历年美赛题目
美赛历年赛题
美赛历年赛题
美国数学建模竞赛（MCM/ICM）自1985年创办以来已有35年的历史，每年都会发布三个模型问题供参赛选手在限定时间内进行研究和解答。
经过不断发展和完善，MCM/ICM成为了世界范围内最具影响力的数学建模竞赛之一。
以下是MCM/ICM历年来的一些典型赛题：
1985年 MCM A题：研究在给定经济情况下，如何规划BMW公司未来的生产计划及车型。
1987年 MCM A题：在地球上一个非常均匀的平面，建立一个小型城市，考虑各种环境因素如何影响城市的设施和功能。
1991年 MCM D题：分析社会上性别和种族歧视。
1997年 MCM C题：分析为什么珊瑚礁的污染问题比林区污染问题显得更为严重。
2002年 MCM A题：研究货轮舱位的装载问题，最大化收益同时保证船上货物负荷均衡。
2006年 MCM A题：建立模型研究地球大气环境中的水循环，探究人类活动对水循环的影响。
2010年 MCM A题：分析美国电力网络的可靠性，研究如何在自然灾害和人为故障的情况下使电力网络正常运作。
2014年 MCM A题：分析对于Fermi问题和经济增长的数学建模，探究经济增长的限制因素和未来发展趋势。
2018年 MCM A题：研究美国国家公园的野生动植物种类和数量变化，确定如何平衡保护野生动植物和国家公园的多个目的。
从这些题目中可以看出，MCM/ICM的竞赛内容涵盖了众多领域，如管理学、环保、气象、物流、生物学等等。
这不仅考验了参赛选手的数学建模水平，更需要他们具备良好的跨学科素养。
正是这种多学科交叉融合的特性，使得MCM/ICM成为了培养未来数学、理工科人才的重要平台之一。
历年美国大学生数学建模竞赛试题MCM.翻译版doc
1985 年美国大学生数学建模竞赛MCM 试题1985年MCM:动物种群选择适宜的鱼类和哺乳动物数据准确模型。
模型动物的自然表达人口水平与环境相互作用的不同群体的环境的重要参数,然后调整账户获取表单模型符合实际的动物提取的方法。
包括任何食物或限制以外的空间限制,得到数据的支持。
考虑所涉及的各种数量的价值,收获数量和人口规模本身,为了设计一个数字量代表的整体价值收获。
找到一个收集政策的人口规模和时间优化的价值收获在很长一段时间。
检查政策优化价值在现实的环境条件。
1985年MCM B:战略储藏管理钴、不产生在美国,许多行业至关重要。
(国防占17%的钴生产。
1979年)钴大局部来自非洲中部,一个政治上不稳定的地区。
1946年的战略和关键材料储藏法案需要钴储藏,将美国政府通过一项为期三年的战争。
建立了库存在1950年代,出售大局部在1970年代初,然后决定在1970年代末建立起来,与8540万磅。
大约一半的库存目标的储藏已经在1982年收购了。
建立一个数学模型来管理储藏的战略金属钴。
你需要考虑这样的问题:库存应该有多大?以什么速度应该被收购?一个合理的代价是什么金属?你也要考虑这样的问题:什么时候库存应该画下来吗?以什么速度应该是画下来吗?在金属价格是合理出售什么?它应该如何分配?有用的信息在钴政府方案在2500万年需要2500万磅的钴。
美国大约有1亿磅的钴矿床。
生产变得经济可行当价格到达22美元/磅(如发生在1981年)。
要花四年滚动操作,和thsn六百万英镑每年可以生产。
1980年,120万磅的钴回收,总消费的7%。
1986 年美国大学生数学建模竞赛MCM 试题1986年MCM A:水文数据下表给出了Z的水深度尺外表点的直角坐标X,Y在码(14数据点表省略)。
深度测量在退潮。
你的船有一个五英尺的草案。
你应该防止什么地区的矩形(75200)X(-50、150)?1986年MCM B:Emergency-Facilities位置迄今为止,力拓的乡牧场没有自己的应急设施。
2022美赛 中文题目
1.李白笔下的“飞流直下三千尺，疑是银河落九天”指的是哪个风景区？A、华山B、黄山C、庐山2. 舟夜书所见月黑见渔灯，孤光一点萤。
微细风簇浪，散作满河星。
这首诗是诗人在（）看见的风景。
A 船上B 街上C 楼上3.《早发白帝城》诗人的目的地是哪里？A.白帝城B.江陵C.彩云间4.《绝句》（杜甫）诗中通过嗅觉展现春天勃勃生机的诗句是( )A.迟日江山丽B.春风花草香C.泥融飞燕子5.《大林寺桃花》中的哪一句指的是“高山古寺中的桃花才刚刚盛开”？( )A.人间四月芳菲尽B.山寺桃花始盛开C.长恨春归无觅处6.王维的《鹿柴》描写的是哪个时间的景物？A早上B中午C傍晚7.下列选项中，对《山行》(杜牧)的理解有误的一项是( )A 《山行》中“行”是“行走”B “停车坐爱枫林晚”中“坐”是“坐下”C 本诗写于深秋时节。
8.结合全诗来看，诗人望洞庭的时间是( )A.春天的清晨B.夏天的正午C.秋天的夜晚9.“莫愁前路无知己，天下谁人不识君？”中的“君”指的是？A、董大B、元二C、高适10.《惠崇春江晚景》中“正是河豚欲上时”指的是( )。
A.春天，河豚鲜嫩肥美，可以上市销售B.春天，河豚要由海入江产卵，逆江而上。
C.春天，河豚由江底游到江面上。
11.孟郊的《游子吟》中，母爱的代名词是( )A.密密缝B.寸草心C.三春晖12.《从军行》中，哪两句诗写出了边疆将士的胸怀与壮志？A.黄沙百战穿金甲，不破楼兰终不还B.青海长云暗雪山，孤城遥望玉门关C.遗民泪尽胡尘里，南望王师又一年13.《元日》(王安石)中没有提到的节日风俗是( )A 燃爆竹B 吃饺子C 换桃符14.《回乡偶书》的“少小离家老大回，乡音无改鬓毛衰”中“鬓毛”的意思是( )？A.胡须B.眉毛C.鬓角的头发15.《九月九日忆山东兄弟》的“佳节”指的是( )A. 端午节B. 中秋节C. 重阳节16.“天门中断楚江开，碧水东流至此回。
”这两句诗侧重写了天门山的( )A.山川之势B.行船路线C.波涛汹涌17.《滁州西涧》第一句中“怜”的意思是( )。
历届美国数学奥林匹克试题集
历届美国数学奥林匹克试题集美国数学奥林匹克（简称USAMO）历史悠久，始于1938年，它是一场美国学生数学挑战赛，旨在识别最杰出的高中数学学者。
下面就是历届美国数学奥林匹克的试题集：一、1938-1962年USAMO试题1、1938年：给出一个三角形的三边，求面积；2、1939年：讨论旋转半径与直径之比的一般性质；3、1940年：定义无限小的超越数，根据某假设，求这个超越数的值；4、1941年：讨论圆柱体表面积与体积的关系；5、1942年：求取3个不相交的、边长为a、b、c的三角形三角形内部与边长有关的值；6、1943年：用三角函数分析，求取某数字列中元素的平均值；7、1944年：根据若干条件求取某个矩形的面积；8、1945年：用三角函数分析求解一个双曲线曲线积分；9、1946年：讨论如何用三角函数求取某区域的面积；10、1947年：讨论以二次函数求取某直线的最大值；11、1948年：用函数渐近方程求取平面上的点的垂直距离；12、1949年：证明某系统的某凸多面体的面积；13、1950年：论及某曲线的长度；14、1951年：用泰勒级数求取某函数值；15、1952年：设计一个实验，用来测量椭圆面积；16、1953年：证明某函数满足一定性质；17、1954年：论及某非凸多面体的三角形边界；18、1955年：用代数方法求取某系统的某函数的分式；19、1956年：求解拉格朗日错误现象的数学模型；20、1957年：书写一个数学程序，用来迭代某函数；21、1958年：论及一元二次方程组的一般性质；22、1959年：求取某函数对某范围的极限；23、1960年：证明某二维函数的最大值与最小值；24、1961年：分析和讨论某系统的特定性质；25、1962年：用数学语言解释某物理系统的相关性质。
二、1963-1984年USAMO试题1、1963年：讨论一元二次方程的不定实根的情况；2、1964年：求取某带因变量的积分；3、1965年：设计一个实验来测量阶乘的值；4、1966年：利用欧拉公式讨论某椭圆的性质；5、1967年：根据（lLp）型的数列求取相应的递推式；6、1968年：用拉格朗日不等式求取某函数的极值点；7、1969年：说明某曲线的曲率、弧长、弧径之间的关系；8、1970年：给出一组数据，求取其中元素的平均数；9、1971年：证明某四次方程的全等式；10、1972年：用数学语言描述某系统的动作；11、1973年：分析牛顿迭代公式在求取函数局部极值时的作用；12、1974年：测算某函数的最大值；13、1975年：给出若干条件，根据某函数的极限求取最大值。
美赛历年题目_pdf
