正确写作美国大学生数学建模竞赛论文（MCM/ICM）

高等教出版社，王杰，美国MCM/ICM竞赛指导丛书“美国MCM/CM竞赛指导丛书”编审委员会顾问Sol garfunkel美国数学及应用联合会( COMAP)Chris Arney美国西点军校主编王杰美国麻省大学罗威尔分校/ COMAP中国合作部朱旭西安交通大学秘书王嘉寅美国康涅狄格大学/西安交通大学委员(按姓氏拼音排序)Jay Belanger美国杜鲁门州立大学陈秀珍美国乔治华盛顿大学冯国灿中山大学龚维博美国麻省大学阿默斯特分校韩中庚解放军信息工程大学李向阳美国伊利诺伊理工大学杨新宇西安交通大学叶正麟西北工业大学张存权美国西弗吉尼亚大学COMAP总裁序美国大学生数学建模竞赛( the Mathematical Contest in Modeling,MCM)已经举办近30年了,时间真是快得难以置信。在此期间,竞赛从最初参赛的90支美国队逐渐发展成为一个国际大赛,今年已有来自世界各地的25个国家超过5000支队伍参赛。尤其令人感动和鼓舞的是我的中国同事们对竞赛赋予的极大热情以及中国参赛队伍的快速增长。 COMAP张开双臂欢迎你们的参与。COMAP每年举办3个建模竞赛,即MCM,ICM( the Interdisciplinary Contest in Modeling)fu HiMCM(the High School Mathematical Contest in Modeling)竞赛。竞赛的目的不仅仅是奖励同学们所作出的努力—无疑这是同样重要的,我们举办各类数学建模竞赛的目的始终是为了推动在世界各国的各级教育体系中增加应用数学及数学建模的比重。建模是人们为了解世间事物的运作规律所做的尝试,数学的使用能够帮助我们建立更好的模型。这不是一个国家的任务,而是所有国家都应该共同关心的问题。 COMAP建模竞赛从孕育到现在已经演变成为实现这一宏伟目标的有力工具。我热切地希望同学们通过阅读这套优秀的丛书,对 COMAP举办的竞赛有更多的了解,并且学到更多有关数学建模的方法与过程。我希望同学们尝试自已解决丛书中讨论的所有建模问题,这些都是令人兴奋并且具有实用价值的问题。我希望更多的同学参加MCM/CM竞赛,并参与推广和普及数学建模的活动,这是很有意义的工作。Sol garfunkel,博士COMAP总裁012年11月Forward by sol garfunkelWhile it is hard for me to believe, the Mathematical Contest in Modeling (MCM)is fast approaching its 30th year. During this time we have grown from 90 US teamsto over 5,000 teams representing 25 countries from all across the globe. We havebeen especially buoyed by the enthusiasm shown by our Chinese colleagues and therapid growth in Chinese participation. COMAP welcomes your involvement withopen armsCOMAP runs three contests in mathematical modeling; they are MCM, ICM(the Interdisciplinary Contest in Modeling), and HiMCM (the High School Mathe-matical Contest in Modeling). The purpose of all of these contests has never beensimply to reward student efforts- as important as that is. Rather, our objectivefrom the beginning has been to increase the presence of applied mathematics andmodeling in education systems at all levels worldwide. Modeling is an attempt tolearn how the world works and the use of mathematics can help us produce bettermodels. This is not a job for one country, but for all. The COMAP modelingcontests were conceived and evolved to be strong instruments to help achieve thismuch larger goalIt is my supreme hope that through this excellent book series the Chinesestudents will learn more about COMaP contests and more about the process ofmathematical modeling. I hope that you will begin to work on the exciting and im-portant problems you see here, and that you will join the MCM/ICM contests andthe rewarding work of increasing the awareness of the importance of mathematicalmodelIng.Sol Garfunkel. PhDExecutive DirectorCOMAPNovember 2012ICM竞赛主席序数学建模的训练与经验能使同学们在解决问题时更有创意,同时也能帮同学们成为更为优秀的研究生。