美国大学生数学建模竞赛翻译必备知识
23年美赛中英文对照版竞赛指南
美赛中英文对照版竞赛指南1. 简介23年美赛中英文对照版竞赛指南是为了帮助参与23年美国大学数学建模竞赛的学生更好地准备和参加比赛而编写的指南。
This guide is intended to help students participating in the 23rd annual MCMASpetition of the United States to prepare for and participate in thepetition.2. 竞赛概况美国大学数学建模竞赛是一项面向全球高校学生的标志性竞赛,旨在提高学生的数学建模、解决问题和团队合作能力。
比赛通常设有团队赛和个人赛两个类别,题目涉及的领域广泛,如数学、统计学、运筹学等。
The MCMAS is a prestigiouspetition for global college students, 本人ming to improve students' mathematical modeling, problem-solving, and teamwork skills. Thepetition usually consists of team and individual categories, covering a wide range of fields such as mathematics, statistics, operations research, etc.3. 竞赛时间和地点23年美国大学数学建模竞赛预计于2023年2月进行,具体的时间和地点将在冠方全球信息站上公布。
参赛学生需要提前关注并根据指定时间和地点参与比赛。
The 23rd annual MCMAS is expected to take place in February 2023, with specific dates and locations to be announced on the official website. Participating students need to pay attention in advance and participate in thepetition according to the specified time and place.4. 竞赛报名学生可以通过冠方全球信息站进行报名,需要填写个人信息并组建队伍报名参赛。
美国大学生数学建模论文及其翻译31552
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Best all time college coach Summary
In order to select the “best all time college coach” in the last century fairly, We take selecting the best male basketball coach as an example, and establish the TOPSIS sort - Comprehensive Evaluation improved model based on entropy and Analytical Hierarchy Process. The model mainly analyzed such indicators as winning rate, coaching time, the time of winning the championship, the number of races and the ability to perceive .Firstly , Analytical Hierarchy Process and Entropy are integratively utilized to determine the index weights of the selecting indicators Secondly,Standardized matrix and parameter matrix are combined to construct the weighted standardized decision matrix. Finally, we can get the college men's basketball com
数模美国赛总结部分英文
数模美国赛总结部分英文第一篇:数模美国赛总结部分英文Conclusions1、As our team set out to come up with a strategy on what would be the most efficient way to 我们提出了一种最有效的方法去解决……2、The first aspect that we took into major consideration was…….Other important findings through research made it apparent that the standard 首先我们考虑到……,其他重要的是我们通过研究使4、We have used mathematical modeling in a……to analyze some of the factors associated with such an activity。
为了分析这类问题的一些因素,我们运用数学模型……5、This “cannon problem” has been used in many forms in many differential equations courses in the Department of Mathematical Sciences for several years.这些年这些问题已经以不同的微分方程形式运用于自然科学部门。
6、In conclusion our team is very certain that the methods we came up with in 总之,我们很确定我们提出的方法7、We already know how well our results worked for…… 我们已经知道我们结果对……8、Now that the problem areas have been defined, we offer some ways to reduce the effect of these problems.既然已经定义了结果,我们提出一些方法减少对问题的影响。
2013年美国大学生数学建模竞赛(MCMICM)参赛规则中英文对照
2013年美国大学生数学建模竞赛(MCMICM)参赛规则中英文对照2 ICM:The InterdisciplinaryContest in ModelingICM:交叉学科建模竞赛ContestRules, Registration and Instructions比赛规则,报名注册和指导(All rules and instructions apply to both ICM and MCM contests, except where otherwisenoted.)(所有MCM的说明和规则除特别说明以外都适用于ICM)To participate in a contest, each team must be sponsored by a faculty advisor fromits institution.参加MCM的每个队伍需有一名在职的高校老师负责指导。
TeamAdvisors: Please read these instructions carefully. It isyour responsibility to make sure that teams are correctly registered and thatall of the following steps required for participation in the contest arecompleted:Pleaseprint a copy of these contest instructions for reference before, during, andafter the contest. Click here for the printer friendly version.指导老师:请认真阅读这些说明事项,确保完成了所有相关的项。
每位指导教师的责任包括确保每个参赛队正确注册并正确完成参加MCM/ICM所要求的相关步骤。
美国数学竞赛AMC单词表
AMC数学单词表分类(汉英)几何geometry点point线line面plane体solid线段segment射线radial平行parallel相交intersect角angle角度degree弧度radian锐角acute angle直角right angle钝角obtuse angle平角straight angle周角paragon底base边side高height线段line segment长length平行线parallel lines正三角形regular triangle等腰三角形isosceles triangle平行四边形parallelogram n.梯形trapezia n.菱形rhombus正方体,立方体,立方cube n.长方体cuboid adj.圆柱column n.圆锥cone尺寸measure n.,v.半圆semicircle半径radius n. (radii pl.)直径diameter n.表面积surface area多边形polygon凸多边形convex polygon正多边形regular polygon直角right-angle直角三角形right-triangle锐角acute-angle空间space四面体tetrahedron五面体pentahedron六面体hexahedron平行六面体parallelepiped立方体cube七面体heptahedron八面体octahedron九面体enneahedron十面体decahedron十一面体hendecahedron十二面体dodecahedron二十面体icosahedron多面体polyhedron棱锥pyramid棱柱prism棱台frustum of a prism旋转rotation轴axis圆锥cone圆柱cylinder圆台frustum of a cone球sphere半球hemisphere底面undersurface表面积surface area体积volume圆circle圆心centre(BrE),center(AmE)半径radius直径diameter圆周率pi弧arc半圆semicircle扇形sector环ring椭圆ellipse圆周circumference周长perimeter面积area轨迹locus,loci(pl.)相似similar全等congruent三角trigonometry正弦sine余弦cosine正切tangent余切cotangent正割secant余割cosecant反正弦arcsine反余弦arccosine反正切arctangent反余切arccotangent反正割arcsecant反余割arccosecant相位phase周期period振幅amplitude内心incentre(BrE)外心excentre(BrE)旁心escentre(BrE)垂心orthocentre(BrE)重心barycentre(BrE)内切圆inscribedcircle外切圆circumcircle三角形triangle锐角三角形acute triangle直角三角形right triangle直角边leg斜边hypotenuse勾股定理Pythagorean theorem钝角三角形obtuse triangle不等边三角形scalene triangle 等腰三角形isosceles triangle 等边三角形equilateral triangle 四边形quadrilateral平行四边形parallelogram矩形rectangle长length宽width菱形rhomb,rhombus,rhombi(pl.),diamond 正方形square梯形trapezoid直角梯形right trapezoid等腰梯形isosceles trapezoid正多边形equilateral polygon代数 algebra整数integer,whole number小数decimal小数点decimal point分数fraction分子numerator分母denominator比ratio正positive负negative零null,zero,nil十进制decimal system二进制binary system十六进制hexadecimal system权weight,significance进位carry截尾truncation四舍五入round下舍入round down上舍入roundup有效数字significant digit无效数字insignificant digit公式formula,formulae(pl.)单项式monomial多项式polynomial,multinomial系数coefficient数学mathematics,maths(BrE),math(AmE)等于equals,is equal to大于is greater than小于is lesser than大于等于is equal or greater than小于等于is equal or lesser than运算符operator数字digit数number自然数natural number公理axiom定理theorem计算calculation运算operation证明prove假设hypothesis,hypotheses(pl.)命题proposition算术arithmetic加plus(prep.),add(v.),addition(n.)被加数augend,summand加数addend和sum减minus(prep.),subtract(v.),subtraction(n.)被减数minuend减数subtrahend余数remainder乘times(prep.),multiply(v.),multiplication(n.)被乘数multiplicand乘法multiplication积product除divided by(prep.),divide(v.),division(n.)质数prime number合数composite number正数positive number平均数mean奇数odd adj.偶数even n.偶数even integer, even number值value最小值minimum最大的,最大值maximum n.最小的,最小值minimum n.最小可能值least possible value约数,除数divisor n.最小公倍数least common multiple正整数positive integer真分数proper fraction普通分数vulgar fraction分母denominator最小公分母least common denominator分子numerator带分数mixed number余数remainder简分数simple(common)fraction 循环小数 circulating decimal 纯小数decimal faction混合小数mixed decimal百分比percentage四分之一quarter大于more than小于less than不大于not more than数字,阿拉伯数字digit n.个位数字unit’s digit十位数字tens digit个位units十位tens十分位tenths和,总数sum n.减,负,负数minus(take away) 乘数multiple差difference相等,等于equal被整除,红利dividend平均数average n.乘方power商quotient方程equation n.满足satisfy v.增加increase n.减少reduce v.坐标系coordinates坐标轴x-axis,y-axis,z-axis 横坐标x-coordinate纵坐标y-coordinate原点origin双曲线hyperbola抛物线parabola集合set元素element空集void子集subset交集intersection并集union补集complement映射mapping函数function定义域domain,field of definition值域range常量constant变量variable单调性monotonicity奇偶性parity周期性periodicity图象image数列,级数series微积分calculus微分differential导数derivative极限limit无穷大infinite(a.)infinity(n.)