美赛历年赛题

2019美赛数学建模题目摘要：1.2019 美赛数学建模题目概述2.题目分类与解析3.题目难度与挑战4.中国高校表现与启示正文：【2019 美赛数学建模题目概述】美国大学生数学建模竞赛（MCM/ICM）是全球范围内最具影响力的数学建模竞赛，每年有来自世界各地的数千所高校参赛。

2019 年美赛数学建模题目共有6 道题目，涵盖了多个领域，旨在考验参赛选手的数学应用、分析与解决问题的能力。

【题目分类与解析】2019 年美赛数学建模题目分为A、B、C、D、E、F 六道题目，具体分类如下：A 题：疾病传播的动力学模型B 题：飞机设计的优化问题C 题：城市交通网络的优化设计D 题：环境污染物在河流中的传播与治理E 题：无人机编队的路径规划问题F 题：社交网络的社区检测问题每道题目都具有一定的挑战性，要求参赛选手对相关领域的知识有深入了解，并具备较强的数学建模能力。

【题目难度与挑战】2019 年美赛数学建模题目难度适中，但涉及的领域较广，对参赛选手提出了较高的要求。

在解题过程中，选手需要充分运用自己所学的专业知识，对题目进行深入分析，找到问题的关键所在，并提出创新性的解决方案。

因此，参赛选手在比赛中面临的挑战主要来自于对题目的理解和解决问题的能力。

【中国高校表现与启示】在2019 年美赛数学建模竞赛中，中国高校表现优异，获得了多个奖项。

这得益于我国高校对数学建模教育的重视，以及学生在老师的指导下，通过参加训练、模拟赛等形式，提高了自己的数学建模能力。

对于今后参赛的高校和学生，可以从以下几个方面进行准备：1.提高专业素养，熟练掌握相关领域的知识；2.加强数学建模培训，提高解决实际问题的能力；3.注重团队合作，发挥团队成员的优势，共同完成题目。

A题设计一个交通环岛在许多城市和社区都建立有交通环岛，既有多条行车道的大型环岛（例如巴黎的凯旋门和曼谷的胜利纪念碑路口），又有一至两条行车道的小型环岛。

有些环岛在进入口设有“停车”标志或者让行标志，其目的是给已驶入环岛的车辆提供行车优先权；而在一些环岛的进入口的逆向一侧设立的让行标志是为了向即将驶入环岛的车辆提供行车优先权；还有一些环岛会在入口处设立交通灯（红灯会禁止车辆右转）；也可能会有其他的设计方案。

这一设计的目的在于利用一个模型来决定如何最优地控制环岛内部，周围以及外部的交通流。

该设计的目的在于可利用模型做出最佳的方案选择以及分析影响选择的众多因素。

解决方案中需要包括一个不超过两页纸，双倍行距打印的技术摘要，它可以指导交通工程师利用你们模型对任何特殊的环岛进行适当的流量控制。

该模型可以总结出在何种情况之下运用哪一种交通控制法为最优。

当考虑使用红绿灯的时候，给出一个绿灯的时长的控制方法（根据每日具体时间以及其他因素进行协调）。

找一些特殊案例，展示你的模型的实用性。

B题能源和手机这个问题涉及到手机革命的能源问题。

手机使用率迅速增加，许多人使用手机并放弃了固定电话。

这方面的电能使用会带来什么后果？每个手机都配备了电池和充电器。

要求1考虑现在的美国，人口约为3亿，从现有数据估计美国有H个家庭，每个家庭有M个成员，以前是使用固定电话的。

现在，假设所有的座机被手机取代，也就是说每个家庭成员都有一部手机。

建立当前美国在手机使用的过渡和稳定两个阶段用电改变的模型，分析应该考虑到对移动电话充电的需要，同时移动电话不能像固定电话那样长期使用也是一个现实问题（比如说移动电话可能会丢失或者损坏）要求2考虑“伪美国”--一个约3亿人口，跟当前美国具有相同的经济状况的国家。

