 Equation is different from arithmetic identity in that it contains unknown quantity which can join operations. （6）方程又称为条件等式，因为其中的未知量通常只允许取某些特定的值。Equipment is called an equation of condition in that it is true only for certain values of unknown quantities in it. （7）方程很有用，可以用它来解决许多实际应用问题。
数学专业英语课文翻译(吴炯圻)第二章 2.
数学专业英语课文翻译(吴炯圻)第二 章 2. 数学专业英语3—A 符号指示集一组的概念如此广泛利用整个现代数学的认识是所需的所有大学生。集是通过集合中一种抽象方式的东西的数学家谈的一种手段。集，通常用大写字母：A、B、C、进程运行·、X、Y、Z ；小写字母指定元素：a、 b 的c、进程运行·，若x、y z.我们用特殊符号x∈S 意味着x 是S 的一个元素或属于美国的x如果x 不属于S，我们写xS.≠当方便时，我们应指定集的元素显示在括号内；例如，符号表示的积极甚至整数小于10 集{2,468} {2，，进程运行·} 作为显示的所有积极甚至整数集，而三个点等的发生。点的和等等的意思是清楚时，才使用。上市的大括号内的一组成员方法有时称为名册符号。涉及
到另一组的第一次基本概念是平等的集。DEFINITIONOFSETEQUALITY。两组A 和B，据说是平等的如果它们包含完全相同的元素，在这种情况下，我们写A = B。如果其中一套包含在另一个元素，我们说这些集是不平等，我们写 A = B。EXAMPLE1。根据对这一定义，于他们都是构成的这四个整数2，和8 两套{2,468} 和{2,864} 一律平等。因此，当我们用来描述一组的名册符号，元素的显示的顺序无关。动作。集{2,468} 和{2,2,4,4,6,8} 是平等的即使在第二组，每个元素 2 和 4 两次列出。这两组包含的四个要素2,468 和无他人；因此，定义要求我们称之为这些集平等。此示例显示了我们也不坚持名册符号中列出的对象是不同。类似的例子是一组在密西西比州，其值等于{M、我、s、p} 一组单词中的字母，组成四个不同字母M、我、s 和体育3 —B 子集S.从给定的集S，我们
数学专业英语第二版-课文翻译-converted
2.4 整数、有理数与实数 4－A Integers and rational numbers There exist certain subsets of R which are distinguished because they have special properties not shared by all real numbers. In this section we shall discuss such subsets, the integers and the rational numbers. 有一些R 的子集很著名，因为他们具有实数所不具备的特殊性质。在本节我们将讨论这样的子集，整数集和有理数集。 To introduce the positive integers we begin with the number 1, whose existence is guaranteed by Axiom 4. The number 1+1 is denoted by 2, the number 2+1 by 3, and so on. The numbers 1,2,3,…, obtained in this way by repeated addition of 1 are all positive, and they are called the positive integers. 我们从数字 1 开始介绍正整数，公理 4 保证了 1 的存在性。1+1 用2 表示，2+1 用3 表示，以此类推，由 1 重复累加的方式得到的数字 1,2,3，…都是正的，它们被叫做正整数。 Strictly speaking, this description of the positive integers is not entirely complete because we have not explained in detail what we mean by the expressions “and so on”, or “repeated addition of 1”. 严格地说，这种关于正整数的描述是不完整的，因为我们没有详细解释“等等”或者“1的重复累加”的含义。 Although the intuitive meaning of expressions may seem clear, in careful treatment of the real-number system it is necessary to give a more precise definition of the positive integers. There are many ways to do this. One convenient method is to introduce first the notion of an inductive set. 虽然这些说法的直观意思似乎是清楚的，但是在认真处理实数系统时必须给出一个更准确的关于正整数的定义。有很多种方式来给出这个定义，一个简便的方法是先引进归纳集的概念。 DEFINITION OF AN INDUCTIVE SET. A set of real number s is cal led an i n ductiv e set if it has the following two properties: (a) The number 1 is in the set. (b) For every x in the set, the number x+1 is also in the set. For example, R is an inductive set. So is the set . Now we shall define the positive integers to be those real numbers which belong to every inductive set. 现在我们来定义正整数，就是属于每一个归纳集的实数。 Let P d enote t he s et o f a ll p ositive i ntegers. T hen P i s i tself a n i nductive set b ecause (a) i t contains 1, a nd (b) i t c ontains x+1 w henever i t c ontains x. Since the m embers o f P b elong t o e very inductive s et, w e r efer t o P a s t he s mallest i nductive set. 用 P 表示所有正整数的集合。那么 P 本身是一个归纳集，因为其中含 1，满足(a)；只要包含x 就包含x+1, 满足(b)。由于 P 中的元素属于每一个归纳集，因此 P 是最小的归纳集。 This property of P forms the logical basis for a type of reasoning that mathematicians call proof by induction, a detailed discussion of which is given in Part 4 of this introduction.
