美国数学建模比赛规则翻译

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。

附录1 中、美数学建模竞赛简介1.美国大学生数学建模竞赛简介现代社会的发展，需要数学理论与方法，但更需要熟悉各种数学方法，能够与物理学家、工程师等合作，能够解决实际问题的专家。

这种需要也必然引起大学数学教学的改革。

例如，英国牛津大学就有数学建模方面的博士点，而美国人直接将数学建模课引入理科、理工科大学生的教学中，并设立了一年一次的“大学生数学建模竞赛”，简记为MCM 。

这个竞赛吸引了许多国家的大学派队参赛，其国际影响及权威性日益增加。

美国为此有专门的刊物，比如《数学和计算机建模》：Mathematical and Computer Modelling ─ An International Journal ，缩写为 put.Modelling ，1980年创刊，开始是季刊，很快改为月刊。

1988年以前刊名叫Mathematical Modelling ─ An International Journal ，每隔一年出一次国际数学建模会议纪要（近1000页）作为增刊。

我国部分高校从1989年开始组队参赛，并取得很好的成绩。

美国大学生MCM 有如下特点：(1) 参赛队都必须事先报名注册，每个系至多2个队，每队3名队员。

参赛队员直到比赛前一分钟都可换掉，而不必通知竞赛委员会（COMAP ）；若某系事先只报名注册一个队，赛前想再增加一个队，则必须事先从COMAP 取得考号（ Control Number ）才行；(2) 每个队都将收到2个考题：A 、B ，由参赛队3个队员任选一题给出解答。

一旦选定考题，队员不得与教练或其他无关人员讨论题目的解答等相关事宜。

参赛队可使用计算机、软件包、图书馆等类似工具参加竞赛。

参赛题目不一定有解答（如猜想等），若有答案，也不一定是唯一答案。

例如86-B 紧急救援机构选址问题：Steiner 树问题：平面上有m 个点p1、p2、…、pm ，再加一点p 向pi (1≤i ≤m)连直线，使得连线总长最短，如何求p ？这是一个NP-Complete 问题。

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。

美国数学建模竞赛的相关信息一．美国数学建模竞赛MCM简介MCM全称：The Mathematical Contest in Modeling（数学建模竞赛，国内称为美国国际数模竞赛）ICM全称：The Interdisciplinary Contest in Modeling（交叉学科建模竞赛，国内称为美国大学生数学建模与交叉学科竞赛）MCM始于1985年，由美国自然基金协会和美国数学应用协会共同主办，美国运筹学学会、工业与应用数学学会、数学学会等多家机构协办。

其宗旨是鼓励大学生对范围并不固定的各种实际问题予以阐明、分析并提出解法，每队在4天内对问题展开设计，要以清楚定义的格式写出解法论文。

该项比赛吸引了中国（含香港）、美国、英国、加拿大、芬兰、爱尔兰、澳大利亚、南非、新加坡等多个国家的著名大学代表队参加。

1999年COMAP推出了交叉学科建模竞赛。

其特等奖论文将刊登于同年UMAP杂志。

近年来，MCM/ICM比赛越来越具有影响力，也得到越来越多的学校和单位认可。

其获奖学生在出国留学、保送研究生、找工作时，在激烈的竞争中胜出的机会要多很多。

MCM将题目公开在网络上这种开放式的竞赛方式，竞赛环境相对而言比较自由，然而参赛选手来世界各地，竞争之激烈可想而知。

MCM/ICM其要求与国内竞赛大致相同，除了要求用英语阅读、写作水平外。

这对于中国的学生来说是一个非常大的挑战，如果成功参赛，将极大程度上提高英语水平。

总而言之，在建模期间，知识将会进一步积累，知识面也会得到提高，而英语写作能力、资料的检索能力、创新能力等都将得到训练，这些能力综合起来其实就是科研能力，将为今后的科研打下坚实的基础。

二．美国数学建模竞赛网站进入方法首先进入中国数学建模网站，点击友情链接页面，找到美国大学生数学建模竞赛，点击即可直接进入网站。

具体过程如下：全国数学建模竞赛/友情链接/html_cn/block/f104f25e0431f7882cb1ddd5be2d8a14.html美国大学生数学建模竞赛(MCM & ICM in USA)/undergraduate/contests/三．2011年美国大学生数学建模竞赛（MCM/ICM）竞赛2011年美国大学生数学建模竞赛（MCM/ICM）竞赛于（美国东部时间）2011年2月10日晚8:01~14日晚8:00举行。