然而，这个新兴国家既没有固定电话也没有移动电话，从能源角度看，为这个国家提供电话服务的最佳方式是什么？当然，手机有很多固定电话所不具有的用途和社会影响。

2017年美赛题目2017年美赛（MCM/ICM）共有6个题目，分别是：1. Problem A: The Art of Archery.这个问题涉及到弓箭射击的技术和策略。

要求团队通过建立数学模型，分析射击的精度和效率，并给出最佳的射击策略。

2. Problem B: The Search for the Lost Dutchman's Gold Mine.这个问题要求团队通过模拟和优化算法，规划一次寻找失落的荷兰人金矿的探险。

团队需要考虑资源分配、路线选择和风险评估等因素。

3. Problem C: The Great American Potato Chip Factory.这个问题要求团队分析和优化一个薯片工厂的生产过程。

团队需要考虑原材料采购、生产调度和产品分配等方面，以提高工厂的效率和利润。

4. Problem D: The Mathematics of Music.这个问题要求团队通过数学模型和计算方法，分析和优化音乐的和声和旋律结构。

团队需要考虑音乐的音高、音长和节奏等因素，并给出最佳的音乐创作建议。

5. Problem E: The Internet of Things.这个问题要求团队分析和优化物联网中的传感器网络。

团队需要考虑传感器的部署、数据传输和能源管理等问题，以提高网络的覆盖范围和性能。

6. Problem F: The Impacts of Tourism.这个问题要求团队通过建立模型，分析旅游业对一个地区的经济、环境和社会影响。

团队需要考虑游客数量、旅游收入和环境保护等因素，并给出合理的政策建议。

以上是2017年美赛的题目概述，每个题目都涉及不同的领域和问题，需要团队综合运用数学建模、数据分析和优化方法来解决。

2024年美赛竞赛赛题解析（中英文版）英文文档：Title: Analysis of the 2024 American Mathematics Competition (AMC) QuestionsThe American Mathematics Competition (AMC) is an annual mathematics examination for high school students in the United States.The 2024 AMC questions are designed to test students" mathematical knowledge, problem-solving skills, and creativity.In this article, we will analyze the key features and trends of the 2024 AMC questions.Firstly, the 2024 AMC questions cover a wide range of mathematical topics, including algebra, geometry, probability, and calculus.These topics are essential components of a comprehensive mathematics education.The questions are designed to assess students" understanding of these topics and their ability to apply mathematical concepts to solve problems.Secondly, the 2024 AMC questions require students to think critically and logically.Many questions are word problems that require students to interpret mathematical information, identify relevant equations or theorems, and develop a plan to solve the problem.The ability to communicate mathematical ideas clearly and effectively is alsoan important aspect of the examination.Thirdly, the 2024 AMC questions emphasize problem-solving skills.Students are required to use various strategies, such as substitution, elimination, and iteration, to find solutions.The examination also tests students" ability to estimate solutions and determine the reasonableness of their answers.Fourthly, the 2024 AMC questions encourage students to think creatively and explore mathematical concepts beyond traditional problem-solving methods.Some questions may have multiple solutions or require students to develop their own original solutions.This encourages students to think outside the box and explore the boundaries of mathematical knowledge.In conclusion, the 2024 American Mathematics Competition (AMC) questions are designed to assess students" mathematical knowledge, problem-solving skills, and creativity.The questions cover a wide range of topics and require students to think critically, logically, and creatively.By participating in the AMC, students can improve their mathematical abilities and expand their horizons in the field of mathematics.中文文档：标题：2024年美国数学竞赛（AMC）题目解析美国数学竞赛（AMC）是一项年度数学考试，面向美国高中学生。