无穷小infinitesimal积分integral定积分definite integral不定积分indefinite integral有理数rational number无理数irrational number实数real number虚数imaginary number复数complex number矩阵matrix行列式determinant未知数unknown,x-factor,y-factor,z-factor 等式,方程式equation一次方程simple equation二次方程quadratic equation三次方程cubic equation四次方程quartic equation不等式inequation阶乘factorial对数logarithm指数,幂exponent乘方power二次方,平方square三次方,立方cuben次方the power of n,the nth power开方evolution,extraction二次方根,平方根square root三次方根,立方根cube rootn次方根the root of n,the nth root统计statistics平均数average加权平均数weighted average方差variance标准差root-mean-square deviation,standard deviation 比例proportion百分比percent百分点percentage百分位数percentile排列permutation组合combination概率probability分布distribution正态分布normal distribution非正态分布abnormal distribution图表graph条形统计图bar graph柱形统计图histogram折线统计图broken line graph曲线统计图curve diagram扇形统计图pie diagramAMC数学单词表分类(英汉)1常见单词side 边长perimeter n. 周长circumference 周长,圆周width宽area n.面积volume体积arithmetic progression(sequence)等差数列altitude高bisect平分divisor因子factor因子common factor公因子common multiple公倍数common divisor公因数common fraction普通分数complex fraction繁分数consecutive number连续整数consecutive even integer连续偶数consecutive odd integer连续奇数direct proportion正比inverse proportion反比distinct不同的factorial阶乘inverse倒数reciprocal倒数progression数列the extremes of a proportion比例外项the means of a proportion比例内medmedian中位数,中值mode众数,一组数据中出现最多的数arranged安排的add,plus加subtract减difference差multiply, times乘product积divide除divisible可被整除的divided evenly被整除dividend被除数divisor因子,除数quotient商remainder余数factorial阶乘power乘方radical sign, root sign根号round to四舍五入to the nearest四舍五入2.有关集合union并集proper subset真子集solution set解集3.有关代数式、方程和不等式algebraic term代数项like terms, similar terms同类项numerical coefficient数字系数literal coefficient字母系数inequality不等式triangle inequality三角不等式range值域original equation原方程equivalent equation同解方程等价方程linear equation线性方程(e.g.2x +6=22)4.有关分数和小数proper fraction真分数improper fraction假分数mixed number带分数vulgar fraction,common fraction普通分数 simple fraction简分数complex fraction繁分数numerator分子denominator分母(least)common denominator(最小)公分母quarter四分之一decimal fraction纯小数infinite decimal无穷小数recurring decimal循环小数tenths unit十分位5.基本数学概念arithmetic mean算术平均值weighted average加权平均值geometric mean几何平均数exponent指数,幂base乘幂的底数,底边cube立方数,立方体square root平方根cube root立方根common logarithm常用对数digit数字constant常数variable变量inverse function反函数complementary function余函数linear一次的,线性的factorization因式分解absolute value绝对值round off四舍五入6.有关数论natural number自然数positive number正数negative number负数odd integer, odd number奇数even integer, even number偶数integer, whole number整数positive whole number正整数negative whole number负整数consecutive number连续整数real number实数rational number有理数irrational(number)无理数inverse倒数composite number合数e.g.4,6,8,9,10,12,14,15…… prime number质数e.g.2,3,5,7,11,13,15……reciprocal倒数common divisor公约数multiple倍数(least)common multiple(最小)公倍数(prime)factor(质)因子common factor公因子ordinary scale, decimal scale十进制nonnegative非负的tens十位units个位mode众数median中数common ratio公比7.数列arithmetic progression(sequence)等差数列 geometric progression(sequence)等比数列8.其它approximate近似(anti)clockwise(逆)顺时针方向cardinal基数ordinal序数direct proportion正比distinct不同的estimation估计,近似parentheses括号proportion比例permutation排列combination组合table表格trigonometric function三角函数unit单位,位几何部分1.所有的角alternate angle内错角corresponding angle同位角vertical angle对顶角central angle圆心角interior angle内角exterior angle外角supplementary angles补角complementary angle余角adjacent angle邻角acute angle锐角obtuse angle钝角right angle直角round angle周角straight angle平角included angle夹角2.所有的三角形equilateral triangle等边三角形scalene triangle不等边三角形isosceles triangle等腰三角形right triangle直角三角形oblique斜三角形inscribed triangle内接三角形3.有关平面图形,除三角形外semicircle半圆concentric circles同心圆quadrilateral四边形pentagon五边形hexagon六边形heptagon七边形octagon八边形nonagon九边形decagon十边形polygon多边形parallelogram平行四边形equilateral等边形plane平面square正方形,平方rectangle长方形regular polygon正多边形rhombus菱形trapezoid梯形4.其它平面图形arc弧line, straight line直线line segment线段parallel lines平行线segment of a circle弧形5.有关立体图形cube立方体,立方数rectangular solid长方体regular solid/regular polyhedron正多面体 circular cylinder圆柱体cone圆锥sphere球体solid立体的6.有关图形上的附属物altitude高depth深度side边长circumference, perimeter周长radian弧度surface area表面积volume体积arm直角三角形的股cross section横截面center of a circle圆心chord弦radius半径angle bisector角平分线diagonal对角线diameter直径edge棱/边face of a solid立体的面hypotenuse斜边included side夹边leg三角形的直角边median of a triangle三角形的中线base底边,底数(e.g.2的5次方,2就是底数) opposite直角三角形中的对边midpoint中点endpoint端点vertex(复数形式vertices)顶点tangent切线的transversal截线intercept截距7.有关坐标coordinate system坐标系rectangular coordinate直角坐标系origin原点abscissa横坐标ordinate纵坐标number line数轴quadrant象限slope斜率complex plane复平面8.其它plane geometry平面几何trigonometry三角学bisect平分circumscribe外切inscribe内切intersect相交perpendicular垂直Pythagorean theorem勾股定理congruent全等的multilateral多边的单位类cent美分penny 1美分硬币nickel5美分硬币dime一角硬币dozen打(12个)score廿(20个)Centigrade摄氏Fahrenheit华氏quart夸脱gallon加仑(1gallon=4quart)yard码meter米micron微米inch英寸foot英尺minute分(角度的度量单位,60分=1度) square measure平方单位制cubic meter立方米pint品脱(干量或液量的单位。
2015年美国大学生数学建模竞赛MCM ICM参赛帮助中文翻译
数学中国MCM/ICM参赛指南翻译(2015版)(任何单位转载须注明来源:)MCM:The Mathematical Contest in ModelingMCM:数学建模竞赛ICM:The Interdisciplinary Contest in ModelingICM:交叉学科建模竞赛Contest Rules, Registration and Instructions比赛规则,比赛注册方式和参赛指南(All rules and instructions apply to both ICM and MCM contests, except where otherwise noted.)(所有MCM的说明和规则除特别说明以外都适用于ICM)To participate in a contest, each team may consist of a maximum of three students and must be sponsored by a faculty advisor from its institution.每个MCM的参赛队需要由最多三名学生构成,并且要有一名所在单位的指导教师负责。
Team Members: A team may consist of up to three students from the same school and is open to all undergraduate and high school students.参赛队的成员:一个队可以由多达3名来自同一个学校的学生组成,对于所有的大学生和高中生都可以参加。
Team Advisors: Please read these instructions carefully. It is your responsibility to make sure that teams are correctly registered and that all of the following steps required for participation in the contest are completed:Please print a copy of these contest instructions for reference before, during, and after the contest. Click here for the printer friendly version.指导老师:请认真阅读这些说明,确保完成了所有相关的步骤。
2012年美国大学生数学建模竞赛题目B题英语达人全配套翻译
PROBLEM B: Camping along the Big Long River问题B:沿着大长河露营Visitors to the Big Long River (225 miles) can enjoy scenic views and exciting white water rapids. 游客到大长河(225英里)可以享受风景和令人兴奋的白色水急流。
The river is inaccessible to hikers, so the only way to enjoy it is to take a river trip that requires河是徒步旅行者无法进入的,所以唯一享受它的方法是采取河之旅,需要几天的露营several days of camping. River trips all start at First Launch and exit the river at Final Exit, 225河旅行都开始在第一次启动和退出河在最后退出,225英里下游。
miles downstream. Passengers take either oar- powered rubber rafts, which travel on average 4乘客乘橡皮艇桨驱动平均每小时4英里,或摩托艇,平均每小时8英里的速度行驶。
mph or motorized boats, which travel on average 8 mph. The trips range from 6 to 18 nights of旅程从开始到完成6到18个晚上,camping on the river, start to finish.. The government agency responsible for managing this river负责管理这条河的政府机关想要,以最少的接触与其他群体在河的小船,享受荒野之旅。
美国数学竞赛amc8的常用数学英语单词
美国数学竞赛amc8的常用数学英语单词美国数学竞赛 AMC8 的常用数学英语单词在准备美国数学竞赛 AMC8 时,掌握一些常用的数学英语单词是非常重要的。
这不仅有助于我们理解题目,还能更准确地解答问题。
以下是为大家整理的一些 AMC8 中常见的数学英语单词。
一、数与代数1、 Number(数)Integer(整数)Positive integer(正整数)Negative integer(负整数)Zero(零)Natural number(自然数)Odd number(奇数)Even number(偶数)Prime number(质数)Composite number(合数)2、 Algebra(代数)Variable(变量)Constant(常量)Expression(表达式)Equation(方程)Inequality(不等式)Linear equation(线性方程)Quadratic equation(二次方程)3、 Operation(运算)Addition(加法)Subtraction(减法)Multiplication(乘法)Division(除法)Sum(和)Difference(差)Product(积)Quotient(商)4、 Ratio and proportion(比例与比率)Ratio(比率)Proportion(比例)二、几何1、 Point(点)Line(线)Straight line(直线)Ray(射线)Line segment(线段)2、 Angle(角)Acute angle(锐角)Right angle(直角)Obtuse angle(钝角)Straight angle(平角)Reflex angle(优角)3、 Triangle(三角形)Equilateral triangle(等边三角形) Isosceles triangle(等腰三角形)Scalene triangle(不等边三角形) Right triangle(直角三角形)4、 Quadrilateral(四边形)Square(正方形)Rectangle(长方形)Parallelogram(平行四边形)Rhombus(菱形)Trapezoid(梯形)5、 Circle(圆)Radius(半径)Diameter(直径)Circumference(周长)Area(面积)6、 Polygon(多边形)Pentagon(五边形)Hexagon(六边形)Heptagon(七边形)Octagon(八边形)三、测量与单位1、 Length(长度)Meter(米)Centimeter(厘米)Millimeter(毫米)Kilometer(千米)2、 Area(面积)Square meter(平方米)Square centimeter(平方厘米) Hectare(公顷)3、 Volume(体积)Cubic meter(立方米)Cubic centimeter(立方厘米) Liter(升)Milliliter(毫升)4、 Mass(质量)Gram(克)Kilogram(千克)Ton(吨)5、 Time(时间)Second(秒)Minute(分钟)Hour(小时)Day(天)Week(周)Month(月)Year(年)6、 Temperature(温度) Celsius(摄氏度)Fahrenheit(华氏度)四、数据与统计1、 Data(数据)Mean(平均数)Median(中位数)Mode(众数)Range(极差)2、 Graph(图表)Bar graph(条形图)Line graph(折线图)Pie chart(饼图)五、概率与组合1、 Probability(概率)Event(事件)Outcome(结果)Random(随机的)2、 Combination(组合)Permutation(排列)掌握这些常用的数学英语单词,能够让我们在 AMC8 竞赛中更加游刃有余。