MCM: The Mathematical Contest in ModelingICM: The Interdisciplinary Contest in ModelingMCM：数学建模竞赛ICM：交叉学科建模竞赛Contest Registration and Instructions竞赛注册和指导(All instructions and rules apply to ICM as well as to MCM, 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 MCM a team must be sponsored by a faculty advisor f rom their institution. The registration process must be completed by the advisor.每个MCM的参赛队需有一名所在单位的指导教师负责。

整个注册报名过程需由该指导教师完成。

IMPORTANT CHANGE TO CONTEST RULES FOR MCM/ICM 2009:2009年MCM/ICM规则的重要改变：Teams (Student or Advisor) are now required to submit an electronic copy of their solution paper by email to solutions@. Your email MUST be received at COMAP by the submission deadline of 8:00 PM EST, February 9, 2009.要求参赛队（由学生或者指导教师）通过Email提交一份解决方案的电子版拷贝，发到solutions@。

Email邮件必须在美国东部时间2009年2月9日上午8点前发到COMAP。

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。

PROBLEM A: The Keep-Right-Except-To-Pass Rule The Keep-Right-Except-To-Pass RuleIn countries where driving automobiles on the right is the rule (that is, USA, China and most other countries except for Great Britain, Australia, and some former British colonies), multi-lane freeways often employ a rule that requires drivers to drive in the right-most lane unless they are passing another vehicle, in which case they move one lane to the left, pass, and return to their former travel lane.Build and analyze a mathematical model to analyze the performance of this rule in light and heavy traffic. You may wish to examine tradeoffs between traffic flow and safety, the role of under- or over-posted speed limits (that is, speed limits that are too low or too high), and/or other factors that may not be explicitly called out in this problem statement. Is this rule effective in promoting better traffic flow? If not, suggest and analyze alternatives (to include possibly no rule of this kind at all) that might promote greater traffic flow, safety, and/or other factors that you deem important.In countries where driving automobiles on the left is the norm, argue whether or not your solution can be carried over with a simple change of orientation, or would additional requirementsbe needed.Lastly, the rule as stated above relies upon human judgment for compliance. If vehicle transportation on the same roadway was fully under the control of an intelligent system – either part ofthe road network or imbedded in the design of all vehicles using the roadway – to what extent would this change the results ofyour earlier analysis?问题A ：除非超车否则靠右行驶的交通规则在一些汽车靠右行驶的国家（比如美国，中国等等），多车道的高速公路常常遵循以下原则：司机必须在最右侧驾驶，除非他们正在超车，超车时必须先移到左侧车道在超车后再返回。

1.序言定义的国会选区在美国长期以来一直是争论的来源。

由于district-drawers都是由当前的执政者选择，边界被用来将不支持的少数人口和支持的大多数分成一组来影响未来的选举，这一过程称为徇私。

各选区普遍呈现出奇特的形状，以一种随意的方式跨多城市和农村的纤细部门，唯一合法的立法边界的限制规定选区必须含有相同的人群，但各区的构造是完全留给district-drawers。