马剑整理历年美国大学生数学建模赛题目录MCM85问题-A 动物群体的管理 (3)MCM85问题-B 战购物资储备的管理 (3)MCM86问题-A 水道测量数据 (4)MCM86问题-B 应急设施的位置 (4)MCM87问题-A 盐的存贮 (5)MCM87问题-B 停车场 (5)MCM88问题-A 确定毒品走私船的位置 (5)MCM88问题-B 两辆铁路平板车的装货问题 (6)MCM89问题-A 蠓的分类 (6)MCM89问题-B 飞机排队 (6)MCM90-A 药物在脑内的分布 (6)MCM90问题-B 扫雪问题 (7)MCM91问题-B 通讯网络的极小生成树 (7)MCM 91问题-A 估计水塔的水流量 (7)MCM92问题-A 空中交通控制雷达的功率问题 (7)MCM 92问题-B 应急电力修复系统的修复计划 (7)MCM93问题-A 加速餐厅剩菜堆肥的生成 (8)MCM93问题-B 倒煤台的操作方案 (8)MCM94问题-A 住宅的保温 (9)MCM 94问题-B 计算机网络的最短传输时间 (9)MCM-95问题-A 单一螺旋线 (10)MCM95题-B A1uacha Balaclava学院 (10)MCM96问题-A 噪音场中潜艇的探测 (11)MCM96问题-B 竞赛评判问题 (11)MCM97问题-A Velociraptor(疾走龙属)问题 (11)MCM97问题-B为取得富有成果的讨论怎样搭配与会成员 (12)MCM98问题-A 磁共振成像扫描仪 (12)MCM98问题-B 成绩给分的通胀 (13)MCM99问题-A 大碰撞 (13)MCM99问题-B “非法”聚会 (14)MCM2000问题-A空间交通管制 (14)MCM2000问题-B: 无线电信道分配 (14)MCM2001问题- A: 选择自行车车轮 (15)MCM2001问题-B 逃避飓风怒吼（一场恶风...） .. (15)MCM2001问题-C我们的水系-不确定的前景 (16)MCM2002问题-A风和喷水池 (16)MCM2002问题-B航空公司超员订票 (16)MCM2002问题-C (16)MCM2003问题-A: 特技演员 (18)MCM2003问题-B: Gamma刀治疗方案 (18)MCM2003问题-C航空行李的扫描对策 (19)MCM2004问题-A：指纹是独一无二的吗？ (19)MCM2004问题-B：更快的快通系统 (19)MCM2004问题-C安全与否？ (19)MCM2005问题A.水灾计划 (19)MCM2005B.Tollbooths (19)MCM2005问题C：不可再生的资源 (20)MCM2006问题A: 用于灌溉的自动洒水器的安置和移动调度 (20)MCM2006问题B: 通过机场的轮椅 (20)MCM2006问题C : 抗击艾滋病的协调 (21)MCM2007问题B ：飞机就座问题 (24)MCM2007问题C：器官移植：肾交换问题 (24)MCM2008问题A:给大陆洗个澡 (28)MCM2008问题B：建立数独拼图游戏 (28)MCM85问题-A 动物群体的管理在一个资源有限，即有限的食物、空间、水等等的环境里发现天然存在的动物群体。
美赛历年题目_pdf
马剑整理历年美国大学生数学建模赛题目录MCM85问题-A 动物群体的管理 (3)MCM85问题-B 战购物资储备的管理 (3)MCM86问题-A 水道测量数据 (4)MCM86问题-B 应急设施的位置 (4)MCM87问题-A 盐的存贮 (5)MCM87问题-B 停车场 (5)MCM88问题-A 确定毒品走私船的位置 (5)MCM88问题-B 两辆铁路平板车的装货问题 (6)MCM89问题-A 蠓的分类 (6)MCM89问题-B 飞机排队 (6)MCM90-A 药物在脑内的分布 (6)MCM90问题-B 扫雪问题 (7)MCM91问题-B 通讯网络的极小生成树 (7)MCM 91问题-A 估计水塔的水流量 (7)MCM92问题-A 空中交通控制雷达的功率问题 (7)MCM 92问题-B 应急电力修复系统的修复计划 (7)MCM93问题-A 加速餐厅剩菜堆肥的生成 (8)MCM93问题-B 倒煤台的操作方案 (8)MCM94问题-A 住宅的保温 (9)MCM 94问题-B 计算机网络的最短传输时间 (9)MCM-95问题-A 单一螺旋线 (10)MCM95题-B A1uacha Balaclava学院 (10)MCM96问题-A 噪音场中潜艇的探测 (11)MCM96问题-B 竞赛评判问题 (11)MCM97问题-A Velociraptor(疾走龙属)问题 (11)MCM97问题-B为取得富有成果的讨论怎样搭配与会成员 (12)MCM98问题-A 磁共振成像扫描仪 (12)MCM98问题-B 成绩给分的通胀 (13)MCM99问题-A 大碰撞 (13)MCM99问题-B “非法”聚会 (14)MCM2000问题-A空间交通管制 (14)MCM2000问题-B: 无线电信道分配 (14)MCM2001问题- A: 选择自行车车轮 (15)MCM2001问题-B 逃避飓风怒吼（一场恶风...） .. (15)MCM2001问题-C我们的水系-不确定的前景 (16)MCM2002问题-A风和喷水池 (16)MCM2002问题-B航空公司超员订票 (16)MCM2002问题-C (16)MCM2003问题-A: 特技演员 (18)MCM2003问题-B: Gamma刀治疗方案 (18)MCM2003问题-C航空行李的扫描对策 (19)MCM2004问题-A：指纹是独一无二的吗？ (19)MCM2004问题-B：更快的快通系统 (19)MCM2004问题-C安全与否？ (19)MCM2005问题A.水灾计划 (19)MCM2005B.Tollbooths (19)MCM2005问题C：不可再生的资源 (20)MCM2006问题A: 用于灌溉的自动洒水器的安置和移动调度 (20)MCM2006问题B: 通过机场的轮椅 (20)MCM2006问题C : 抗击艾滋病的协调 (21)MCM2007问题B ：飞机就座问题 (24)MCM2007问题C：器官移植：肾交换问题 (24)MCM2008问题A:给大陆洗个澡 (28)MCM2008问题B：建立数独拼图游戏 (28)MCM85问题-A 动物群体的管理在一个资源有限，即有限的食物、空间、水等等的环境里发现天然存在的动物群体。
美国(MCM)(ICM)试题(96年-09年)(英文版)
美国大学生数学建模竞赛试题1996 American MCM Problems Problem AThe world's oceans contain an ambient noise field. Seismic disturbances, surface shipping, and marine mammals are sources that, in different frequency ranges,contribute to this field. We wish to consider how this ambient noise might be used to detect large moving objects, e.g., submarines located below the ocean surface. Assuming that a submarine makes no intrinsic noise, developa method for detecting the presence of a moving submarine, its size, and its direction of travel, using only information obtained by measuring changes to the ambient noise field. Begin with noise at one fixed frequency and amplitude.Problem BWhen determining the winner of a competition like the Mathematical Contest inModeling, there are generally a large number of papers to judge. Let's saythere are P=100 papers.A group of J judges is collected to accomplish thejudging. Funding for the contest constains both the number of judges that canbe obtained and amount of time that they can judge. For eample if P=100, thenJ=8 is typical.Ideally, each judge would read paper and rank-order them, but there are toomany papers for this. Instead, there will be a number of screening rounds inwhich each judge will read some number of papers and give them scores. Thensome selection scheme is used to reduce the number of papers under consideration: If the papers are rank-ordered, then the bottom 30% that eachjudge rank-orders could be rejected. Alternatively, if the judges do