美国数学大联盟常用英文词汇
美国数学大联盟常用英文词汇一、基础数学词汇1. Arithmetic 算术2. Algebra 代数3. Geometry 几何4. Trigonometry 三角学5. Calculus 微积分6. Statistics 统计学7. Probability 概率论8. Combinatorics 组合数学9. Number theory 数论10. Set theory 集合论二、代数词汇1. Variable 变量2. Equation 方程3. Inequality 不等式4. Function 函数5. Graph 图像6. Polynomial 多项式7. Factorization 因式分解8. Exponent 指数9. Logarithm 对数10. Matrix 矩阵三、几何词汇1. Point 点2. Line 线3. Plane 平面4. Angle 角度5. Triangle 三角形6. Quadrilateral 四边形7. Circle 圆8. Perimeter 周长9. Area 面积10. Volume 体积四、三角学词汇1. Sine 正弦2. Cosine 余弦3. Tangent 正切4. Cosecant 余割5. Secant 正割6. Cotangent 余切7. Arcsine 反正弦8. Arccosine 反余弦9. Arctangent 反正切10. Radian 弧度五、微积分词汇1. Derivative 导数2. Integral 积分3. Limit 极限4. Series 级数5. Sequence 数列6. Differentiation 微分7. Integration 积分8. Differential equation 微分方程9. Taylor series 泰勒级数10. Fourier series 傅里叶级数六、统计学词汇1. Data 数据2. Sample 样本3. Population 总体4. Mean 平均值5. Median 中位数6. Mode 众数7. Standard deviation 标准差8. Variance 方差9. Probability distribution 概率分布10. Hypothesis testing 假设检验七、概率论词汇1. Event 事件2. Probability 概率3. Random variable 随机变量4. Probability space 概率空间5. Conditional probability 条件概率6. Bayes' theorem 贝叶斯定理7. Independence 独立性8. Law of large numbers 大数定律9. Central limit theorem 中心极限定理10. Random walk 随机游走八、组合数学词汇1. Permutation 排列2. Combination 组合3. Binomial coefficient 二项式系数4. Pascal's triangle 帕斯卡三角形5. Catalan number 卡塔兰数6. Fibonacci sequence 斐波那契数列7. Partition 分割8. Graph theory 图论9. Ramsey theory 拉姆齐理论10. Combinatorial design 组合设计九、数论词汇1. Prime number 质数2. Composite number 合数3. Divisor 因数4. GCD 最大公约数5. LCM 最小公倍数6. Modular arithmetic 模运算7. Fermat's little theorem 费马小定理8. Euler's theorem 欧拉定理9. Chinese remainder theorem 中国剩余定理10. RSA encryption RSA加密十、集合论词汇1. Set 集合2. Element 元素3. Union 并集4. Intersection 交集5. Complement 补集6. Power set 幂集7. Cartesian product 笛卡尔积8. Function 函数9. Relation 关系10. Equivalence relation 等价关系美国数学大联盟常用英文词汇一、基础数学词汇1. Arithmetic 算术2. Algebra 代数3. Geometry 几何4. Trigonometry 三角学5. Calculus 微积分6. Statistics 统计学7. Probability 概率论8. Combinatorics 组合数学9. Number theory 数论10. Set theory 集合论二、代数词汇1. Variable 变量2. Equation 方程3. Inequality 不等式4. Function 函数5. Graph 图像6. Polynomial 多项式7. Factorization 因式分解8. Exponent 指数9. Logarithm 对数10. Matrix 矩阵三、几何词汇1. Point 点2. Line 线3. Plane 平面4. Angle 角度5. Triangle 三角形6. Quadrilateral 四边形7. Circle 圆8. Perimeter 周长9. Area 面积10. Volume 体积四、三角学词汇1. Sine 正弦2. Cosine 余弦3. Tangent 正切4. Cosecant 余割5. Secant 正割6. Cotangent 余切7. Arcsine 反正弦8. Arccosine 反余弦9. Arctangent 反正切10. Radian 弧度五、微积分词汇1. Derivative 导数2. Integral 积分3. Limit 极限4. Series 级数5. Sequence 数列6. Differentiation 微分7. Integration 积分8. Differential equation 微分方程9. Taylor series 泰勒级数10. Fourier series 傅里叶级数六、统计学词汇1. Data 数据2. Sample 样本3. Population 总体4. Mean 平均值5. Median 中位数6. Mode 众数7. Standard deviation 标准差8. Variance 方差9. Probability distribution 概率分布10. Hypothesis testing 假设检验七、概率论词汇1. Event 事件2. Probability 概率3. Random variable 随机变量4. Probability space 概率空间5. Conditional probability 条件概率6. Bayes' theorem 贝叶斯定理7. Independence 独立性8. Law of large numbers 大数定律9. Central limit theorem 中心极限定理10. Random walk 随机游走八、组合数学词汇1. Permutation 排列2. Combination 组合3. Binomial coefficient 二项式系数4. Pascal's triangle 帕斯卡三角形5. Catalan number 卡塔兰数6. Fibonacci sequence 斐波那契数列7. Partition 分割8. Graph theory 图论9. Ramsey theory 拉姆齐理论10. Combinatorial design 组合设计九、数论词汇1. Prime number 质数2. Composite number 合数3. Divisor 因数4. GCD 最大公约数5. LCM 最小公倍数6. Modular arithmetic 模运算7. Fermat's little theorem 费马小定理8. Euler's theorem 欧拉定理9. Chinese remainder theorem 中国剩余定理10. RSA encryption RSA加密十、集合论词汇1. Set 集合2. Element 元素3. Union 并集4. Intersection 交集5. Complement 补集6. Power set 幂集7. Cartesian product 笛卡尔积8. Function 函数9. Relation 关系10. Equivalence relation 等价关系十一、数学竞赛相关词汇1. Contest 竞赛2. Problem 问题3. Solution 解答4. Strategy 策略5. Practice 练习6. Challenge 挑战7. Competition 比赛8. Award 奖项9. Medal 奖牌10. Rank 排名十二、数学教育相关词汇1. Curriculum 课程2. Lesson 课3. Exercise 练习4. Homework 作业5. Test 测试6. Assessment 评估7. Instruction 指导8. Resource 资源9. Tool 工具10. Technique 技巧十三、数学研究相关词汇1. Research 研究2. Theory 理论3. Hypothesis 假设4. Proof 证明5. Result 结果6. Experiment 实验7. Observation 观察8. Analysis 分析9. Conclusion 结论10. Publication 发表十四、数学应用相关词汇1. Application 应用2. Model 模型3. Algorithm 算法4. Simulation 模拟5. Optimization 优化6. Data 数据7. Analysis 分析8. Solution 解答9. Design 设计10. Evaluation 评估十五、数学文化相关词汇1. History 历史2. Development 发展3. Influence 影响4. Mathematician 数学家5. Theory 理论6. Concept 概念7. Idea 思想8. Innovation 创新9. Tradition 传统10. Legacy 遗产通过掌握这些常用英文词汇,你将能够更好地理解和参与美国数学大联盟的数学竞赛、教育、研究以及应用等领域的讨论和交流。
数模美赛论文常用词汇
exclusively专门undobtedly毫无疑问的notable 值得注意的tremedous/significant极大的notion概念definition定义——defineInterpret……as…… 理解……为invoke(+模型援引,引用equation方程式,等式function 因变量——提示符号的含义matrix矩阵,模型constant 常数,常量It requires I t o be a constant for …to be truealgorithm演算方法——a general algorithm 通用算法simplify the algorithm 简化算法we have produced a general algrrithm to solve this tpye of problems.derivative微分,倒数antiderivative 不定积分optimal results 最优结果invesgate the problem from different point of view调查问题——investgation调查survey 调查subproblem 子问题,次要问题——major problem 主要问题metric 度量标准,指标digit 数字delete some digitselement /component 元素解题思路seek/explore——explore different ideas探索不同的想法we seek to device a new model for solving the problem by exploring the new direction suggested by their investigations.解决方案design/device ——develop/establish/conductBased on our analysis, we design a model for the problem using integral linear programming(线性积分). We then devise a polynominal-time apprximation algorithm toproduce near optimal ing integral linear programming.We then device a polynominal-time approximation toWe conduct sensitivity analysis on…to find…xxx analysis is al so performed.解决结果tackle/solveWe tackle the problem using the new technique we developed in the previous section.While it is difficult to solve the problem completely, we are able to solve a major subproblem.计划与打算approach/proposeWe approach the problem using the proposed method.We propose a new approach to tackling the problem.词组Based on…以……为基础According to根据Devide …into…——subdivide into细分…is applied to…使用了……模型来……——we apply our model into将我们的模型运用于Model proves to be efficient in other sports.模型被证明在其他方面有效….,which indicates that………反映了…,which led to the change of…导致了……的变化We…..only to find that..我们……只是发现了……… doesn’t matter ……是无关的Take…as example/as a case study 举例formulate and justify the assumptions 阐述并证明假说design/establish a model设计模型devise an algorithm 设计一个运算法/计算程序carry out numerical simulations 进行数学模拟for our problem a relationship exists that(… 我们的问题中存在一个关系式,使……we will assume/suppose that…我们假设……compare with different approaches 与不同的措施相比较There are at least two notions of where the sweet spot should be—an impact location on the bat that either· minimizesthe discomfort to the hands, or· maximizes the outgoing velocity Of the ball.We focus exclusively on the second definition我们专注于第二种定义We interpret the error of +2 as a normal distribution,.一with standard deviation of 1。
美国数学竞赛mathcount技巧中英对照