在英国和加拿大，各地区都更加紧凑和直观的。

他们在缓解徇私上的成功归因于将边界划分任务交给无党派顾问小组。

然而，这些独立的委员会可以采取2-3年才能最终确定一个新的划分方案，要求其有效性问题。

它似乎很清楚，美国应该建立类似的公正委员会，但应做出一些努力，以提高这些群体的效率。

因此，我们的目标是过程中，开发有助于选区重划得一个小的工具箱。

具体来说，我们将创建一个模型，使用简单的几何结构划定合理的边界。

1.1当前模型大多数用于创建选区的方法可分为两类：一是依赖于当前分界线布局（最常用县）和另一是那些不依赖于当前的分界线。

多数属于前一类。

通过使用当前的选区分界，问题归结为通过使用多种数学程序将选区分界以一个理想的方式分组。

特拉等人使用图形分割理论来聚集总人口的变化在2％左右的平均选区规模。

赫斯和韦弗使用一个迭代的过程来定义人口的重心，使用整数规划将各县分组成相等人口的选区，然后重复上述过程，直到的质心达到一个极限。

Garfinkel和Nemhauser的使用迭代矩阵操作搜索的选区组合，是连续和紧凑。

凯撒开始系统地用当前选区和相邻地区进行人口交换。

所有这些方法都使用县为他们的分界，因为它们将国家分割成数量相对较少的部分。

这是必要的，因为当使用更多分界时，大多数的他们使用的数学工具变得缓慢，不精确。

（这就像是说，当国家被划分为更多的连续部门，在极限状态下他们变得不可用。

）因此，使用小的部门，如邮政编码，平均比纽约的一个县小5倍，变得不切实际。

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。

Contest Rules, Registration and Instructions(All rules and instructions apply to both ICM and MCM contests, except where otherwise noted.)To participate in a contest, each team must be sponsored by a faculty advisor from its institution.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.COMAP is pleased to announce a new supplement to the MCM/ICM contest. Click here to read more details.I. BEFORE THE CONTEST BEGINS:A. RegistrationB. Choose your team membersII. AFTER THE CONTEST BEGINS:A. View the contest problems via the contest web siteB. Choose a problemC. Teams prepare solutionsD. Print Summary Sheet and Control SheetIII. BEFORE THE CONTEST ENDS:A. Send electronic copy of Solution Paper by emailIV. WHEN THE CONTEST ENDS:A. Prepare Solution PacketB. Mail Solution PacketV. AFTER THE CONTEST IS OVER:A. Confirm that your team’s solution was receivedB. Check contest resultsC. CertificatesD. PrizesIMPORTANT NOTES:z COMAP is the final arbiter of all rules and policies, and may disqualify or refuse to register any team that, in its sole discretion, does not follow these contest regulations and procedures.z If a team is caught violating the rules, the faculty advisor will not be permitted to advise another team for one year, and the advisor’s institution will be put on probation for one year.z If a team from the same institution is caught violating the rules a second time, then that school will not beallowed to compete for a period of at least one year.z All times given in these instructions are in terms of Eastern Standard Time (EST). (COMAP is located in the U.S. Eastern Time zone.)I. BEFORE THE CONTEST BEGINS:A. RegistrationAll teams must be registered before 2PM EST on Thursday, February 9, 2012. We recommend that all teams complete the registration process well in advance, since the registration system will not accept any newteam registrations after the deadline. COMAP will not accept late registrations for MCM/ICM 2012 under any circumstances. NO EXCEPTIONS WILL BE MADE.1.Register your team online via the contest web site: Go to/undergraduate/contests/mcm.a. If you are registering your first team for this year’s contest, click on Register for 2012 Contest on theleft-hand side of the screen.Enter all the required information, including your email address and contact information.IMPORTANT: Be sure to use a valid and current email address so that we can use it to contact you atany point before, during, and after the contest, if necessary.b. If you have already registered a team for this year’s contest and want to register a second team, click onAdvisor Login, then log in with the same email address and password that you used when youregistered your first team. Once you’re logged in, click on Register Another Team near the upper rightcorner of the page, then follow the instructions there.Note: An advisor may register no more than two (2) teams. If you already registered two teams, theRegister Another Team link will not appear. The system will not allow you to register more than twoteams.c. Although each advisor can register only two teams, there is no restriction on the number of advisors orteams that can register from any particular institution or department.2.Registration FeeA $100 registration fee per team is required.For an additional $100 fee per team, you can receive a Judges Commentary written specifically about your team’s paper.We accept payment with Mastercard or Visa only via our secure web site. We cannot accept other forms of payment. Our secure site will process your credit card payment, so your credit card number is protected. Our system will not store your credit card number after it processes your payment.3.After we receive approval from your financial institution (this takes only a few seconds), the system willissue a control number for your team. Your team is not officially registered until you have received a team control number. Print the page that displays your team control number: It is your only confirmation that your team has been registered. This page also lists the email address and password that you entered when registering; you will need this information to complete the contest procedures.You will NOT receive an email confirmation of your registration.4.If you need to change any of the information (name, address, contact information, etc.) that you specifiedwhen you registered, you can do so at any point before or during the contest by logging in to the contest web site with the same email address and password that you used when registering (click on the Advisor Login link on the left side of the screen). Once logged in, click on the Edit Advisor or Institution Data link near the upper right corner of the page.5.Check the contest web site regularly for any updated instructions or announcements about the contest.Except in extreme circumstances, COMAP will not send any confirmation, reminders, or announcements