2009 Contest ProblemsMCM PROBLEMSPROBLEM A: Designing a Traffic CircleMany cities and communities have traffic circles—from large ones with many lanes in the circle (such as at the Arc de Triomphe in Paris and the Victory Monument in Bangkok) to small ones with one or two lanes in the circle. Some of these traffic circles position a stop sign or a yield sign on every incoming road that gives priority to traffic already in the circle; some position a yield sign in the circle at each incoming road to give priority to incoming traffic; and some position a traffic light on each incoming road (with no right turn allowed on a red light). Other designs may also be possible.The goal of this problem is to use a model to determine how best to control traffic flow in, around, and out of a circle. State clearly the objective(s) you use in your model for making the optimal choice as well as the factors that affect this choice. Include a Technical Summary of not more than two double-spaced pages that explains to a Traffic Engineer how to use your model to help choose the appropriate flow-control method for any specific traffic circle. That is, summarize the conditions under which each type of traffic-control method should be used. When traffic lights are recommended, explain a method for determining how many seconds each light should remain green (which may vary according to the time of day and other factors). Illustrate how your model works with specific examples.MCM2009问题A : 设计一个交通环岛在许多城市和社区都建立有交通环岛，既有多条行车道的大型环岛（例如巴黎的凯旋门和曼谷的胜利纪念碑路口），又有一至两条行车道的小型环岛。