not rank-order, but instead give them numerical score (say, from 1 to 100),then all papers below some cut-off level could be rejected.The new pool of papers is then passed back to the judges, and the process is repeated.A concern is then the total number of papers that judge reads must besubstantially less than P. The process is stopped when there are only W papersleft. There are the winners. Typically for P=100, W=3.Your task is to determine a selection scheme, using a combination of rank-ordering, numerical scoring, and other methods, by which the final Wpapers will include only papers from among the "best" 2W papers. (By "best",we assume that there is an absolute rank-ordering to which all judges wouldagree.) For example, the top three papers. Among all such methods, the one thatrequired each judge to read the least number of papers is desired.Note the possibility of systematic bias in a numerical scoring scheme. For example, for a specific collection of papers, one judge could average 70points, while another could average 80 points. How would you scale your schemeto accommodate for changes in the contest parameters (P, J, and W)?1997 American MCM ProblemsProblem A The Velociraptor ProblemThe velociraptor,Velociraptor mongoliensis, was a predatory dinosaur that lived during the late Cretaceous period, approximately 75 million years ago. Paleontologists think that it was a very tenacious hunter, and may have hunted in pairs or largerpacks .Unfortunately, there is no way to observe its hunting behavior in the wild as can be done with modern mammalian predators. A group of paleontologists has approached your team and asked for help in modeling the hunting behavior of the velociraptor. They hope to compare your results with field data reported by biologists studying the behaviors of lions, tigers, and similar predatory animals.The average adult velociraptor was 3 meters long with a hip height of 0.5 meters and an approximate mass of 45 kg. It is estimated that the animal could run extremely fast at speed of 60 km/hr for about 15 seconds. After the initial burst of speed ,the animal needed to stop and recover from a buildup of lactic acid in its muscles.Suppose that velociraptor preyed on Thescelosaurus neglectus, a herbivorous biped approximately the same size as the Velociraptor. A biomachanical analysis of a fossilized Thescelosaurus indicates that it could run at a speed of about 50 km/hr. for long period of time.Part1Assuming the velociraptor is a solitary hunter, design a mathematical model that describe a hunting strategy for a single velociraptor stalking and chasing a single Thescelosaurus as well as the evasive strategy of the prey. Assume that the Thescelosaurus can always detect the velociraptor when it comes within 15 meters .but may detect the predator at even greater ranges (up to 50 meters depending upon the habitat and weather conditions. Additionally ,due to its physical structure and strength, the velociraptorhas a limited turning radius when running at full speed. This radius is estimated to be three times the animal's hip height. On the other hand, the Thescelosaurus is extremely agile and has a turning radius of 0.5 meters.Part2Assuming more realistically that the velociraptor hunted in pairs, design a new model that describes a hunting strategy for two velociraptor stalking and chasing a single Thescelosaurus as well as the evasive strategy of the prey. Use the other assumptions and limitations given in Part 1.Problem B Mix Well For Fruitful DiscussionsSmall group meeting for the discussions of important issues, particular long-range planning ,are gaining popularity. It is believed that large groups discourage productive discussion and that a dominant personality will usually control and direct the discussion. Thus ,in corporate board meetings the board will meet in small groups to discuss issues before meeting as a whole, these smaller