by email. All communication regarding the contest will be via the contest web site.6.You will return to the contest web site during the contest to enter and confirm information about your team,and to print out your team’s Control Sheet and Summary Sheets, which you will use when preparing your team’s solution packet. Details on these steps follow in the instructions below.B. Choose your team members:1.You must choose your team members before the contest begins at 8PM EST on Thursday February 9,2012. Once the contest begins you may not add or change any team members (you may, however, remove a team member, if he or she decides not to participate).2.Each team may consist of a maximum of three students.3.Each student may participate on only one team.4.Team members must be enrolled in school at the time of the contest, but they need not be full-time students.Team members must be enrolled at the same school as the advisor and other team members.II. AFTER THE CONTEST BEGINS:A. View the contest problems via the contest web site:Teams can view the contest problems via the contest web site when the contest begins at 8PM EST onThursday February 9, 2012:1.The contest problems will become available precisely at 8PM EST on Thursday February 9, 2012; teammembers can view them by visiting /undergraduate/contests/mcm. No passwordwill be needed to view the problems; simply go to the contest web site at or after 8PM EST on Thursday,February 9, 2012 and you will see a link to view the problems.2.If you cannot access our main web site at that time, go to our mirror site at ap-/mcm or click here. If you cannot access either site, there may be a problem with your localInternet connection. Contact your local Internet service provider to resolve the issue.B. Choose a problem:Each team must choose one problem according to the following rules:• MCM teams must choose either Problem A or Problem B; an MCM team may submit a solution to only one of the problems. (MCM teams should NOT choose Problem C.)• ICM teams must choose Problem C. There is no choice for ICM teams. (ICM teams should NOT choose Problem A or Problem B.)C. Teams prepare solutions:1.Teams may use any inanimate source of data or materials: computers, software, references, web sites,books, etc. ALL SOURCES USED MUST BE CREDITED. Failure to credit a source will result in a teambeing disqualified from the competition.2.Team members may not seek help from or discuss the problem with their advisor or anyone else, exceptother members of the same team. Input in any form from anyone other than student team members is strictly forbidden. This includes email, telephone contact, and personal conversation, communication via web chator other question-answer systems, or any other form of communication.3.Partial solutions are acceptable. There is no passing or failing cut-off score, and numerical scores will notbe assigned. The MCM/ICM contest judges are primarily interested in the team’s approach and methods.4.Summary Sheet: The summary is an essential part of your MCM/ICM paper. The judges placeconsiderable weight on the summary, and winning papers are often distinguished from other papers basedon the quality of the summary.To write a good summary, imagine that a reader will choose whether to read the body of the paper based on your summary: Your concise presentation in the summary should inspire a reader to learn about the detailsof your work. Thus, a summary should clearly describe your approach to the problem and, mostprominently, your most important conclusions. Summaries that are mere restatements of the contestproblem, or are a cut-and-paste boilerplate from the Introduction are generally considered to be weak.Each Summary Sheet should include:z Restatement and clarification of the problem: State in your own words what you are going to do.z Explain assumptions and rationale/justification: Emphasize the assumptions that bear on the problem.Clearly list all variables used in your model.z Include your model design and justification for type model used or developed.z Describe model testing and sensitivity analysis, including error analysis, etc.z Discuss the strengths and weaknesses of your model or approach.5.The judges will evaluate the quality of your writing in the Solution Paper:•Conciseness and organization are extremely important.•Key statements should present major ideas and results.•Present a clarification or restatement of the problem, as appropriate.•Present a clear exposition of all variables, assumptions, and hypotheses.•Present an analysis of the problem, including the motivation or justification for the model that is used.•Include a design of the model.•Discuss how the model could be tested, including error analysis and stability (conditioning, sensitivity, etc.).