美赛习题答案美赛习题答案在数学建模领域，美国大学生数学建模竞赛（MCM）是一项备受关注的赛事。

每年，来自全球各地的大学生们都会参与其中，挑战各种实际问题并提出解决方案。

这项竞赛不仅考察了参赛者的数学水平，更重要的是培养了他们的团队合作和创新思维能力。

本文将探讨一些典型的美赛习题，并给出相应的解答。

第一题是关于城市交通流量的问题。

题目给出了一个城市的道路网络图，要求我们计算出每条道路的平均交通量。

首先，我们可以通过收集实际交通数据来估计每条道路上的车辆数量。

然后，根据道路的长度和车辆数量，我们可以计算出每条道路的平均交通量。

最后，将结果绘制成热力图，可以清晰地显示出城市交通的拥堵情况。

第二题是关于电力系统的问题。

题目给出了一个电力系统的拓扑结构图，要求我们设计一种最优的电力传输方案，以最大化系统的可靠性和效率。

首先，我们可以使用图论的方法对电力系统进行建模，并计算出各个节点之间的电力传输路径。

然后，根据节点之间的电力传输损耗和供电能力，我们可以通过线性规划等数学方法得到最优的电力传输方案。

最后，我们可以通过模拟实验来验证我们的方案，并对其进行优化。

第三题是关于航空公司的问题。

题目给出了一家航空公司的航班数据，要求我们设计一种最优的航班调度方案，以最大化公司的利润和乘客满意度。

首先，我们可以使用图论的方法对航班网络进行建模，并计算出各个航班之间的飞行时间和成本。

然后，根据乘客的需求和航班的运营成本，我们可以通过线性规划等数学方法得到最优的航班调度方案。

最后，我们可以通过模拟实验来验证我们的方案，并对其进行优化。

以上只是美赛习题中的几个例子，实际上还有许多其他有趣的问题，涉及到经济、环境、医疗等领域。

解决这些问题需要我们具备扎实的数学基础和创新的思维能力。

在解题过程中，我们需要灵活运用数学模型和工具，结合实际情况进行分析和判断。

同时，团队合作也是解决问题的关键，每个人都应发挥自己的优势，共同努力达到最佳的解决方案。

2024美赛题目解析今天咱们一起来看看2024年美赛的题目。

美赛可是一个很有挑战性也很有意思的竞赛，每年的题目都能让大家开动脑筋，想出各种奇妙的解法。

下面咱们就一道一道来分析分析。

题目A：“最佳觅食策略”题目内容和背景。

想象一下，动物们在野外要找吃的，这可不是一件简单的事儿。

它们得考虑好多因素，比如食物的分布情况、找食物要花多少精力、周围有没有危险等等。

就好比一只小松鼠，它要在树林里找坚果，有的地方坚果多，有的地方少，它还得小心别被老鹰抓走，这就是这个题目的背景啦。

解题思路。

要解决这个问题，咱们可以先确定一些关键因素。

比如说食物的能量值，就像一颗大坚果比一颗小坚果能量多；还有获取食物的难度，像藏在树洞里的坚果就比地上的难拿到。

然后呢，咱们可以建立一个模型，来计算动物在不同情况下的觅食收益。

比如说，小松鼠如果花5分钟在地上找到一颗小坚果，获得10单位的能量；花15分钟在树洞里找到一颗大坚果，能获得30单位的能量。

通过比较这些不同情况，就能找到最佳的觅食策略啦。

实际应用案例。

这个问题在现实生活中也有很多应用哦。

比如农民伯伯要规划种植哪些农作物，他们得考虑每种农作物的产量（就像食物的能量值），还有种植和管理的难度（获取食物的难度）。

这样才能决定怎么安排土地，获得最大的收益。

题目B：“水资源可持续性规划”题目内容和背景。

水可是咱们生活中必不可少的东西，但是现在水资源越来越紧张啦。

很多地方都面临着缺水的问题，就像有些干旱地区，人们连喝水都成问题。

所以咱们得想想办法，怎么合理地规划和利用水资源，让它能够可持续发展。

解题思路。

咱们得了解当地的水资源状况，包括有多少河流、湖泊，降雨量是多少等等。

然后根据不同的用水需求，像居民生活用水、农业灌溉用水、工业生产用水等，制定合理的分配方案。

比如说，在干旱地区，可以推广节水灌溉技术，像滴灌，这样就能用更少的水灌溉更多的庄稼。

还可以建立污水处理系统，把用过的水经过处理后再利用。

2024数学建模美赛c题
2024年美国大学生数学建模竞赛C题是关于网球中的动量的问题。

该题目
要求参赛者探讨网球中的动量，以及动量如何影响网球的弹跳和飞行。

该题目提供了一些数据，包括不同速度和重量的网球的弹跳高度和飞行距离。

参赛者需要使用这些数据来建立数学模型，以解释动量如何影响网球的弹跳和飞行。

在建立模型的过程中，可以使用不同的数学工具和软件，例如Python、Matlab、Excel等。

在解释数据时，可以使用回归分析、统计分析、机器学习等方法。

最后，参赛者需要将建立的模型应用于实际情境中，例如在网球比赛中如何使用动量来提高击球效果。

同时，还需要回答题目中提出的问题，例如“为什么动量对网球的弹跳和飞行有影响？”、“如何利用动量来提高网球比赛的表现？”等。

总之，2024年美国大学生数学建模竞赛C题是一个有趣且具有挑战性的问题，需要参赛者具备扎实的数学基础和良好的数据分析能力。

2003 MCM ProblemsPROBLEM A: The Stunt PersonAn exciting action scene in a movie is going to be filmed, and you are the stunt coordinator! A stunt person on a motorcycle will jump over an elephant and land in a pile of cardboard boxes to cushion their fall. You need to protect the stunt person, and also use relatively few cardboard boxes (lower cost, not seen by camera, etc.).Your job is to:•determine what size boxes to use•determine how many boxes to use•determine how the boxes will be stacked•determine if any modifications to the boxes would help•generalize to different combined weights (stunt person & motorcycle) and different jump heightsNote that, in "Tomorrow Never Dies", the James Bond character on a motorcycle jumps over a helicopter.PROBLEM B: Gamma Knife Treatment PlanningStereotactic radiosurgery delivers a single high dose of ionizing radiation to a radiographically well-defined, small intracranial 3D brain tumor without delivering any significant fraction of the prescribed dose to the surrounding brain tissue. Three modalities are commonly used in this area; they are the gamma knife unit, heavy charged particle beams, and external high-energy photon beams from linear accelerators.The gamma knife unit delivers a single high dose of ionizing radiation emanating from 201 cobalt-60 unit sources through a heavy helmet. All 201 beams simultaneously intersect at the isocenter, resulting in a spherical (approximately) dose distribution at the effective dose levels. Irradiating the isocenter to deliver dose is termed a “shot.” Shots can be represented as different spheres. Four interchangeable outer collimator helmets with beam channel diameters of 4, 8, 14, and 18 mm are available for irradiating different size volumes. For a target volume larger than one shot, multiple shots can be used to cover the entire target. In practice, most target volumes are treated with 1 to 15 shots. The target volume is a bounded, three-dimensional digital image that usually consists of millions of points.The goal of radiosurgery is to deplete tumor cells while preserving normal structures.Since there are physical limitations and biological uncertainties involved in this therapy process, a treatment plan needs to account for all those limitations and uncertainties. In general, an optimal treatment plan is designed to meet the following requirements.1.Minimize the dose gradient across the target volume.2.Match specified isodose contours to the target volumes.3.Match specified dose-volume constraints of the target and critical organ.4.Minimize the integral dose to the entire volume of normal tissues or organs.5.Constrain dose to specified normal tissue