“美国MCM/ICM竞赛指导丛书”的出版,将通过数学建模竟赛题目和概念的解析,帮助同学们掌握数学建模的技能,并为同学们在今后的工作中获得成功打下坚实的基础。数学建模是一种过程,也是一种理念,或者说是一种哲学。作为过程,学生在理解及使用建模过程或框架时需要指导并积累经验。作为经验,学生需要使用不同的数学方法(离散、连续、线性、非线性、随机、几何及分析)构造数学模型,从中体验不同的细节及复杂程度。作为理念,学生需要发现各种相关的、具有挑战性的及有趣的实际问题,从中培养数学建模的兴趣,并认识到数学建模在实际生活中的作用。数学建模的主要目的是指导学生用建模的方法解决实际问题。尽管在实际中,有些问题或许可以使用已有的算法和公式来求解,但数学建模的方法比简单使用已有算法和公式能解决更多的问题,特别是解决新的、没有固定答案及没有被解决过的问题。为了积累经验,同学们应尽早地接受数学建模的训练,至少应该在大学低年级就开始,这样可以在以后的课程学习中进一步强化数学建模能力。由于数学建模的综合与交叉特性,各个专业的学生都能够从数学建模活动中受益。本套丛书从将数学模型作为研究工具的角度出发,包括介绍模型的构造,分析建模过程,这些都是帮助学生更好地掌握数学建模技能的重要因素。数学建模是充满挑战的高级技能,更重要的是能够帮助学生更快地成长。当今世界需要解决的问题往往很复杂,所以建立的数学模型也很复杂,通常需要通过精细的计算和模拟才能获得解答或得到对模型结果的分析与检验。由于数据可视化技术的普及,解题方法的增加,所以现在是培养更多数学建模高手的最佳时期。我希望同学们在数学建模探索中取得进步,也希望指导教师在使用这套丛书提供的例子及方法指导学生时取得很好的效果。尽管学生的层次可能不同,但我对你们的忠告是同样的:树立你的信心,发展你的技能,用你的才能解决社会中最具挑战性及最重要的问题。祝各位建模好运Chris Arney,博士美国西点军校数学系教授ICM竞赛主席2011年10月Forward by Chris ArneyUndergraduate students who receive instruction and experiences in mathematicalmodeling become better and more creative problem solvers and graduate studentsThis book series is being published to prepare and educate students on the topicsand concepts of mathematical modeling to help them establish a problem solvingfoundation for a successful careerMathematical modeling is both a process and a mindset or philosophy. Asa process, students need instruction and experience in understanding and usingthe modeling process or framework. As part of their experience, they need to seevarious levels of sophistication and complexity, along with various types of mathematical structures(discrete, continuous, linear, nonlinear, deterministic, stochasticgeometric, and analytic). As a mindset, students need to see problems that arerelevant, challenging, and interesting so they build a passion for the process andits utility in their lives. A major goal in modeling is for students to want to modeloroblems and find their solutions. Recipes for structured or prescribed problesolving(canned algorithms and formulas) do exist in the real world, but mathe-matical modelers can do much more than execute recipes or formulas. Modelersare empowered to solve new, open, unsolved problemsIn order to build sufficient experience in modeling, student exposure must begin as early as possible -definitely by the early undergraduate years. Then themodeling process can be reinforced and used throughout their undergraduate pro-gram. Since modeling is interdisciplinary, students from all areas of undergraduatetudy benefit from this experienceThe