数学专业英语(Doc版).10
学专业英语－How to Write Mathematics? How to Write Mathematics? ------ Honesty is the Best Policy The purpose of using good mathematical language is, of course, to make the u nderstanding of the subject easy for the reader, and perhaps even pleasant. The style should be good not in the sense of flashy brilliance, but good in the se nse of perfect unobtrusiveness. The purpose is to smooth the reader’s wanted, not pedantry; understanding, not fuss. The emphasis in the preceding paragraph, while perhaps necessary, might see m to point in an undesirable direction, and I hasten to correct a possible misin terpretation. While avoiding pedantry and fuss, I do not want to avoid rigor an d precision; I believe that these aims are reconcilable. I do not mean to advise a young author to be very so slightly but very very cleverly dishonest and to gloss over difficulties. Sometimes, for instance, there may be no better way t o get a result than a cumbersome computation. In that case it is the author’s duty to carry it out, in public; the he can do to alleviate it is to extend his s ympathy to the reader by some phrase such as “unfortunately the only known proof is the following cumbersome computation.” Here is the sort of the thing I mean by less than complete honesty. At a certa in point, having proudly proved a proposition P, you feel moved to say: “Not e, however, that p does not imply q”, and then, thinking that you’ve done a good expository job, go happily on to other things. Your motives may be per fectly pure, but the reader may feel cheated just the same. If he knew all abo ut the subject, he wouldn’t be reading you; for him the nonimplication is, qui te likely, unsupported. Is it obvious? (Say so.) Will a counterexample be suppl ied later? (Promise it now.) Is it a standard present purposes irrelevant part of the literature? (Give a reference.) Or, horrible dictum, do you merely mean th at you have tried to derive q from p, you failed, and you don’t in fact know whether p implies q? (Confess immediately.) any event: take the reader into y our confidence. There is nothing wrong with often derided “obvious”and “easy to see”, b ut there are certain minimal rules to their use. Surely when you wrote that so mething was obvious, you thought it was. When, a month, or two months, or six months later, you picked up the manuscript and re-read it, did you still thi nk that something was obvious? (A few months’ripening always improves ma nuscripts.) When you explained it to a friend, or to a seminar, was the someth ing at issue accepted as obvious? (Or did someone question it and subside, mu ttering, when you reassured him? Did your assurance demonstration or intimida
数学专业英语第二版的课文翻译
1－A What is mathematics Mathematics comes from man’s social practice, for example, industrial and agricultural production, commercial activities, military operations and scientific and technological researches. And in turn, mathematics serves the practice and plays a great role in all fields. No modern scientific and technological branches could be regularly developed without the application of mathematics. 数学来源于人类的社会实践，比如工农业生产，商业活动，军事行动和科学技术研究。反过来，数学服务于实践，并在各个领域中起着非常重要的作用。没有应用数学，任何一个现在的科技的分支都不能正常发展。