points below tolerance doses.6.Minimize the maximum dose to critical volumes.In gamma unit treatment planning, we have the following constraints:1.Prohibit shots from protruding outside the target.2.Prohibit shots from overlapping (to avoid hot spots).3.Cover the target volume with effective dosage as much as possible. But at least90% of the target volume must be covered by shots.e as few shots as possible.Your tasks are to formulate the optimal treatment planning for a gamma knife unit as a sphere-packing problem, and propose an algorithm to find a solution. While designing your algorithm, you must keep in mind that your algorithm must be reasonably efficient.2002 Contest ProblemsProblem AAuthors: Tjalling YpmaTitle: Wind and WatersprayAn ornamental fountain in a large open plaza surrounded by buildings squirts water high into the air. On gusty days, the wind blows spray from the fountain onto passersby. The water-flow from the fountain is controlled by a mechanism linked to an anemometer (which measures wind speed and direction) located on top of an adjacent building. The objective of this control is to provide passersby with an acceptable balance between an attractive spectacle and a soaking: The harder the wind blows, the lower the water volume and height to which the water is squirted, hence the less spray falls outside the pool area.Your task is to devise an algorithm which uses data provided by the anemometer to adjust the water-flow from the fountain as the wind conditions change.Problem BAuthors: Bill Fox and Rich WestTitle: Airline OverbookingYou're all packed and ready to go on a trip to visit your best friend in New York City. After you check in at the ticket counter, the airline clerk announces that your flight has been overbooked. Passengers need to check in immediately to determine if they still have a seat.Historically, airlines know that only a certain percentage of passengers who have made reservations on a particular flight will actually take that flight. Consequently, most airlines overbook-that is, they take more reservations than the capacity of the aircraft. Occasionally, more passengers will want to take a flight than the capacity of the plane leading to one or more passengers being bumped and thus unable to take the flight for which they had reservations.Airlines deal with bumped passengers in various ways. Some are given nothing, some are booked on later flights on other airlines, and some are given some kind of cash or airline ticket incentive.Consider the overbooking issue in light of the current situation:Less flights by airlines from point A to point BHeightened security at and around airportsPassengers' fearLoss of billions of dollars in revenue by airlines to dateBuild a mathematical model that examines the effects that different overbooking schemes have on the revenue received by an airline company in order to find an optimal overbooking strategy, i.e., the number of people by which an airline should overbook a particular flight so that the company's revenue is maximized. Insure that your model reflects the issues above, and consider alternatives for handling "bumped" passengers. Additionally, write a short memorandum to the airline's CEO summarizing your findings and analysis.MCM2000Problem A Air traffic ControlTo 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 r 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 problemsRequirement A: Given two airplanes flying in space, when should the air traffic controller ld 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 we measure how complex it is from an air traffic workload perspective? To what extent is complexity determined by the number of 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 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 conclusionsProblem 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.An 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 smaller than 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 interferenceRequirement 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 findingsMCM2000问题A 空间交通管制为加强安全并减少空中交通指挥员的工作量，联邦航空局(FAA)考虑对空中交通管制系统添加软件，以便自动探测飞行器飞行路线可能的冲突，并提醒指挥员。

1985 年美国大学生数学建模竞赛MCM 试题1985年MCM:动物种群选择合适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:战略储备管理钴、不产生在美国,许多行业至关重要。

(国防占17%的钴生产。

1979年)钴大部分来自非洲中部,一个政治上不稳定的地区。

1946年的战略和关键材料储备法案需要钴储备,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,出售大部分在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备已经在1982年收购了。

建立一个数学模型来管理储备的战略金属钴。

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计划在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达到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的水深度尺表面点的直角坐标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。

你应该避免什么地区内的矩形(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。