美国数学竞赛mathcount技巧中英对照1. Read each problem carefully and multiple timesI cannot stress this point enough. This is the single most important part of MATHCOUNTS for a great number of students, myself included. Misreading the problem is likely one of the leading causes, if not the leading cause, of incorrect answers. Personally, I would have made Nationals in 7th grade had I read some key words correct ("smallest" instead of "largest", "first" instead of "last", etc.). I also would likely have made National CD had I managed to read "Positive" on the final Target question.2. Manage your timeThis falls second on the list of importance, just below misreading. Note that poor time management will likely hamper your ability to read carefully (and multiple times), which will likely lead to even more time wasted. Know when to "give up" on a problem in favor of easier questions. They're all worth the same.3. Do all the questionsDifficulty is extremely difficult to gauge (heh) in general, but even more so when the problems are all roughly the same difficulty level. Don't be intimidated by the question number - many times a #26 will be a giveaway question, while #14 will be one of the more difficult problems. You should aim to at least read through all of the questions (carefully!) and to make a serious attempt on most of them.4. Organize your workIn MATHCOUNTS, you will likely spend a lot of time checking your answers, something that will be much harder to do if your paper is messy and disorganized. The method that you choose will be up to you, but my recommended method is to eithersection off your paper before the test begins, or to section off your paper as you complete problems. Write down all non-trivial steps - you'll use these for reference. You should include computation, either to the side or in the problem, as this is where you'll do most of your checking.5. Do problems multiple waysMost problems will have several valid approaches to the answer. In most cases, one approach will immediately jump out to you, and you will follow it to the answer. A great way to check your answer is to do the problem in another way, even if it's just slightly different. For example, if you do 5(3+5) as 5*3+5*5 and 5*8, you'll be significantly less likely to make a computation error. Similarly, if use similar triangles and Power of a Point, getting the same answer, you can bereasonably sure your answer is correct (but if they're different, time to find out why!). When using a second method, you shouldn't know what answer you're trying to achieve - you may consciously or subconsciously force yourself to get that answer.6. Make assumptionsThis is a very dangerous, but potentially rewarding technique. Mostly used for time-saving (and especially in CD), what looks like it's true usually is. Rely on your intuition - it's usually a very powerful tool. A combination of practice and experience gives you an intuition that can easily outweigh the time needed for a rigorous solution. This isn't to say guess; rather to make educated guesses.For example, take 2011 Chapter Target #8. From experience, I was able to immediately guess that the b in was 2 ( is highly associated with 45-degree angles and squares), which immediately led to (there's no other possible answer that makesit between 0 and 1). This gives the correct answer of 3 without any effort, on a relatively difficult problem (for chapter).Disclaimer: Only use this technique when necessary. If you have time, focus on checking problems you used this method on FIRST, before checking others.7. Don't check in orderIt's usually a waste of time to check from #1 to #30 in that order. You'll end up using your precious time checking problems that are almost certainly correct instead of checking those that need it. Make a mark on your paper next to the question number signifying that you are unsure of your answer. Make a seperate mark if you arrived at the answer without a rigorous solution (see tip 6). Focus on checking these first. After that, focus on checking problems that you aren't 100% sure of, then go to the easier problems. I also made notes of problems that were essentially just computation, because I always made computational errors on early problems. You may decide that you need marks for certain issues that you typically encounter, which is also fine.8. CD - Buzz in before you know the answerAnother dangerous but rewarding technique, only do so if you know you can get the answer within 3 seconds. For example, if you know that the answer is 15*16, that would be a good time to buzz in. Countdown is also an important time to utilize tip 6 - use your intution! With only 45 second per problem, and the "race" element, you need to be very fast in order to pick up your points. For example, this question: If , compute n, from the 2011 State CDround, was one that I instantly recognized as a question I could solve within 3 seconds (btw, so did my opponent). I instantly buzzed in (before I knew the answer!), gave the correctanswer of 5, and ended up winning my next match to make Nationals. Had I not buzzed in when I did, my opponent would have (he was going for his buzzer as well), and I would have missed out. In this case, the extra few milliseconds were incredibly important.9. Take it easyFinally, don't dwell on your results, good or bad, however cliche that sounds. Poor results do not really indicate much in a competition like MATHCOUNTS, where the difference between a national winner and a person just missing out on State CD is generally very small. It comes down to tiny speed tricks that makes one person just a little bit faster than the other guy, which can be enough. I know it won't feel like it at the time, but you're the lucky ones. As middle schoolers, you have so much time left to improve, both math-wise and competition-wise (yes, they can be seperate things). If you get 11th written at State (which I did in 7th grade), or 5th CD (which my friend did last year at States [because I beat him]), you'll be originally crushed, but in the end, it really makes so little difference. Both me and my friend do decently at math now, despite our... failures at MATHCOUNTS. There's a lot more to life than it.第1条:仔细、多次读题这点再怎么强调也不过分这是MATHCOUNTS最重要的一条技巧,不仅对学生,也包括我自己。
美赛翻译新
这里: • •
•
v 是截面平均速度 n 是 Gauckler-Manning 系数 Rh 是液压半径(L; ft, m); S 是液压级线的斜率或线性液压头损失(L / L); k 是 SI 与英文单位之间的转换因子。
该公式可以通过使用维度分析获得。 利用这个公式,很容易发现,当水流到达大坝时,其平
4.1 水流的行为
在我们的模型中,我们需要计算每个水坝的供电能力。 其中一个关键变量是水流到达大坝时 的平均流速。 我们假设赞比西河的水流是一个通道。 因此,我们可以采用经验公式 Manning 公 式来估计这个速度。 ������ */" v = ������) ������ -/* ������
其中 a 是体积到费用系数。
4.3 iMoDS:串联大坝综合模型(这翻译感觉不错)
在水坝达到一个水坝和一个水坝后,调查了水的行为,进一步提出了水坝综合模型。 该模型 由风险成本模型,供电能力模型和系列安全模型三个主要部分组成。 如图 3 所示,我们的模型作 为一个评估单一坝和整个组的综合机器。 基本上,我们可以将其视为非线性规划方法。 三个主 要部分作为来自不同领域的三个特征。 他们也根据自己对整个系统的贡献,分配不同的权重。
其中 d 是两个相邻水坝之间的平均距离。
4.3.4
电源能力模型
卡里巴被设计为一个单一用途的水电项目。 开始任何水电站发电项目,计算其水电数量至关 重要。 在我们的模型中,最后一部分是估计这种经济效益。 如果我们总结每个水坝的电力供应, 这个模型可以数值计算我们的新系统的电力供应。 基于水电方程[6],直观地得到等式 7,这是液 压头和流体流量的函数。 一个单位的水可以做多少工作取决于它的头部的重量。 并且可以通过水的密度,重力加速度, 流量和坠落高度来测量坝上的功率。
数学建模美国赛单词分析解析
(留给这次的数学建模美国赛吧)Aabsolute 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Bbalanced 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Ccalculate 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c oefficient 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con sistency 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Ddata 数据default 默认的definition 定义deleted residual 剔除残差density function 密度函数d ependent 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discrimin ant function 判别函数discriminatory analysis 判别分析distance 距离distribution 分布D-optim al design D-优化设计Eeaqual 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Ggamma distribution 伽玛分布geometric mean 几何均值group 组Hharmomic mean 调和均值heterogeneity 不齐性histogram 直方图homogeneity 齐性homogen eity of variance 方差齐性hypothesis 假设hypothesis test 假设检验Iindependence 独立independent variable 自变量independent-samples 独立样本index 指数ind ex of correlation 相关指数interaction 交互作用interclass correlation 组内相关interval estimat e 区间估计intraclass correlation 组间相关inverse 倒数的iterate 迭代Kkernal 核Kolmogorov-Smirnov test柯尔莫哥洛夫-斯米诺夫检验kurtosis 峰度Llarge sample problem 大样本问题layer 层least-significant difference 最小显著差数least-squar e 