groups still tun the risk of control by a dominant personality. In an attempt to reduce this danger it is common to schedule several sessions with a different mix of people in each group.A meeting of An Tostal Corporation will be attended by 29 Board Members of which nine are in-house members(i.e., corporate employees).The meeting is to be an all-day affair with three sessions scheduled for the morning and four for the afternoon. Each session will take 45 minutes, beginning on the hour from 9:00 A.M. to 4:00 P.M., with lunch scheduled at noon. Each morning session will consist of six discussion groups with each discussion group led by one of the corporation's six senior officers. None of these officers are board members. Thus each senior officers will not be involved in the afternoon sessions and each of these sessions will consist of only four different discussion groups.The president of the corporation wants a list of board-member assignment to discussion groups for each of the seven sessions. The assignments should achieve as much of a mix of the members as much as possible. The ideal assignment would have each board member in a discussion group the same number of times while minimizing common membership of groups for the different sessions.The assignment should also satisfy the following criteria:1.For the morning sessions ,no board member should be in the same senior officer's discussion group twice.2.No discussion group should contain a disproportionate number of in-house members.Give a list of assignments for members 1-9 and 10-29 and officers 1-6.Indicate how well the criteria in the previous paragraphs are met. Since it is possible that some board members will cancel at the last minute or that some not scheduled will show up, an algorithm that the secretary could use to adjust the assignments with an hour's notice would be appreciated. It would be ideal if the algorithm could also be used to make assignments for future meetings involving different levels of participation for each type of attendee.1998 American MCM ProblemsProblem A MRI ScannersIntroductionIndustrial medical diagnostic machines known as Magnetic Resonance Imager (MRI) scan a three-dimensional object such as a brain, and deliver their results in the form of a three-dimensional array of pixel. Each pixel consists of one number indicating a color or a shade of gray that encodes a measure of water concentration in a small region of the scanned object at the location of the pixel .For instance,0 can picture high water concentration in black (ventricles, blood vessels),128 can picture a medium water concentration in gray(brain nuclei and gray matter),and 255 can picture a low water density in white (liquid-rich white matter consisting of myelinated axons).Such MRI scanners also include facilities to picture on a screen any horizontal or vertical slice through the three-dimensional array (slices are parallel to any of the three Cartesian coordinate axes ).Algorithms for picturing slices through oblique planes ,however ,are proprietary .Current algorithms are limited in terms of the angles and parameter options available ;are implemented only on heavily used dedicated workstations ;lack input capabilities for marking points in the picture before slicing; and tend to blur and "feather out" sharp boundaries between the original pixels.A more faithful, flexible algorithm implemented on a personal computer would be useful.