2012年研究生数模竞赛A题综述

21世纪是生物学的世纪.生物科学与技术也是我国赶超世界发达国家生产力水平,实现国力后发优势和经济快速发展最有前景和希望的领域.第九届全国研究生数学建模竞赛A题:基因识别问题及其算法实现,是生物信息学结构基因组研究中的一个基本问题.虽然该类问题的研究已经历了十多年时间,但由于基因问题的复杂性,问题的研究远远没有结束.除了基因的统计特征识别方法外,频谱特征识别正受到人们的重视.如果通过该赛题的研究,使得研究生们更加了解生物信息学相关研究课题的重要性,对生物信息学领域产生更大的兴趣,启发大家把数学,物理学以及计算机与信息处理等其它学科的方法引入到生物信息学问题的研究中来,引导研究生们从数学建模走向解决实际问题,那么赛题命题的目的就基本达到了.     

军事领域建模问题研究——2015年研究生数模竞赛A题综述

和平是我们向往和追求的目标,研究战争问题并非我们热衷于战争,恰恰相反,只有建立起强大的国防,任何敌人才不敢轻易发起战争,才能赢得世界的长久和平!第十二届全国研究生数学建模竞赛A题:水面舰艇编队防空和信息化战争评估模型,是军事领域的建模问题,战争是残酷和复杂的,应用建模手段研究战争问题是科学有效的方法.针对水面舰艇编队防空和信息化战争评估这两个方面的建模问题,介绍了军事领域建模问题研究的一般方法.通过该赛题的研究,使得研究生们更加关心国防建设,关心海洋,了解军事领域相关问题,对军事领域建模产生更大的兴趣,启发大家把数学,物理学以及计算机与信息处理等其它学科的方法引入到军事领域建模中来,引导研究生们从数学建模走向解决实际问题.     

军事行动避空侦察的时机和路线选择的评述

建模竞赛D题"军事行动避空侦察的时机和路线选择"来源于国家反卫星侦察的军事背景,其核心是要找出卫星的运行规律并建立相关预测模型,体现了全国研究生数学建模竞赛的特色.阐述了命题背景,分析了本赛题的建模及求解思路.通过赛题的研究,使得研究生们更加关心国防建设,引导学生把数学建模应用到军事领域建模中来,解决实际问题.     

关于A题竞赛论文的评论

建立食品卫生安全保障体系数学模型是国家科技支撑计划项目的内容,是关系国计民生的重大实际问题和当前的热点问题,具有强烈的实际背景和重要的应用价值.我们认为应该通过研究生数学建模活动把研究生的注意力吸引到这些问题上来,让广大研究生在研究、解决这些重大实际问题中学习数学建模、增长才干,体现全国研究生数学建模竞赛的正确的导向.因此我们根据项目内容改编成竞赛题"建立食品卫生安全保障体系数学模型及改进模型的若干理论问题".     

2010年全国研究生数模竞赛D题的评阅综述

2010年全国研究生数学建模竞赛D题的素材取自一项科研项目.将本题建为何种模型取决于建模人的数学基础和对本题描述运动过程的认识深度.评述介绍了三种建模思路:刚体平面运动模型,最优控制模型和微分方程模型,其中微分方程模型是在阅卷过程中从考生答卷中发现的,从答卷中发现了不少有共性的毛病,反应出国内大学和研究生数学教育中的弊病,值得有识之士们重视.     

第十一届全国研究生数学建模竞赛

<正>2014年12月13日在天津大学隆重举行的第十一届"华为杯"全国研究生数学建模竞赛颁奖大会标志着2014年研究生数学建模竞赛成功地落下帷幕.在竞赛的主办单位教育部学位与研究生教育发展中心的领导下和竞赛承办单位一天津大学的精心组织下,2014年的竞赛,共有30个省(市、自治区)的371所高校、研究所的4900队、14700名研究生,(其中包括691名博士生)参赛,规模空前.十一年来全国研究生数学建模竞赛不断发展壮大的事实说明在培养研究生创新能力、解决实际问题能力和团队意识方面研究生数学建模活动确实发挥了积极的作用,深受广大研究生欢迎,成效是显著的.     

2014年全国研究生数学建模竞赛D题赛题点评

首先阐明了2014年全国研究生数学建模竞赛D题"人体营养健康角度的中国果蔬发展战略研究"的研究背景.接着,针对每一个问题,从研究思路、研究方法、研究结论等方面均作了叙述.最后,对学生论文出现的问题、难点以及创新性等方面均做了点评.     

B题的赛后综述

第6届全国研究生数学建模竞赛B题来源于真实的科研项目,对参赛队员的创造性能力,分析和解决实际问题的能力具有很强的挑战性.从9个方面简述了这种挑战性.     

一道应用问题的解法与探究

<正>实际应用问题的解决是学生培养数学建模能力的重要载体,而对于一道实际问题,如果我们能从不同的角度去考察它,往往可以得到不同的解题途径,在这一过程中需要对现实问题进行数学抽象,再用数学语言表达问题,后用数学方法构建模型解决问题,以提升数学素养.下面以教材中一道例题为例,探究并运用不同的方法解决问题.     