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log arithms 对数logistic 逻辑的lost function 损失函数Mmain 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mo de 众数model 模型Monte Carle method 蒙特卡罗法moving average 移动平均值multicollineari ty 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multivariat e analysis 多元分析Nnegative 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n umber of cases 个案数Oone-sample 单样本one-tailed test 单侧检验one-way ANOVA 单向方差分析one-way classificat ion 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Ppaired observations 成对观测数据paired-sample 成对样本parameter 参数parameter estimatio n 参数估计partial correlation 偏相关partial correlation coefficient 偏相关系数partial regressio n 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Qqadratic 二次的Q-Q plot Q-Q概率图quadratic term 二次项quality control 质量控制quantitati ve 数量的,度量的quartiles 四分位数Rrandom 随机的random number 随机数random number 随机数random sampling 随机取样ra ndom seed 随机数种子random variable 随机变量randomization 随机化range 极差rank 秩r ank correlation 秩相关rank statistic 秩统计量regression analysis 回归分析regression coefficie nt 回归系数regression line 回归线reject 拒绝rejection region 拒绝域relationship 关系reliab ility 可*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 s ample problem 小样本问题smooth 平滑sort 排序soruces of variation 方差来源space 空间s pread 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 assumpt ion 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Ttable 表t-distribution t分布test 检验test criterion 检验判据test for linearity 线性检验test o f 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Uunbalanced 不平衡的unbiased estimation 无偏估计unbiasedness 无偏性uniform distribution 均匀分布Vvalue of estimator 估计值variable 变量variance 方差variance components 方差分量varianc e ratio 方差比various 不同的vector 向量Wweight 加权,权重weighted average 加权平均值within groups 组内的ZZ score Z分数2. 最优化方法词汇英汉对照表Aactive 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Bbandwidth 带宽be equivalent to 等价于best-fit 最佳拟合bound 边界Ccoefficient 系数complex-value 复数值component 分量constant 常数constrained 有约束的co nstraint 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Ddata-fitting 数据拟合default 默认的,默认的define 定义diagonal 对角的direct search metho d 直接搜索法direction of search 搜索方向discontinuous 不连续Eeigenvalue 特征值empty matrix 空矩阵equality 等式exceeded 溢出的Ffeasible 可行的feasible solution 可行解finite-difference 有限差分first-order 一阶GGauss-Newton method 高斯-牛顿法goal attainment problem 目标达到问题gradient 梯度gradi ent method 梯度法Hhandle 句柄Hessian matrix 海色矩阵Independent variables 独立变量inequality 不等式infeasibility 不可行性infeasible 不可行的init ial feasible solution 初始可行解initialize 初始化inverse 逆invoke 激活iteration 迭代iteration 迭代JJacobian 雅可比矩阵LLagrange multiplier 拉格朗日乘子large-scale 大型的least square 最小二乘least squares sens e 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li near 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Nnonlinear 非线性的norm 范数Oobjective 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Pparameter 参数partial derivatives 偏导数polynomial interpolation method 多项式插值法Qquadratic 二次的quadratic interpolation method 二次内插法quadratic programming 二次规划Rreal-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Ttermination 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Uunconstrained 无约束的under-determined system 负定系统Vvariable 变量vector 矢量Wweighting matrix 加权矩阵3 样条词汇英汉对照表Aapproximation 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Bbivariate spline function 二元样条函数break/breaks 断点Ccoefficient/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Ddegree of freedom 自由度dimension 维数Eend conditions 约束条件input argument 输入参数interpolation 插值/内插interval 取值区间Kknot/knots 节点Lleast-squares approximation 最小二乘拟合Mmultiplicity 重次multivariate function 多元函数Ooptional argument 可选参数order 阶次output argument 输出参数P point/points 数据点Rrational spline 有理样条rounding error 舍入误差(相对误差)Sscalar 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Ttolerance 允许精度Uunivariate function 一元函数Vvector 向量Wweight/weights 权重4 偏微分方程数值解词汇英汉对照表Aabsolute error 绝对误差absolute tolerance 绝对容限adaptive mesh 适应性网格Bboundary condition 边界条件Ccontour plot 等值线图converge 收敛coordinate 坐标系Ddecomposed 分解的decomposed geometry matrix 分解几何矩阵diagonal matrix 对角矩阵Diri chlet boundary conditions Dirichlet边界条件Eeigenvalue 特征值elliptic 椭圆形的error estimate 误差估计exact solution 精确解Ggeneralized Neumann boundary condition 推广的Neumann边界条件geometry 几何形状geome try description matrix 几何描述矩阵geometry matrix 几何矩阵graphical user interface(GUI)图形用户界面Hhyperbolic 双曲线的Iinitial mesh 初始网格Jjiggle 微调LLagrange multipliers 拉格朗日乘子Laplace equation 拉普拉斯方程linear interpolation 线性插值loop 循环Mmachine precision 机器精度mixed boundary condition 混合边界条件NNeuman boundary condition Neuman边界条件node point 节点nonlinear solver 非线性求解器normal vector 法向量PParabolic 抛物线型的partial differential equation 偏微分方程plane strain 平面应变plane stres s 平面应力Poisson's equation 泊松方程polygon 多边形positive definite 正定Qquality 质量Rrefined 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Ssingular 奇异的。
美国“数学大联盟杯赛”常用英文词汇
美国“数学大联盟杯赛”(中国赛区)初赛常用英文词汇$美元符号Aacute 锐角的add 计算…总和/加,做加法addition 加,加法adjacent angle 邻角adjacent 邻近的altitude (尤指海拔)高度A.M. 上午amount 数量angle 角arc 弧,弓形area 范围,区域,面积arithmetic 算术,算法arithmetic sequence 等差数列arrangement 排列assume 假定average 平均,平均数/平均的Bbag 袋子base 底billion 十亿/十亿的bisector 二等分线,平分线blond 白肤金发碧眼的Ccalculate 计算calculation 计算capacity 容量cent 美分center 中心/中央的centimeter 厘米circular 圆形的circle 圆周,圆circumference 圆周column 列common 共通的, 公约的congruent 全等的constant 常数/不变的coordinate 坐标corner 角count 数,计算/计数,计算cousin 堂[表]兄弟,堂[表]姊妹crate 箱子cross 交叉的cube 立方体,立方cubic 立方体的,立方的cylindrical 圆柱的Ddecimal 十进制的,小数的/小数define 定义degree 度数denominator 分母determine 确定diagonal 对角线的,对角线diagram 图表diameter 直径diamond 菱形difference 差额digit 阿拉伯数字dime (美元)十美分dimension 尺寸divide 除division 除法divisor 除数,约数dollar (符号为$) 美元double 两倍/使加倍Eeight 八,第八eighteen 十八的,十八个的equal 相等的/等于equation 方程式,等式equilateral 等边的/等边形equivalent 相等的,相当的/相等estimate 估计evaluate 估计,求…的值even 偶数的/偶数example 例子,例题expansion 展开express 表达,表示expression 式,表达式,符号exterior 外部的Fface 表面factor因子,因数female 女的,雌性的fifteen 十五fifth 第五的figure 圆形find 得到first 首先,第一/第一的five 五,五个formula 公式forklift 铲车four 四,四个fraction 分数function 函数Ggeometrical 几何学的,几何的geometric sequence 等比数列graph 图表greatest common divisor 最大公约数,最大公因子Hhalf 一半/一半的hectare 公顷(等于1万平方米) height 高度,海拔hexagon 六角形,六边形horizontal 水平的how 多少,多么hundred 百,百个hyperbola 双曲线hypotenuse 直角三角形之斜边Iinequality 不等式infinite 无限的,无数的inscribe 使内切integer 整数interior 内部的intersect 相交,交叉intersection 交集,交叉点isosceles等腰三角形Kkilometer 千米,公里Lleast common multiple 最小公倍数length 长度less 少的,小的lift 举起,使升起,提起,抬起line segment 线段line 直线liter 公升Mmale 男的,雄性的map 地图,图mark 记号,符号,标记mass 质量mathematics 数学maximum 最大量/最大极限的mean 平均的/平均数measure 测量meter 米,公尺midpoint 中点,正中央million 百万,百万个minimum 最小的,最低的mixed number 带分数multiply 乘Nnatural number 自然数negative 负数/负的nickel (美元)五美分nine 九,九个ninety 九十number 数,数字numerator 分子numerical 数字的,用数表示的Ooctagon 八边形,八角形odd 奇数的one 一,一个operation 运算Pparabola 抛物线parallel 平行的parallelogram 平行四边形penny 一美分pentagon 五角形,五边形per 每一percent 百分比,百分数percentage 百分比,百分数,百分率perfect cube 完全立方perfect square 完全平方perimeter 周长,周界perpendicular 垂直的,正交的plus 加上P.M. 下午point 点,分数polygon 多变形,多角形polynomial 多项式positive 正的prime 质数prism 棱柱probability 概率product 乘积proportion 比例pyramid 角锥,棱锥Qquadrilateral 四边形quarter 四分之一,二十五(美分) quotient 商Rradius半径ratio 比,比率real number 实数reciprocal 倒数,倒数的rectangle长方形,矩形rectangular矩形的,成直角的region 区域regular 等边的remainder 余数rhombus 菱形,斜方形right 直角的root根rotation 旋转,轮转,循环row 行Ssatisfy 满足scale 比例second 秒/第二sector 扇形segment 段semi 半sequence 数学sequence 数列,序列series 连续,系列,级数seven 七,七个seventh 第七shape 外形side 边sign 符号simplify 简化six 六,六个size 大小,尺寸slope 斜率solid 立体solution 解答,解决sphere 球,球体,范围square root 平方根square 正方形straight 直的subtract 减去,减subtraction 减少sum 总和suppose 假设surface 表面surface area 表面积symmetric 对称性的Tten 十,十个tenth 第十,十分之一term 项third 第三,三分之一thousand 一千,一千个three 三time 次,度,回,倍trapezoid 梯形triangle 三角形tub 桶twelve 十二twenty 二十,二十个two 二,两个tangent 切线,相切的than 与…相比较total 总数/总的triple 三倍数twice 两次,两倍Vvalue 值variable 变数/变量的vertex 顶点vertical 垂直的volume 体积Wwidth 宽度Zzero 零点,零。