(1)for planning minimally invasive treatments,(2)for calibrating the MRI machines,(3)for investigating structures oriented obliquely in space, such as post-mortem tissue sections in a animal research,(4)for enabling cross-sections at any angle through a brain atlas consisting (4)for enabling cross-sections at any angle through a brain atlas consistingof black-and-white line drawingTo design such an algorithm, one can access the value and locations of the pixels, but not the initial data gathered by the scanners.ProblemDesign and test an algorithm that produces sections of three-dimensional arrays by planes in any orientation in space, preserving the original gray-scale value as closely as possible.Data SetsThe typical data set consists of a three-dimensional array A of numbers A(i,j,k) which indicates the density A(i,j,k) of the object at the location (x,y,z)i,j,k. Typically A(i,j,k) can range from 0 to 255.In most applications the data set is quite large.Teams should design data sets to test and demonstrate their algorithms. The data sets should reflect conditions likely Teams should design data sets to test and demonstrate their algorithms. The data sets should reflect conditions likely to be of diagnostic interest. Teams should also characterize data sets the limit the effectiveness of their algorithms.SummaryThe algorithm must produce a picture of the slice of the three-dimensional array by a plane in space. The plane can have any orientation and any location in space.(The plane can miss some or all data points.)The result of the algorithm should be a model of the density of the scanned object over the selected plane.Problem B Grade InflationBackgroundSome college administrators are concerned about the grading at A Better Class(ABC) college. On average, the faculty at ABC have been giving out high grades(the average grade now given out is an A-),and it is impossible to distinguish between the good and mediocre students .The terms of a very generous scholarship only allow the top 10% of the students to be funded, so a class ranking is required.The dean had the thought of comparing each student to the other students in each class ,and using this information to build up a ranking. For example, if a student obtains an A in a class in which all students obtain an A, then this student is only "average" in this class. On the other hand, if a student obtain the only A in a class, then that student is clearly "above average". Combining information from several classes might allow students to be placed in deciles (top 10%,next 10%,ect.)across the college.ProblemAssuming that the grades given out are(A+,A-,B+,B-,...)can the dean's idea be made to work?Assuming that the grades given out are only (A,B,C,...)can the dean's idea be made to work?Can any other schemes produce a desired ranking?A concern is that the grade in a single class could change many student's deciles. Is this possible?Data SetsTeams should design data sets to test and demonstrate their algorithms. Teams should characterize data sets that limit the effectiveness of their algorithms.Mathematical Contest in Modeling 1999 ProblemsProblem A - Deep ImpactFor some time, the National Aeronautics and Space Administration (NASA) has been considering the consequences of a large asteroid impact on the earth.As part of this effort, your team has been asked to consider the effects of such an impact were the asteroid to land in Antarctica. There are concerns that an impact there could have considerably different consequences than one striking elsewhere on the planet.You are to assume that an asteroid is on the order of 1000 m in diameter, and that it strikes the Antarctic continent directly at the South Pole.Your team has been asked to provide an assessment of the impact of such an asteroid. In particular, NASA would like an estimate of the amount and location of likely human casualties from this impact, an estimate of the damage done to the food production regions in the oceans of the southern hemisphere, and an estimate of possible coastal flooding caused by large-scale melting of the Antarctic polar ice sheet.Problem B - Unlawful AssemblyMany public facilities have signs in rooms used for public gatherings which state that it is "unlawful" for the rooms to be occupied by more than a specified number of people. Presumably, this number is based on the speed with which people in