From the early need of man came the concepts of numbers and forms. Then, geometry developed out of problems of measuring land , and trigonometry came from problems of surveying . To deal with some more complex practical problems, man established and then solved equation with unknown numbers ,thus algebra occurred. Before 17th century, man confined himself to the elementary mathematics, . , geometry, trigonometry and algebra, in which only the constants are considered. 很早的时候，人类的需要产生了数和形式的概念，接着，测量土地的需要形成了几何，出于测量的需要产生了三角几何，为了处理更复杂的实际问题，人类建立和解决了带未知参数的方程，从而产生了代数学，17世纪前，人类局限于只考虑常数的初等数学，即几何，三角几何和代数。The rapid development of industry in 17th century promoted the progress of economics and technology and required dealing with variable quantities. The leap from constants to variable quantities brought about two new branches of mathematics----analytic geometry and calculus, which belong to the higher mathematics. Now there are many branches in higher mathematics, among which are mathematical analysis, higher algebra, differential equations, function theory and so on. 17世纪工业的快速发展推动了经济技术的进步，从而遇到需要处理变量的问题，从常数带变量的跳跃产生了两个新的数学分支-----解析几何和微积分，他们都属于高等数学，现在高等数学里面有很多分支，其中有数学分析，高等代数，微分方程，函数论等。Mathematicians study conceptions and propositions, Axioms, postulates, definitions and theorems are all propositions. Notations are a special and powerful
数学专业英语
第二章精读课文-- 入门必修 2.1 数学方程与比例 （Mathematics，Equation and Ratio） 一、词汇及短语： 1. Cha nge the terms about变形 2. full of ：有许多的充满的 例The StreetS are full of people as on a holiday像假日一样，街上行人川流不息） 3. in groups of ten?? 4. match SOmething against sb. “匹配” 例Long ago ,when people had to Count many things ,they matChed them against their fingers. 古时候，当人们必须数东西时，在那些东西和自己的手指之间配对。 5. grow out of 源于由…引起 例Many close friendships grew out of common acquaintance 6. arrive at 得出（到达抵达达到达成） 例We both arrived at the Same COnclusion我们俩个得出了相同的结论） 7. stand for “表示，代表” 8. in turn “反过来，依次” 9. bring about 发生导致造成 10. arise out of 引起起源于 11. express by “用…表示” 12. occur 发生，产生 13. come from 来源于，起源于 14. resulting method 推论法 15. be equal to 等于的相等的
数学专业英语第二版2.2课文翻译
2.2 A 为什么要研究几何？ 我们为什么研究几何？开始此文本研究的学生也许会问，"什么是几何。什么可以预料从这项研究获得？" 许多居于领导地位的学术机构承认，所有学习这个数学分支的人都将得到确实的收益，许多学校把几何的学习作为入学考试的先决条件，从这一点上可以证明。 几何学起源于很久以前巴比伦人和埃及人测量他们被尼罗河洪水淹没的土地，希腊语几何来源于geo ，意思是“土地”，和metron, 意思是"度量值"。早在公元前2000 年，我们发现这些民族的土地测量者利用几何知识重新确定消失了的土地标志和边界。 几何是研究由线所组成的图形的科学。几何的学习是成功工程师、科学家、建筑师和制图员培训的重要部分。木匠、机械师、采石者、艺术家和设计师在他们的职业中都应用几何的知识。在这门课程中，学生将学到大量几何图形，例如线条、角、三角形、圆和许多种设计和模式。 所得的几何研究的最重要的目标之一是使学生在他的听力、阅读和思维更审慎。学习几何他远离盲目接受语句和思想的实践领导和教想清楚与批判前形成的结论。学习几何使他被领导远离语句和思想的盲目接受的做法，教导形成结论之前，考虑清楚和审慎。（学生通过几何的学习而达到的最重要目标是：在听，读，和思考时变得更加审慎。在学习几何的过程中，他们不再盲目地接受一些陈述和思想，而是在得出结论之前学会了清楚和审慎的思考。） 学习几何的学生可以获得许多其他不太直接的利益。这些人当中必须包括训练英语的精确使用和分析新情况与新问题时直达基本要素，以及利用毅力、创意和逻辑推理来解决问题的能力。（这些人当中必须包括训练英语的精确使用和分析新情况与新问题时直达基本要素的能力，以及利用毅力、创意和逻辑推理来解决问题。）大自然的创作将作为一种几何研究的副产品。一种鉴赏能力属于几何形成的规律和审美在人们的作品中。学生也应该发展数学与我们的文化和文明数学家贡献的意识。 2.2B 一些几何术语 1.立体和平面。立体是一个三维图形。立体的常见示例是立方体、球体、柱体、圆锥和棱锥。立方体有光滑、平整的六个面。这些面被称为平面曲面，或简称平面。平面曲面是二维的，有长度和宽度。黑板或桌面的表面都是平面曲面的一个例子。 2、线条和线段。我们都很熟悉线，但很难定义这术语。一条线可由在一张纸上移动的钢笔或铅笔标记表示。一条线，可以被看做是一维的，即只有长度。尽管我们绘制一条直线时会赋予它宽度和厚度，但是当考虑线时，只考虑痕迹的长度。点没有长度、宽度和厚度，但标记了一个位置。我们熟悉铅笔尖，针尖这样的表达。我们可以用一个小圆点来表示一个点，在它旁边用打印体大写字母来命名，如图2-2-1中的点A。 直线用大写字母标志它上面的两个点或者旁边的一个小写字母来命名。图2-2-2 的直线是读"直线AB "或者“直线l"。直线向两个方向无限延伸，没有终点。线上两点间的部分被称为一条直线段。直线段用两个端点命名。因此，图2-2-2，我们称为AB 是线l 的一条直线段。当不引起混淆时，表达"直线段AB 通常被线段AB代替，或者简称直线AB。 有三种线：直线、折线和曲线。弯曲的线条或，简单地说，曲线是指其中没有任何部分是直的折线是由连起来的直线段构成，如图2-2-3的ABCDE。 3.圆的部分。平面上的闭曲线当其中每点到一个固定点的距离均相当时叫做圆。固定点称为圆心。图2-2-4，O 是ABC 中心，或简单的O.A连接圆心到圆周上点的直线段称为圆的半径。OA，OB，以及OC都是圆O的半径。经过圆心并且两个端点在圆周上的直线段被称为圆的直径。直径等于两个半径。连接圆周上两点的任意直线段被称为弦。图2-2-4 圆的弦是ED。 从这个定义很明显直径是弦。圆周的任何部分都是一条弧线，如弧AE，其中由AE 表示。