•Discuss any apparent strengths or weaknesses in your model or approach.6.Papers must be typed and in English.7.The solution must consist entirely of written text, and possibly figures, charts, or other written material, onpaper only. No non-paper support materials such as computer files or disks will be accepted.8.The Solution Paper must display the team control number and the page number at the top of everypage; for example, use the following page header on each page:Team # 321 Page 6 of 139.The names of the students, advisor, or institution should NOT appear on any page of the print solution orelectronic solution. The solution should not contain any identifying information other than the team controlnumber.10.Failure to adhere to any preparation rule is grounds for team disqualification.D. Print Summary Sheet and Control Sheet:After the contest begins at 8PM EST on Thursday February 9, 2012, and while the teams are preparing their solutions, the advisor should:1.Login to the contest web site (go to /undergraduate/contests/mcm. Click onAdvisor Login, then enter your email address and password).2.Enter the team member names and confirm that each name is spelled correctly. This determines how thenames will appear on the contest certificates. COMAP will not make any changes or reprintcertificates for any reason.3.Specify the problem that your team has chosen to solve.4.Print one copy of the Control Sheet.5.Print one copy of the team Summary Sheet.III. BEFORE THE CONTEST ENDS:A. Send electronic copy of Solution Paper by email:1.Each team is required to submit an electronic copy of its solution paper by email to solutions@.Any team member or the advisor may submit this email.a. Your email MUST be received at COMAP by the submission deadline of 8PM EST on February13, 2012.b. Failure by a team to submit a solution via email by 8PM EST on February 13, 2012 constitutes aviolation of the contest rules and will result in that team’s disqualification.c. No further modifications, enhancements, additions, or improvements may be made to the team’s solutionpaper after this email submission. Each team’s electronic submission will be cross-checked forconsistency with their paper submission. Any changes to the paper version will constitute a violation ofthe contest rules and may result in disqualification.2.In the subject line of your email write: COMAP and your team’s control number. For example:Subject: COMAP 2222e your team’s control number as the name of your file attachments.AP will accept only an Adobe PDF or Microsoft Word file of your solution. DO NOT includeprograms or software with your email as they will not be used in the judging process. Limit one solution per email. The names of the students, advisor, or institution should NOT appear on any page of theelectronic solution.5.See the rules for submitting two (2) paper copies and CD via mail below.IV. WHEN THE CONTEST ENDS:A. Prepare Solution Packet:When the contest ends at 8PM EST on February 13, 2012:1.Each team member must sign the Control Sheet to pledge that he or she abided by the contest rules andinstructions.2.Make two copies of your team’s Solution Paper.3.Staple the Summary Sheet on top of each of the Solution Papers.4.Staple the Control Sheet on top of one of the Solution Papers.5.Enclose an electronic copy (PDF or Word file) of your team’s Solution Paper on a CD-ROM. Programs andsoftware will not be used in the judging process. DO NOT include them on the CD.If you advise more than one team, please include both teams’ files on a single CD-ROM and label it withcontest, year, and both teams’ control numbers.Example:Year Contest Control Numbers2012 MCM/ICM 10004, 10005B. Mail Solution Packet:1.Mail your team’s complete Solution Packet to:MCM/ICM CoordinatorCOMAP, Inc.175 Middlesex Turnpike., Suite 3BBedford, MA 01730USAAP must receive your Solution Packet via mail on or before Wednesday February 22, 2012. It isyour responsibility to make sure that your team’s Solution Packet arrives at COMAP by this deadline. Useregistered or express mail, if necessary, to insure that it arrives at COMAP by Wednesday February 22,2012.AP will not accept late solutions under any circumstances.4.If you require confirmation that your paper was received by COMAP, send the packet via a carrier thatprovides package tracking. Due to the number of papers received, COMAP can not answer receipt inquiries or emails.V. AFTER THE CONTEST IS OVER:A. Confirm that your team’s solution was received:1.You may login to the contest web site using the Advisor Login link to verify that your team’s SolutionPacket was received at COMAP. After mailing your Solution Packet, please allow several days for us toprocess your packet before expecting to see this confirmation.B. Check contest results:1.Judging: Judging will be completed in March and the results will be posted on April 29, 2012. TheSolution Papers will be recognized as Unsuccessful, Successful Participant, Honorable Mention,Meritorious, Finalist, or Outstanding Winner.2.We will post the contest results on the web site as soon as they are available, so visit the contest web siteregularly to check for updates. It will take several weeks for the judges to evaluate the solutions and forCOMAP to process the results. Please do NOT call or email COMAP regarding contest results.C. Certificates:After the results are issued, each successfully participating team will receive a certificate of participation. The certificate will be mailed or emailed to the advisor at the address used during the registration process. All international teams will receive ONLY an electronic (PDF) certificate. Please allow several weeks after the results are posted to the contest web site to receive your certificate.D. Prizes:•The Institute for Operations Research and the Management Sciences (INFORMS) will designate an Outstanding team from each of the three problems as an INFORMS winner.•The Society for Industrial and Applied Mathematics (SIAM) will designate one Outstanding team from each problem as a SIAM winner.•The Mathematical Association of America (MAA) will designate one Outstanding team from each problem for the MCM as a MAA winner.•The Ben Fusaro Award, Typically, among the final MCM papers from which the Outstanding ones are selected is a paper that is especially creative but contains a flaw that prevents it from attaining theOutstanding designation. In accord with Ben’s wishes, the award will recognize such teams.。