the room could be evacuated from the room's exits in case of an emergency. Similarly, elevators and other facilities often have "maximum capacities" posted.Develop a mathematical model for deciding what number to post on such a sign as being the "lawful capacity". As part of your solution discuss criteria, other than public safety in the case of a fire or other emergency, that might govern the number of people considered "unlawful" to occupy the room (or space). Also, for the model that you construct, consider the differences between a room with movable furniture such as a cafeteria (with tables and chairs), a gymnasium, a public swimming pool, and a lecture hall with a pattern of rows and aisles. You may wish to compare and contrast what might be done for a variety of different environments: elevator, lecture hall, swimming pool, cafeteria, or gymnasium. Gatherings such as rock concerts and soccer tournaments may present special conditions.Apply your model to one or more public facilities at your institution (or neighboring town). Compare your results with the stated capacity, if one is posted. If used, your model is likely to be challenged by parties with interests in increasing the capacity. Write an article for the local newspaper defending your analysis.2000 Mathematical Contest in ModelingProblem A Air traffic ControlDedicated to the memory of Dr. Robert Machol, former chief scientist of the Federal Aviation Agency To improve safety and reduce air traffic controller workload, the Federal Aviation Agency (FAA) is considering adding software to the air traffic control system that would automatically detect potential aircraft flight path conflicts and alert the controller. To that end, an analyst at the FAA has posed the following problems.Requirement A: Given two airplanes flying in space, when should the air traffic controller consider the objects to be too close and to require intervention?Requirement B: An airspace sector is the section of three-dimensional airspace that one air traffic controller controls. Given any airspace sector, how do we measure how complex it is from an air traffic workload perspective? To what extent is complexity determined by the number of aircraft simultaneously passing through that sector (1) at any one instant?(2) during any given interval of time?(3) during a particular time of day? How does the number of potential conflicts arising during those periods affect complexity?Does the presence of additional software tools to automatically predict conflicts and alert the controller reduce or add to this complexity?In addition to the guidelines for your report, write a summary (no more than two pages) that the FAA analyst can present to Jane Garvey, the FAA Administrator, to defend your conclusions.Problem B Radio Channel AssignmentsWe seek to model the assignment of radio channels to a symmetric network of transmitter locations over a large planar area, so as to avoid interference. One basic approach is to partition the region into regular hexagons in a grid (honeycomb-style), as shown in Figure 1, where a transmitter is located at the center of each hexagon.Figure 1An interval of the frequency spectrum is to be allotted for transmitter frequencies. The interval will be divided into regularly spaced channels, which we represent by integers 1, 2, 3, ... . Each transmitter will be assigned one positive integer channel. The same channel can be used at many locations, provided that interference from nearby transmitters is avoided. Our goal is to minimize the width of the interval in the frequency spectrum that is needed to assign channels subject to some constraints. This is achieved with the concept of a span. The span is the minimum, over all assignments satisfying the constraints, of the largest channel used at any location. It is not required that every channel smallerthan the span be used in an assignment that attains the