数学专业英语(Doc版).12
数学专业英语－Linear Programming Linear Programming is a relatively new branch of mathematics.The cornerstone of this exciting field was laid independently bu Leonid V. Kantorovich,a Russ ian mathematician,and by Tjalling C,Koopmans, a Yale economist,and George D. Dantzig,a Stanford mathematician. Kantorovich’s pioneering work was moti vated by a production-scheduling problem suggested by the Central Laboratory of the Leningrad Plywood Trust in the late 1930’s. The development in the U nited States was influenced by the scientific need in World War II to solve lo gistic military problems, such as deploying aircraft and submarines at strategic positions and airlifting supplies and personnel. The following is a typical linear programming problem: A manufacturing company makes two types of television sets: one is black and white and the other is color. The company has resources to make at most 30 0 sets a week. It takes $180 to make a black and white set and $270 to mak e a color set. The company does not want to spend more than $64,800 a wee k to make television sets. I f they make a profit of $170 per black and white set and $225 per color set, how many sets of each type should the company make to have a maximum profit? This problem is discussed in detail in Supplementary Reading Material Lesson 14. Since mathematical models in linear programming problems consist of linear in equalities, the next section is devoted to such inequalities. Recall that the linear equation lx+my+n=0represents a straight line in a plane. Every solution (x,y) of the equation lx+my+n=0is a point on this line, and vice versa. An inequality that is obtained from the linear equation lx+my+n=0by replacin g the equality sign “=”by an inequality sign < (less than), ≤(less than or equal to), > (greater than), or ≥(greater than or equal to) is called a linear i nequality in two variables x and y. Thus lx+my+n≤0, lx+my+n≥0are all lin ear liequalities. A solution of a linear inequality is an ordered pair (x,y) of nu mbers x and y for which the inequality is true. EXAMPLE 1 Graph the solution set of the pair of inequalities SOLUTION Let A be the solution set of the inequality x+y-7≤0 and B be th at of the inequality x-3y +6 ≥0 .Then A∩B is the solution set of the given pair of inequalities. Set A is represented by the region shaded with horizontal lines and set B by the region shaded with vertical lines in Fig.1. Therefore the
数学专业英语
MATHS ENGLISH absolute value 绝对值 acceptable region 接受域 additivity 可加性alternative hypothesis 对立假设 analysis of covariance 协方差分析analysis of variance 方差分析 arithmetic mean 算术平均值 association 相关性 assumption checking 假设检验 availability 有效度 band 带宽bar chart 条形图 beta-distribution 贝塔分布 between groups 组间的binomial distribution 二项分布binomial test 二项检验center of gravity 重心 central tendency 中心趋势 hi-square distribution 卡方分布 chi-square test 卡方检验 classify 分类 cluster analysis 聚类分析coefficient 系数 coefficient of correlation 相关系数 collinearity 共线性 components 构成，分量 compound 复合的 confidence interval 置信区间consistency 一致性continuous variable 连续变量control charts 控制图 correlation 相关 covariance 协方差 covariance matrix 协方差矩阵 critical point 临界点 critical value 临界值 cross tab 列联表 cubic term 三次项 cumulative distribution function 累加分布函数curve estimation 曲线估计 default 默认的 deleted residual 剔除残差density function 密度函数dependent variable 因变量design of experiment 试验设计 df.