美国AMC数学联赛常用英语词汇
美国AMC数学联赛常用英语词汇数学 mathematics, maths(BrE), math(AmE)被除数 dividend除数 divisor商 quotient等于 equals, is equal to, is equivalent to大于 is greater than小于 is lesser than大于等于 is equal or greater than小于等于 is equal or lesser than运算符 operator数字 digit数 number自然数 natural number公理 axiom定理 theorem计算 calculation运算 operation证明 prove假设 hypothesis, hypotheses(pl.)命题 proposition算术 arithmetic加 plus(prep.), add(v.), addition(n.)被加数 augend, summand加数 addend和 sum减 minus(prep.), subtract(v.), subtraction(n.)被减数 minuend减数 subtrahend差 remainder乘 times(prep.), multiply(v.), multiplication(n.)被乘数 multiplicand, faciend乘数 multiplicator积 product除 divided by(prep.), divide(v.), division(n.)整数 integer小数 decimal小数点 decimal point分数 fraction分子 numerator分母 denominator比 ratio正 positive负 negative零 null, zero, nought, nil十进制 decimal system二进制 binary system十六进制 hexadecimal system权 weight, significance进位 carry截尾 truncation四舍五入 round下舍入 round down上舍入 round up有效数字 significant digit无效数字 insignificant digit代数 algebra公式 formula, formulae(pl.)单项式 monomial多项式 polynomial, multinomial系数 coefficient未知数 unknown, x-factor, y-factor, z-factor 等式,方程式 equation一次方程 simple equation二次方程 quadratic equation三次方程 cubic equation四次方程 quartic equation不等式 inequation阶乘 factorial对数 logarithm指数,幂 exponent乘方 power二次方,平方 square三次方,立方 cube四次方 the power of four, the fourth powern次方 the power of n, the nth power开方 evolution, extraction二次方根,平方根 square root三次方根,立方根 cube root四次方根 the root of four, the fourth rootn次方根 the root of n, the nth root集合 aggregate元素 element空集 void子集 subset交集 intersection并集 union补集 complement映射 mapping函数 function定义域 domain, field of definition 值域 range常量 constant变量 variable单调性 monotonicity奇偶性 parity周期性 periodicity图象 image数列,级数 series微积分 calculus微分 differential导数 derivative极限 limit无穷大 infinite(a.) infinity(n.)无穷小 infinitesimal积分 integral定积分 definite integral不定积分 indefinite integral有理数 rational number无理数 irrational number实数 real number虚数 imaginary number复数 complex number矩阵 matrix行列式 determinant几何 geometry点 point线 line面 plane体 solid线段 segment射线 radial平行 parallel相交 intersect角 angle角度 degree弧度 radian锐角 acute angle直角 right angle钝角 obtuse angle平角 straight angle周角 perigon底 base边 side高 height三角形 triangle锐角三角形 acute triangle直角三角形 right triangle直角边 leg斜边 hypotenuse勾股定理 Pythagorean theorem钝角三角形 obtuse triangle不等边三角形 scalene triangle等腰三角形 isosceles triangle等边三角形 equilateral triangle四边形 quadrilateral平行四边形 parallelogram矩形 rectangle长 length宽 width菱形 rhomb, rhombus, rhombi(pl.), diamond 正方形 square梯形 trapezoid直角梯形 right trapezoid等腰梯形 isosceles trapezoid五边形 pentagon六边形 hexagon七边形 heptagon八边形 octagon九边形 enneagon十边形 decagon十一边形 hendecagon十二边形 dodecagon多边形 polygon正多边形 equilateral polygon圆 circle圆心 centre(BrE), center(AmE)半径 radius直径 diameter圆周率 pi弧 arc半圆 semicircle扇形 sector环 ring椭圆 ellipse圆周 circumference周长 perimeter面积 area轨迹 locus, loca(pl.)相似 similar全等 congruent四面体 tetrahedron五面体 pentahedron六面体 hexahedron平行六面体 parallelepiped立方体 cube七面体 heptahedron八面体 octahedron九面体 enneahedron十面体 decahedron十一面体 hendecahedron十二面体 dodecahedron二十面体 icosahedron多面体 polyhedron棱锥 pyramid棱柱 prism棱台 frustum of a prism旋转 rotation轴 axis圆锥 cone圆柱 cylinder圆台 frustum of a cone球 sphere半球 hemisphere底面 undersurface表面积 surface area体积 volume空间 space坐标系 coordinates坐标轴 x-axis, y-axis, z-axis 横坐标 x-coordinate纵坐标 y-coordinate原点 origin双曲线 hyperbola抛物线 parabola三角 trigonometry正弦 sine余弦 cosine正切 tangent余切 cotangent正割 secant余割 cosecant反正弦 arc sine反余弦 arc cosine反正切 arc tangent反余切 arc cotangent反正割 arc secant反余割 arc cosecant相位 phase周期 period振幅 amplitude内心 incentre(BrE), incenter(AmE)外心 excentre(BrE), excenter(AmE)旁心 escentre(BrE), escenter(AmE)垂心 orthocentre(BrE), orthocenter(AmE)重心 barycentre(BrE), barycenter(AmE)内切圆 inscribed circle外切圆 circumcircle统计 statistics平均数 average加权平均数 weighted average方差 variance标准差 root-mean-square deviation, standard deviation 比例 propotion百分比 percent百分点 percentage百分位数 percentile排列 permutation组合 combination概率,或然率 probability分布 distribution正态分布 normal distribution非正态分布 abnormal distribution图表 graph条形统计图 bar graph柱形统计图 histogram折线统计图 broken line graph曲线统计图 curve diagram扇形统计图 pie diagram。
美国大学生数学建模竞赛优秀论文翻译
优化和评价的收费亭的数量景区简介由於公路出来的第一千九百三十,至今发展十分迅速在全世界逐渐成为骨架的运输系统,以其高速度,承载能力大,运输成本低,具有吸引力的旅游方便,减少交通堵塞。
以下的快速传播的公路,相应的管理收费站设置支付和公路条件的改善公路和收费广场。
然而,随着越来越多的人口密度和产业基地,公路如花园州公园大道的经验严重交通挤塞收费广场在高峰时间。
事实上,这是共同经历长时间的延误甚至在非赶这两小时收费广场。
在进入收费广场的车流量,球迷的较大的收费亭的数量,而当离开收费广场,川流不息的车辆需挤缩到的车道数的数量相等的车道收费广场前。
因此,当交通繁忙时,拥堵现象发生在从收费广场。
当交通非常拥挤,阻塞也会在进入收费广场因为所需要的时间为每个车辆付通行费。
因此,这是可取的,以尽量减少车辆烦恼限制数额收费广场引起的交通混乱。
良好的设计,这些系统可以产生重大影响的有效利用的基础设施,并有助于提高居民的生活水平。
通常,一个更大的收费亭的数量提供的数量比进入收费广场的道路。
事实上,高速公路收费广场和停车场出入口广场构成了一个独特的类型的运输系统,需要具体分析时,试图了解他们的工作和他们之间的互动与其他巷道组成部分。
一方面,这些设施是一个最有效的手段收集用户收费或者停车服务或对道路,桥梁,隧道。
另一方面,收费广场产生不利影响的吞吐量或设施的服务能力。
收费广场的不利影响是特别明显时,通常是重交通。
其目标模式是保证收费广场可以处理交通流没有任何问题。
车辆安全通行费广场也是一个重要的问题,如无障碍的收费广场。
封锁交通流应尽量避免。
模型的目标是确定最优的收费亭的数量的基础上进行合理的优化准则。
主要原因是拥挤的随着经济的发展,交通系统逐渐形成和完善自己。
不同种类的车辆已迅速改善的数量,质量,速度,和类型。
为了支付维修费用的高速公路,收费站系统的建立。
然而,费时费给我们带来的拥塞,高度增加烦恼的司机。
一般来说,在收费亭的数量大于数量的车道。
2012年美国大学生数学建模竞赛B题特等奖文章翻译要点
2012年美赛B题题目翻译:到Big Long River(225英里)游玩的游客可以享受那里的风景和振奋人心的急流。
远足者没法到达这条河,唯一去的办法是漂流过去。
这需要几天的露营。
河流旅行始于First Launch,在Final Exit结束,共225英里的顺流。
旅客可以选择依靠船桨来前进的橡皮筏,它的速度是4英里每小时,或者选择8英里每小时的摩托船。
旅行从开始到结束包括大约6到18个晚上的河中的露营。
负责管理这条河的政府部门希望让每次旅行都能尽情享受野外经历,同时能尽量少的与河中其他的船只相遇。
当前,每年经过Big Long河的游客有X组,这些漂流都在一个为期6个月时期内进行,一年中的其他月份非常冷,不会有漂流。
在Big Long上有Y处露营地点,平均分布于河廊。
随着漂流人数的增加,管理者被要求应该允许让更多的船只漂流。
他们要决定如何来安排最优的方案:包括旅行时间(以在河上的夜晚数计算)、选择哪种船(摩托还是桨船),从而能够最好地利用河中的露营地。
换句话说,Big Long River在漂流季节还能增加多少漂流旅行数?管理者希望你能给他们最好的建议,告诉他们如何决定河流的容纳量,记住任两组旅行队都不能同时占据河中的露营地。
此外,在你的摘要表一页,准备一页给管理者的备忘录,用来描述你的关键发现。
沿着大朗河露营摘要我们开发了一个模型来安排沿大河的行程。
我们的目标是为了优化乘船旅行的时间,从而使6个月的旅游旺季出游人数最大化。
我们模拟团体从营地到营地旅行的过程。
根据给定的约束条件,我们的算法输出了每组沿河旅行最佳的日程安排。
通过研究算法的长期反应,我们可以计算出旅行的最大数量,我们定义为河流的承载能力。
我们的算法适应于科罗多拉大峡谷的个案分析,该问题的性质与大长河问题有许多共同之处。
最后,我们考察当改变推进方法,旅程时间分布,河上的露营地数量时承载能力的变化的敏感性。
我们解决了使沿大朗河出游人数最大化的休闲旅行计划。
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Aabsolute 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Bbalanced 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Ccalculate 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 distributionfunction 累加分布函数curve estimation 曲线估计Ddata 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Eeaqual 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Ffactor 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Ggamma distribution 伽玛分布geometric mean 几何均值group 组Hharmomic 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Iindependence 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Kkernal 核Kolmogorov-Smirnov test 柯尔莫哥洛夫-斯米诺夫检验kurtosis 峰度Llarge 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Mmain effect 主效应matrix 矩阵maximum 最大值maximum likelihoodestimation 极大似然估计mean squareddeviation(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 correlationcoefficient 复相关系数multiple correlationcoefficient 多元相关系数multiple regression analysis多元回归分析multiple regressionequation 多元回归方程multiple response 多响应multivariate analysis 多元分析Nnegative 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Oone-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Ppaired 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Qqadratic 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Rrandom 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Ssample 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 regressionanalysis 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Ttable 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Uunbalanced 不平衡的unbiased estimation 无偏估计unbiasedness 无偏性uniform distribution 均匀分布Vvalue 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Wweight 加权,权重weighted average 加权平均值within groups 组内的ZZ score Z分数Ⅱ.2 最优化方法词汇英汉对照表Aactive 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Bbandwidth 带宽be equivalent to 等价于best-fit 最佳拟合bound 边界Ccoefficient 