span.Let s be the length of a side of one of the hexagons. We concentrate on the case that there are two levels of interference.Requirement A: There are several constraints on frequency assignments. First, no two transmitters within distance of each other can be given the same channel. Second, due to spectral spreading, transmitters within distance 2s of each other must not be given the same or adjacent channels: Their channels must differ by at least 2. Under these constraints, what can we say about the span in,Requirement B: Repeat Requirement A, assuming the grid in the example spreads arbitrarily far in all directions.Requirement C: Repeat Requirements A and B, except assume now more generally that channels for transmitters within distance differ by at least some given integer k, while those at distance at most must still differ by at least one. What can we say about the span and about efficient strategies for designing assignments, as a function of k?Requirement D: Consider generalizations of the problem, such as several levels of interference or irregular transmitter placements. What other factors may be important to consider?Requirement E: Write an article (no more than 2 pages) for the local newspaper explaining your findings.2001 Mathematical Contest in Modeling (MCM)Problem A: Choosing a Bicycle WheelCyclists have different types of wheels they can use on their bicycles. The two basic typesof wheels are those constructed using wire spokes and those constructed of a solid disk (see Figure 1) The spoked wheels are lighter, but the solid wheels are more aerodynamic.A solid wheel is never used on the front for a road race but can be used on the rear of the bike.Professional cyclists look at a racecourse and make an educated guess as to what kind of wheels should be used. The decision is based on the number and steepness of the hills, the weather, wind speed, the competition,and other considerations. The director sportif of your favorite team would like to have a better system in place and has asked your team for information to help determine what kind of wheel should be used fora given course.Figure 1: A solid wheel is shown on the left and a spoked wheel is shown on the right. The director sportif needs specific information to help make a decision and has asked your team to accomplish the tasks listed below. For each of the tasks assume that the same spoked wheel will always be used on the front butthere is a choice of wheels for the rear.Task 1. Provide a table iving the wind peed at which the power required for a solid rear wheel is less than for a spoked rear wheel. The table should include the wind speeds for different road grades starting from zero percent to ten percent in one percent increments. (Road grade is defined to be the ratio of the total rise of a hill divided by the length of the road. If the hill is viewed as a triangle, the grade is the sine of the angle at the bottom of the hill.) A rider starts at the bottom of the hill at a speed of 45 kph, and the deceleration of the rider is proportional to the road grade.A rider will lose about 8 kph for a five percent grade over 100 meters.Task 2. Provide an example of how the table could be used for a specific time trial courseTask 3. Determine if the table is an adequate means for deciding on the wheel configuration and offer other suggestions as to how to make this decision.Problem B: Escaping a Hurricane's Wrath (An Ill Wind...)Evacuating the coast of South Carolina ahead of the predicted landfallof Hurricane Floydin 1999 led to a monumental traffic jam. Traffic slowed to a standstill on Interstate I-26, which is the principal route going inland from Charleston to the relatively safe haven of Columbia in the center of the state. What is normally an easy two-hour drive took up to 18 hours to complete. Many cars simply ran out of gas along the way.Fortunately, Floyd turned north and spared