(degree of freedom) 自由度 diagnostic 诊断discrete variable 离散变量discriminant function 判别函数discriminatory analysis 判别分析 D-optimal design D-优化设计 effects of interaction 交互效应eigenvalue 特征值equal size 等含量estimation of parameters 参数估计 estimations 估计量 exact value 精确值 expected value 期望值 exponential指数的 exponential distribution 指数分布 extreme value 极值 factor analysis 因子分析 factor score 因子得分 factorial designs 析因设计 factorial experiment 析因试验fitted line 拟合线fitted value 拟合值fixed variable 固定变量fractional factorial design 部分析因设计 F-test F检验 full factorial design 完全析因设计 gamma distribution 伽玛分布 geometric mean 几何均值 harmonic mean 调和均值 heterogeneity 不齐性 histogram 直方图homogeneity 齐性homogeneity of variance 方差齐性 hypothesis test 假设检验independence独立independent variable 自变量independent-samples 独立样本index of correlation 相关指数interclass correlation 组内相关 interval estimate 区间估计inverse 倒数的iterate 迭代kurtosis 峰度large sample problem 大样本问题least-significant difference 最小显著差数 least-square estimation 最小二乘估计 least-square method 最小二乘法 level of significance 显著性水平 leverage value 中心化杠杆值 life test 寿命试验likelihood function 似然函数 likelihood ratio test 似然比检验 linear estimator 线性估计linear model 线性模型 linear regression 线性回归 linear relation 线性关系 linear term 线性项 logarithmic 对数的 logarithms 对数 lost function 损失函数 main effect 主效应matrix 矩阵 maximum 最大值maximum likelihood estimation 极大似然估计mean squared deviation(MSD) 均方差 mean sum of square 均方和 measure 衡量 media
数学专业英语
学号：10901040201 姓名：曹菁 lg LinearA ebra Non-trivial linear combination. This is a contradiction and proves 1).Part 2) follows from 1) because dim(V)=n. Exercise Let A=0110?? ?-?? ()2R ∈. Find an invertible 2C C ∈ such that 1 c AC - is diagonal. Show that C cannot be selected in 2R .Find the characteristic polynomial of A . Exercise Suppose V is a 3-dimensional vector space and :f V V → is an endomorphism with ()()3 f CP x x λ=-.Show that ()f I λ- has characteristic polynomial and is thus a nilpotent endomorphism. Show there is a basis for V so that the matrix representing is 001001λλλ?? ? ? ??? ,001000λλλ?? ? ? ???or.000000λλλ?? ? ? ??? . We could continue and finally give an ad hoc proof of the Jordan canonical form,but in this chapter we prefer to press on to inner product spaces.The Jordan form will be developed in Chapter 6 as of the general theory of finitely generated modules over Euclidean domains.The next section is included only as a convenient reference. This section should be just skimmed or omitted entirely.It is unnecessary for the rest of this chapter,and is not properly part of the flow of the chapter.The basic facts of Jordan form are summarized here simply for reference. The statement that a square matrix B over a field F is a Jordanblock means that F λ?∈ Such that B is a lower triangular matrix of the form 0101B λλ λ?? ? ? ?= ? ? ??? .B gives a homomorphism :m m g F F →with ()m m g e e λ= and ()1i i i e e e λ+=+ for 1i m ≤<.Note that ()()m B CP x x m =-and so λ is the only eigenvalue of B ,and B satisfies its characteristic polynomial,i.e.,()0B CP B =. Definition A matrix n D F ∈ is in Jordan if ?Jordan blocks i ni B F ∈ such that