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 polynomialinterpolation method三次多项式插值法curve-fitting 曲线拟合Ddata-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Eeigenvalue 特征值empty matrix 空矩阵equality 等式exceeded 溢出的Ffeasible 可行的feasible solution 可行解finite-difference 有限差分first-order 一阶GGauss-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Iindependent 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JJacobian 雅可比矩阵LLagrange 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-Marquardtmethod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 programmingproblem 线性规划问题local solution 局部解Mmedium-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Nnonlinear 非线性的norm 范数Oobjective 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Pparameter 参数partial derivatives 偏导数polynomial interpolation method多项式插值法Qquadratic 二次的quadratic interpolation method 二次内插法quadratic programming 二次规划Rreal-value 实数值residuals 残差robust 稳健的robustness 稳健性,鲁棒性Sscalar 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 regionmethod 子空间置信域法sum-of-squares 平方和symmetric matrix 对称矩阵Ttermination message 终止信息termination tolerance 终止容限the exit condition 退出条件the method of steepestdescent 最速下降法transpose 转置Uunconstrained 无约束的under-determined system负定系统Vvariable 变量vector 矢量Wweighting matrix 加权矩阵Ⅱ.3 样条词汇英汉对照表Aapproximation 逼近array 数组a spline in b-form/b-splineb样条a spline of polynomial piece/ppform spline分段多项式样条Bbivariate spline function 二元样条函数break/breaks 断点Ccoefficient/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Ddegree of freedom 自由度dimension 维数Eend conditions 约束条件Iinput argument 输入参数interpolation 插值/内插interval 取值区间Kknot/knots 节点Lleast-squaresapproximation 最小二乘拟合Mmultiplicity 重次multivariate function 多元函数Ooptional argument 可选参数order 阶次output argument 输出参数Ppoint/points 数据点Rrational spline 有理样条rounding error 舍入误差(相对误差)Sscalar 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Ttolerance 允许精度Uunivariate function 一元函数Vvector 向量Wweight/weights 权重Ⅱ.4 偏微分方程数值解词汇英汉对照表Aabsolute error 绝对误差absolute tolerance 绝对容限adaptive mesh 适应性网格Bboundary condition 边界条件Ccontour plot 等值线图converge 收敛coordinate 坐标系Ddecomposed 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Eeigenvalue 特征值elliptic 椭圆形的error estimate 误差估计exact solution 精确解Ggeneralized Neumann boundary condition推广的Neumann边界条件geometry 几何形状geometry descriptionmatrix 几何描述矩阵geometry matrix 几何矩阵graphical user interface(GUI)图形用户界面Hhyperbolic 双曲线的Iinitial mesh 初始网格Jjiggle 微调LLagrange multipliers 拉格朗日乘子Laplace equation 拉普拉斯方程linear interpolation 线性插值loop 循环Mmachine precision 机器精度mixed boundary condition混合边界条件NNeuman boundarycondition Neuman边界条件node point 节点nonlinear solver 非线性求解器normal vector 法向量PParabolic 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Qquality 质量Rrefined 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Ssingular 奇异的sparce matrix 稀疏矩阵stiffness matrix 刚度矩阵subregion 子域Ttriangular mesh 三角形网格Uundetermined 未定的uniform refinement 均匀加密uniform triangle net 均匀三角形网络Wwave equation 波动方程Algebraic Equation代数方程Elementary Operations-Addition基础混算-加法ElementaryOperations-Subtaction基础混算-减法ElementaryOperations-Multiplication基础混算-乘法Elementary Operations-Division基础混算-除法Elementary Operation基础四则混算Decimal Operations 小数混算Fractional Operations分数混算Convert fractional no. intodecimal no.分数转小数Convert fractional no. intopercentage.分数转百分数Convert decimal no. intopercentage.小数转百分数Convert percentage into decimal no.百分数转小数Percentage百分数Numerals数字符号Common factors and multiples公因子及公倍数Sorting数字排序Area图形面积Perimeter图形周界Change Units : Time单位转换-时间Change Units : Weight 单位转换-重量Change Units :Length单位转换-长度Directed Numbers 有向数Fractional Operations 分数混算Decimal Operations 小数混算Convert fractional no. into decimal no.分数转小数Convert fractional no. into percentage.分数转百分数Convert decimal no. into percentage.小数转百分数Convert percentage into decimal no.百分数转小数Percentage百分数Indices指数Algebraic Substitution 代数代入Polynomials多项式Co-Geometry坐标几何学Solving Linear Equation解一元线性方程Solving Simultaneous Equation解联立方程Slope直线斜率Equation of Straight Line直线方程x-intercept ( Equation of St. Line )直线x轴截距y-intercept ( Equation of St. Line )直线y轴截距Factorization因式分解Quadratic Equation 二次方程x-intercept ( Quadratic Equation )二次曲线x轴截距Geometry几何学Inequalities不等式Rate and Ratio比和比例Bearing方位角Trigonometry三角学Probability概率Statistics-Graph统计学-统计图表Statistics-Measure of centraltendency统计学-量度集中趋势Salary Tax薪俸税Bridging Game汉英对对碰Indices指数Function函数Rate and Ratio比和比例Trigonometry三角学Inequalities不等式Linear Programming线性规划Co-Geometry坐标几何学Slope直线斜率Equation of Straight Line直线方程x-intercept ( Equation of St. Line )直线x轴截距y-intercept ( Equation of St. Line )直线y轴截距Factorization因式分解Quadratic Equation二次方程x-intercept ( Quadratic Equation )二次曲线x轴截距Method of Bisection分半方法Polynomials多项式Probability概率Statistics-Graph统计学-统计图表Statistics-Measure of centraltendency统计学-量度集中趋势Statistics-Measure of dispersion统计学-量度分布Statistics-Normal Distribution统计学-正态分布Surds根式Probability概率Statistics-Measure of dispersion统计学-量度离差Statistics-Normal Distribution统计学-正态分布Statistics-Binomial Distribution统计学Statistics-Poisson Distribution统计学Statistics-Geometric Distribution统计学Co-Geometry坐标几何学Sequence序列十万Hundred thousand三位数3-digit number千Thousand千万Ten million小数Decimal分子Numerator分母Denominator分数Fraction五位数5-digit number公因子Common factor公倍数Common multiple中国数字Chinese numeral平方Square平方根Square root古代计时工具Ancient timingdevice古代记时工具Ancienttime-recording device古代记数方法Ancient countingmethod古代数字Ancient numeral包含Grouping四位数4-digit number四则计算Mixed operations (Thefour operations)加Plus加法Addition加法交换性质Commutativeproperty of addition未知数Unknown百分数Percentage百万Million合成数Composite number多位数Large number因子Factor折扣Discount近似值Approximation阿拉伯数字Hindu-Arabic numeral定价Marked price括号Bracket计算器Calculator差Difference真分数Proper fraction退位Decomposition除Divide除法Division除数Divisor乘Multiply乘法Multiplication乘法交换性质Commutative property of multiplication乘法表Multiplication table乘法结合性质Associative property of multiplication被除数Dividend珠算Computation using Chinese abacus倍数Multiple假分数Improper fraction带分数mixed number现代计算工具Modern calculating devices售价Selling price万Ten thousand最大公因子Highest Common Factor (H.C.F.)最小公倍数Lowest Common Multiple (L.C.M.)减Minus / Subtract减少Decrease减法Subtraction等分Sharing 等于Equal进位Carrying短除法Short division单数Odd number循环小数Recurring decimal零Zero算盘Chinese abacus亿Hundred million增加Increase质数Prime number积Product整除性Divisibility双数Even number罗马数字Roman numeral数学mathematics, maths(BrE),math(AmE)公理axiom定理theorem计算calculation运算operation证明prove假设hypothesis, hypotheses(pl.)命题proposition算术arithmetic加plus(prep.), add(v.),addition(n.)被加数augend, summand加数addend和sum减minus(prep.), subtract(v.),subtraction(n.)被减数minuend减数subtrahend差remainder乘times(prep.), multiply(v.),multiplication(n.)被乘数multiplicand, faciend乘数multiplicator积product除divided by(prep.), divide(v.),division(n.)被除数dividend除数divisor商quotient等于equals, is equal to, isequivalent to大于is greater than小于is lesser than大于等于is equal or greater than小于等于is equal or lesser than运算符operator平均数mean算术平均数arithmatic mean几何平均数geometric mean n个数之积的n次方根倒数(reciprocal)x的倒数为1/x有理数rational number无理数irrational number实数real number虚数imaginary number数字digit数number自然数natural number整数integer小数decimal小数点decimal point分数fraction分子numerator分母denominator比ratio正positive负negative零null, zero, nought, nil十进制decimal system二进制binary system十六进制hexadecimal system权weight, significance进位carry截尾truncation四舍五入round下舍入round down上舍入round up有效数字significant digit无效数字insignificant digit代数algebra公式formula, formulae(pl.)