the state this time, but the public outcry is forcing state officials to find ways to avoid a repeat of this traffic nightmare.The principal proposal put forth to deal with this problem is the reversalof traffic onI-26, so that both sides, including the coastal-bound lanes,have traffic headed inland from Charleston to Columbia. Plans to carry this out have been prepared (and posted on the Web)by the South Carolina Emergency Preparedness Division. Traffic reversal on principal roads leading inland from Myrtle Beach and Hilton Head is also planned.A simplified map of South Carolina is shown. Charleston has approximately 500,000 people, Myrtle Beach has about 200,000 people, and another 250,000 people are spread out along the rest of the coastal strip. (More accurate data,if sought, are widely available.)The interstates have two lanes of traffic in each direction except in the metropolitan areas where they have three. Columbia, another metro area of around 500,000 people, does not have sufficient hotel space to accommodate the evacuees (including some coming from farther northby other routes), so some traffic continues outbound on I-26 towards Spartanburg; on I-77 north to Charlotte; and on I-20 east to Atlanta. In 1999, traffic leaving Columbia going northwest was moving only very slowly. Construct a model for the problem to investigate what strategies may reduce the congestion observed in 1999. Here are the questions that need to be addressed:1.Under what conditions does the plan for turning the two coastal-bound lanes of I-26 into two lanes of Columbia-bound traffic, essentially turning the entire I-26 into one-way traffic, significantly improve evacuation traffic flow?2.In 1999, the simultaneous evacuation of the state's entire coastal region was ordered. Would the evacuation traffic flow improve under an alternative strategy that staggers the evacuation, perhaps county-by-county over some time period consistent with the pattern of how hurricanes affect the coast?3.Several smaller highways besides I-26 extend inland from the coast. Under what conditions would it improve evacuation flow to turn around traffic on these?4.What effect would it have on evacuation flow to establish more temporary shelters in Columbia, to reduce the traffic leaving Columbia?5.In 1999, many families leaving the coast brought along their boats, campers, and motor homes. Many drove all of their cars. Under what conditions should there be restrictionson vehicle types or numbers of vehicles brought in order to guarantee timely evacuation? 6.It has been suggested that in 1999 some of the coastal residents of Georgia and Florida, who were fleeing the earlier predicted landfalls of Hurricane Floyd to the south, came upI-95 and compounded the traffic problems. How big an impact can they have on the evacuation traffic flow? Clearly identify what measures of performance are used to compare strategies. Required: Prepare a short newspaper article, not to exceed two pages,explaining the results and conclusions of your study to the public.问题 A: 选择自行车车轮骑自行车的人有几种不同类型的车轮可以用在他们的自行车上。
美赛历年题目汇总
美赛历年题目汇总
以下是美赛历年的一些题目汇总：
2018年的题目是“多跳HF无线电传播语言传播趋势”；
2017年的题目是“管理赞比西河高速路收费合并”；
2016年的题目是“浴缸的水温模型解决空间碎片问题”；
2015年的题目是“根除病毒寻找失踪的飞机”；
2014年的题目是“(交通流、路况)优化(体育教练)综合评价”；
2013年的题目是“平底锅受热，热力学、几何(大模型解答所有题目)，可利用淡水资源的匮乏，(水资源)预测、最优化”；
2012年的题目是“一棵树的叶子沿着BigLongRiver野营，(流程)优化”；
需要注意的是，这里只列出了部分美赛历年的题目，而且每年的题目都可能有所不同。
同时，美赛赛题的难度较高，需要具备一定的数学建模和计算机编程能力。
因此，在参加美赛前，建议充分准备，提高自己的数学建模和计算机编程能力。
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近几年美国大学生数学建模竞赛（USMCM）的题目包括：
2019年：建立一个模型来模拟东海和黄海的湍流。
2018年：预测联合国安理会和联合国大会决策结果及党派之间的关系。
2017年：建立一个模型来识别投资者风险偏好并帮助他们优化投资组合。
2016年：建立一个模型来识别用户a浏览网页时的行为特征，以便更好地理解和预测用户的行为。
2015年：建立一个模型，根据通信终端的传输速率，识别用户的实时视听传输需求。
2014年：建立一个模型来模拟社会文化传播的影响。
2013年：建立一个模型，根据用户的行为来预测新闻传播的趋势，并建议相关策略。
2012年：建立一个模型来优化公共汽车系统，以满足不同地区乘客的旅行需求。
2011年：建立一个模型，根据居民就医环境的不同，构建卫生保健系统的合理结构。
2010年：建立一个模型，预测印度洋及其邻近海域的风暴强度，以及其对当地的影响。