articles and chapters in this series expose the readers tomodel construction, model analysis, and modeling as a research tool. All these areas are importantand build the students'modeling skills. Modeling is a challenging and advancedskill, but one that is empowering and important in student development. In to-day 's world, models are often complex and require sophisticated computation orsimulation to provide solutions or insights into model behavior. Now is an excitingiForward by chnns Arneytime to be a skilled modeler since methodology to provide visualization and findsolutions are more prevalent and more powerful than ever beforeI wish the students well in their adventure into modeling and I likewise wishfaculty well as they use the examples and techniques in this book series to teach themodeling process to their students. My advice to all levels of modelers is to buildyour confidence and skills and use your talents to solve societys most challengingand important problems. Good luck in modelingChris Arney, PhDUnited States Military Academy at West PointProfessor of mathematicsDirector of the Interdisciplinary Contest in ModelingOctber,2011从书简介美国大学生数学建模竞赛( the Mathematical Contest in modeling,MCM/the Interdisciplinary Contest in Modeling,ICM),即“数学建模竟赛”和“交叉学科建模竞赛”,是一项国际级的竞赛活动,为现今各类数学建模竞赛的鼻祖。1985年,在美国教育部的资助下,在美国针对在校大学生创办了一个名为“数学建模竞赛”的竞赛,其宗旨是鼓励大学师生对不同领域的各种实际问题进行阐明、分析并提出解决方案。它是一种完全公开的竞赛,参赛形式为学生三人组成一队,在三天(72小时)(近年改为四天,即96小时)内任选一题,完成数学建模的全过程,并就问题的重述、简化和假设及其合理性的论述、数学模型的建立和求解〔及软件)、检验和改进、模型的优缺点及其可能的应用范围与自我评价等内容写出论文。MCM/ICM非常重视解决方案的原创性、团队合作与交流以及结果的合理性。由专家组成的评阅组进行评阅,评出优秀论文。除了不允许在竞赛期间与团队外的任何人(包括指导教师)讨论赛题之外,允许使用图书资料、互联网上的资料、任何类型的计算机程序和软件等各种资料和途径,从而为参赛学生提供了广阔的创作空间。第一届竞赛时,只有美国的158个队报名参加,其中只有90个队提交了解答论文。2012年MCM/ICM共有5026个队参加,其中MCM有3697个队,ICM有1329个队,遍及五大洲。MCM/ICM已经成为最著名的国际大学生竞赛之一,影响极其广泛。近年来,已有越来越多的中国学生组队参加美国大学生数学建模竟赛,其中不乏被评为优胜论文( Outstanding winners)的佼佼者,这充分显示了我国大学生参加 MCM/ICM的积极性与实力。学生在准备竟赛的时候,除了在指导教师的帮助下阅读和研究以往竞赛的优胜论文以外,普遍希望能有一些专门针对美国大学生数学建模竞赛的书籍,指导和帮助备赛。美国MCM/ICM竞赛指导丛书”就是为了满足读者的这一需求而出版的,目的是帮助学生学习从全局出发,不受固定模式的限制,用建模的手段解决开放性问题的研究方法,并提高写作能力。丛书的读者对象包括参赛学生及对数学建模与算法感兴趣的研究生、专业人员和业余爱好者。我们邀请到 COMAP中国合作总监、美国麻省大学罗威尔分校王杰教授担任丛书主编,他曾为MCM/ICM命题,对竟赛具有很多独到的认识。丛书作者i丛书简介来自各高校,他们都是有经验的指导教师或参加过竟赛的优秀成员。丛书包括本《正确写作美国大学生数学建模竞赛论文》和若干辑《美国大学生数学建模竞赛题解析与研究》,前者为一本指导学生如何正确写作MCM/CM论文的工具书,后者中的每一辑将讨论若干赛题,包括问题的背景、分析技巧、建模与测试方法及算法设计,并引导读者列出进一步研究的课题。目标是培养学生多方面的能力,如数学、编程、写作及课题研究等的训练,提高学生分析问题、解决问题的水平。丛书的出版计划得到了美国数学建模专家的广泛支持, COMAP总裁SolGarfunkel博士及ICM主席、美国西点军校数学系教授 Chris Arney博士受邀担任丛书顾问并为丛书作序。我们热切希望通过这套丛书的出版,进一步活跃我国大学生参加MCM/CM的积极性,提高他们的自信心,并最终取得满意的成绩。更为重要的是,提高学生的研究和解决实际问题的能力。