单项式monomial多项式polynomial, multinomial 系数coefficient未知数unknown, x-factor, y-factor, z-factor等式,方程式equation一次方程simple equation二次方程quadratic equation三次方程cubic equation四次方程quartic equation不等式inequation阶乘factorial对数logarithm指数,幂exponent乘方power二次方,平方square三次方,立方cube四次方the power of four, the fourth powern次方the power of n, the nth power开方evolution, extraction二次方根,平方根square root 三次方根,立方根cube root四次方根the root of four, the fourth rootn次方根the root of n, the nth rootsqrt(2)=1.414sqrt(3)=1.732sqrt(5)=2.236常量constant变量variable坐标系coordinates坐标轴x-axis, y-axis, z-axis横坐标x-coordinate纵坐标y-coordinate原点origin象限quadrant截距(有正负之分)intercede(方程的)解solution几何geometry点point线line面plane 体solid线段segment射线radial平行parallel相交intersect角angle角度degree弧度radian锐角acute angle直角right angle钝角obtuse angle平角straight angle周角perigon底base边side高height三角形triangle锐角三角形acute triangle直角三角形right triangle直角边leg斜边hypotenuse勾股定理Pythagorean theorem钝角三角形obtuse triangle不等边三角形scalene triangle等腰三角形isosceles triangle等边三角形equilateral triangle四边形quadrilateral平行四边形parallelogram矩形rectangle长length宽width周长perimeter面积area相似similar全等congruent三角trigonometry正弦sine余弦cosine正切tangent余切cotangent正割secant余割cosecant反正弦arc sine反余弦arc cosine反正切arc tangent反余切arc cotangent反正割arc secant反余割arc cosecant补充:集合aggregate元素element空集void子集subset交集intersection并集union补集complement映射mapping函数function定义域domain, field ofdefinition值域range单调性monotonicity奇偶性parity周期性periodicity图象image数列,级数series微积分calculus微分differential导数derivative极限limit无穷大infinite(a.) infinity(n.)无穷小infinitesimal积分integral定积分definite integral不定积分indefinite integral复数complex number矩阵matrix行列式determinant圆circle圆心centre(BrE), center(AmE)半径radius直径diameter圆周率pi弧arc半圆semicircle扇形sector环ring椭圆ellipse圆周circumference轨迹locus, loca(pl.)平行六面体parallelepiped立方体cube七面体heptahedron八面体octahedron九面体enneahedron十面体decahedron十一面体hendecahedron十二面体dodecahedron二十面体icosahedron多面体polyhedron旋转rotation轴axis球sphere半球hemisphere底面undersurface表面积surface area体积volume空间space双曲线hyperbola抛物线parabola四面体tetrahedron五面体pentahedron六面体hexahedron菱形rhomb, rhombus, rhombi(pl.), diamond正方形square梯形trapezoid直角梯形right trapezoid等腰梯形isosceles trapezoid五边形pentagon六边形hexagon七边形heptagon八边形octagon九边形enneagon十边形decagon十一边形hendecagon十二边形dodecagon多边形polygon正多边形equilateral polygon相位phase周期period振幅amplitude内心incentre(BrE), incenter(AmE)外心excentre(BrE),excenter(AmE)旁心escentre(BrE),escenter(AmE)垂心orthocentre(BrE),orthocenter(AmE)重心barycentre(BrE),barycenter(AmE)内切圆inscribed circle外切圆circumcircle统计statistics平均数average加权平均数weighted average方差variance标准差root-mean-squaredeviation, standard deviation比例propotion百分比percent百分点percentage百分位数percentile排列permutation组合combination概率,或然率probability分布distribution正态分布normal distribution非正态分布abnormaldistribution图表graph条形统计图bar graph柱形统计图histogram折线统计图broken line graph曲线统计图curve diagram扇形统计图pie diagramEnglish Chineseabbreviation 简写符号;简写abscissa 横坐标absolute complement 绝对补集absolute error 绝对误差absolute inequality 绝不等式absolute maximum 绝对极大值absolute minimum 绝对极小值absolute monotonic 绝对单调absolute value 绝对值accelerate 加速acceleration 加速度acceleration due to gravity 重力加速度; 地心加速度accumulation 累积accumulative 累积的accuracy 准确度act on 施于action 作用; 作用力acute angle 锐角acute-angled triangle 锐角三角形add 加addition 加法addition formula 加法公式addition law 加法定律addition law(of probability) (概率)加法定律additive inverse 加法逆元; 加法反元additive property 可加性adjacent angle 邻角adjacent side 邻边adjoint matrix 伴随矩阵algebra 代数algebraic 代数的algebraic equation 代数方程algebraic expression 代数式algebraic fraction 代数分式;代数分数式algebraic inequality 代数不等式algebraic number 代数数algebraic operation 代数运算algebraically closed 代数封闭algorithm 算法系统; 规则系统alternate angle (交)错角alternate segment 内错弓形alternating series 交错级数alternative hypothesis 择一假设;备择假设; 另一假设altitude 高;高度;顶垂线;高线ambiguous case 两义情况;二义情况amount 本利和;总数analysis 分析;解析analytic geometry 解析几何angle 角angle at the centre 圆心角angle at the circumference 圆周角angle between a line and a plane 直 与平面的交角angle between two planes 两平面的交角angle bisection 角平分angle bisector 角平分线 ;分角线angle in the alternate segment 交错弓形的圆周角angle in the same segment 同弓形内的圆周角angle of depression 俯角angle of elevation 仰角angle of friction 静摩擦角; 极限角angle of greatest slope 最大斜率的角angle of inclination 倾斜角angle of intersection 相交角;交角angle of projection 投射角angle of rotation 旋转角angle of the sector 扇形角angle sum of a triangle 三角形内角和angles at a point 同顶角angular displacement 角移位angular momentum 角动量angular motion 角运动angular velocity 角速度annum(X% per annum) 年(年利率X%)anti-clockwise direction 逆时针方向;返时针方向anti-clockwise moment 逆时针力矩anti-derivative 反导数; 反微商anti-logarithm 逆对数;反对数anti-symmetric 反对称apex 顶点approach 接近;趋近approximate value 近似值approximation 近似;略计;逼近Arabic system 阿刺伯数字系统arbitrary 任意arbitrary constant 任意常数arc 弧arc length 弧长arc-cosine function 反余弦函数arc-sin function 反正弦函数arc-tangent function 反正切函数area 面积Argand diagram 阿根图, 阿氏图argument (1)论证; (2)辐角argument of a complex number 复数的辐角argument of a function 函数的自变量arithmetic 算术arithmetic mean 算术平均;等差中顶;算术中顶arithmetic progression 算术级数;等差级数arithmetic sequence 等差序列arithmetic series 等差级数arm 边array 数组; 数组arrow 前号ascending order 递升序ascending powers of X X 的升幂assertion 断语; 断定associative law 结合律assumed mean 假定平均数assumption 假定;假设asymmetrical 非对称asymptote 渐近asymptotic error constant 渐近误差常数at rest 静止augmented matrix 增广矩阵auxiliary angle 辅助角auxiliary circle 辅助圆auxiliary equation 辅助方程average 平均;平均数;平均值average speed 平均速率axiom 公理axiom of existence 存在公理axiom of extension 延伸公理axiom of inclusion 包含公理axiom of pairing 配对公理axiom of power 幂集公理axiom of specification 分类公理axiomatic theory of probability 概率公理论axis 轴axis of parabola 拋物线的轴axis of revolution 旋转轴axis of rotation 旋转轴axis of symmetry 对称轴back substitution 回代bar chart 棒形图;条线图;条形图;线条图base (1)底;(2)基;基数base angle 底角base area 底面base line 底线base number 底数;基数base of logarithm 对数的底basis 基Bayes' theorem 贝叶斯定理bearing 方位(角);角方向(角)bell-shaped curve 钟形图belong to 属于Bernoulli distribution 伯努利分布Bernoulli trials 伯努利试验bias 偏差;偏倚biconditional 双修件式; 双修件句bijection 对射; 双射; 单满射bijective function 对射函数; 只射函数billion 十亿bimodal distribution 双峰分布binary number 二进数binary operation 二元运算binary scale 二进法binary system 二进制binomial 二项式binomial distribution 二项分布binomial expression 二项式binomial series 二项级数binomial theorem 二项式定理bisect 平分;等分bisection method 分半法;分半方法bisector 等分线 ;平分线Boolean algebra 布尔代数boundary condition 边界条件boundary line 界(线);边界bounded 有界的bounded above 有上界的;上有界的bounded below 有下界的;下有界的bounded function 有界函数bounded sequence 有界序列brace 大括号bracket 括号breadth 阔度broken line graph 折线图calculation 计算calculator 计算器;计算器calculus (1) 微积分学; (2) 演算cancel 消法;相消canellation law 消去律canonical 典型; 标准capacity 容量cardioid 心脏Cartesian coordinates 笛卡儿坐标Cartesian equation 笛卡儿方程Cartesian plane 笛卡儿平面Cartesian product 笛卡儿积category 类型;范畴catenary 悬链Cauchy sequence 柯西序列Cauchy's principal value 柯西主值Cauchy-Schwarz inequality 柯西- 许瓦尔兹不等式central limit theorem 中心极限定理central line 中线central tendency 集中趋centre 中心;心centre of a circle 圆心centre of gravity 重心centre of mass 质量中心centrifugal force 离心力centripedal acceleration 向心加速度centripedal force force 向心力centroid 形心;距心certain event 必然事件chain rule 链式法则chance 机会change of axes 坐标轴的变换change of base 基的变换change of coordinates 坐标轴的变换change of subject 主项变换change of variable 换元;变量的换characteristic equation 特征(征)方程characteristic function 特征(征)函数characteristic of logarithm 对数的首数; 对数的定位部characteristic root 特征(征)根chart 图;图表check digit 检验数位checking 验算chord 弦chord of contact 切点弦circle 圆circular 圆形;圆的circular function 圆函数;三角函数circular measure 弧度法circular motion 圆周运动circular permutation 环形排列;圆形排列; 循环排列circumcentre 外心;外接圆心circumcircle 外接圆circumference 圆周circumradius 外接圆半径circumscribed circle 外接圆cissoid 蔓叶class 区;组;类class boundary 组界class interval 组区间;组距class limit 组限;区限class mark 组中点;区中点classical theory of probability 古典概率论classification 分类clnometer 测斜仪clockwise direction 顺时针方向clockwise moment 顺时针力矩closed convex region 闭凸区域closed interval 闭区间coaxial 共轴coaxial circles 共轴圆coaxial system 共轴系coded data 编码数据coding method 编码法co-domain 上域coefficient 系数coefficient of friction 摩擦系数coefficient of restitution 碰撞系数; 恢复系数coefficient of variation 变差系数cofactor 余因子; 余因式cofactor matrix 列矩阵coincide 迭合;重合collection of terms 并项collinear 共线collinear planes 共线面collision 碰撞column (1)列;纵行;(2) 柱column matrix 列矩阵column vector 列向量combination 组合common chord 公弦common denominator 同分母;公分母common difference 公差。