推进课堂教学转型 落实数学核心素养——以“体重与脉搏”的高中数学建模教学为例北大核心

浙江省教研室为了落实指向核心素养的教学与学习,推进课堂转型,在浙江省高中数学优质课评比中,以数学建模为课题,要求参赛选手通过一节课的时间,让学生初步了解和经历用数学解决实际问题的过程,体验数学与生活的联系[1].学生虽然已经储备了一定的高中数学基础知识;对于生物学及计算机技术也已经有一定的了解,但是,对于数学建模这类学习主题还是陌生的.对教师而言,建模过程中还涉及到跨学科通识性教学问题及实践性学科教学问题,如何在一节课内建立数学模型并落实相关的数学核心素养也很有挑战性.     

Use of Inappropriate and Inaccurate Conceptual Knowledge to Solve an Osmosis Problem

Two outstanding high school science students each generated a correct answer to an osmosis problem. The solution processes are noteworthy because the problem solvers did not blindly use algorithms. They relied, instead, on conceptual knowledge which was inaccurate and inappropriate to the problem. They thought the osmosis problem was about air pressure, and some of their knowledge about air pressure was inaccurate. Thus, even when students rely on conceptual knowledge to solve a problem, correct answers need not indicate adequate understanding. Characteristics of the problem solvers, salient properties of the problem that could contribute to the problem misrepresentation, and spurious correct answers are identified. Finally, some instructional recommendations and research questions are presented.     

Exploring Students' Conceptual Understanding of the Averaging Algorithm

Conceptual understanding of arithmetic average includes both an understanding of the computational algorithm and the statistical aspects of the concept. This study focused on the examination of 250 sixth-grade students' understanding of the arithmetic average by assessing their understanding of the computational algorithm. The results of the study showed that the majority of the students knew the “add-them-all-up-and-divide” averaging algorithm, but only about half of the students were able to correctly apply the algorithm to solve a contextualized average problem. Students were able to use various solution strategies and representations to solve the average problem. Those who used algebraic and arithmetic representations were better problem solvers than those who used pictorial and verbal representations. This study not only suggests that the average concept is more complex than the simplicity suggested by the computational algorithm, but also indicates the need for teaching the concept of average, both as a statistical idea for describing and making sense of data sets and as a computational algorithm for solving problems.     

Numerical Solution of the Positional Boundary Control Problem for the Wave Equation with Unknown Initial Data

The problem of one-sided boundary Neumann control is considered for the onedimensional wave equation. Information about the initial state of the process is absent. Instead, the values of Dirichlet observations are received in real time at the controlled boundary. The aim is to bring the process to a complete rest by means of positional boundary controls. To solve this problem, we propose an efficient numerical algorithm with an optimal guaranteed damping time. Some results of numerical experiments are presented.     

The Isis problem as an experimental probe and teaching resource

The Isis problem, which has a link with the Isis cult of ancient Egypt, asks: “Find which rectangles with sides of integral length (in some unit) have area and perimeter (numerically) equal, and prove the result.” Since the solution requires minimal technical mathematics, the problem is accessible to a wide range of students. Further, it is notable for the variety of proofs (empirically grounded, algebraic, geometrical) using different forms of argument, and their associated representations, and it provides an instrument for probing students’ ideas about proof, and the interplay between routine and adaptive expertise. A group of 39 Flemish pre-service mathematics teachers was confronted with the Isis problem. More specifically, we first asked them to solve the problem and to look for more than one solution. Second, we invited them to study five given contrasting proofs and to rank these proofs from best to worst. The results highlight a preference of many students for algebraic proofs as well as their rejection of experimentation. The potential of the problem as a teaching tool is outlined.     

An analysis of the amount and characteristics of writing prompts in Grade 3 mathematics student books

Curriculum guidelines and professional organizations’ recommendations lack details about how often and how much students should write in mathematics and what characteristics should define their writing. This study presents an analytic framework that addresses how often students are prompted in student mathematics books to write, how much they may be encouraged to write, and the characteristics of the writing prompts. Consequently, 2,095 writing prompts in student books across 10 comprehensive Grade 3 resources were analyzed. Findings indicate a marked variation in how often and how much students are positioned to write. Most prompts have students explain what they did to solve a problem and why about number concepts, with most pressing for procedures. The greatest percentage of prompts had students write about their own solutions and do not urge them to include specific writing features.     

复振幅法在再生放大器增益研究中的应用

在激光原理教学中,针对再生放大器的增益问题,应用复振幅法,并参考多光束干涉的处理方法,给出了增益表达式的详细推导过程,可促进学生对该问题的理解和掌握,并可作为现有教材的一点补充.     

Structures in decision making: On the subjective geometry of hierarchies and networks

In the field of decision making, creating a structure is the first step in organizing, representing and solving a problem. A structure is a model, an abstraction of a problem. It helps us visualize and understand the relevant elements within it that we know from the real world and then use our understanding to solve the problem represented in the structure with greater confidence. In general, there are two kinds of structures used to represent problems: hierarchies and networks. Both rely to a varying degree on the interactions. Some examples are given followed by a discussion about how to structure the problem. At a minimum, a structure must satisfy two requirements: that it be logical in identifying and grouping similar things together, and that it relates them accurately according to the flow of influence among them. It must be complete with nothing left out that has an important influence. The structure is then tested as to whether it helps solve the problem to one’s satisfaction.     

一种高压开关产品的装配过程优化问题研究

本文针对高压开关产品的装配线提出一个实际的装配过程优化问题:高压开关产品的装配过程优化问题。该问题是在传统的空间布局问题中,加入了装配线工艺流程约束,是一类新的优化问题。本文为该问题建立了整数规划模型,并为该模型开发了启发式算法。然后以ZF11-252产品的装配过程为例,采用启发式算法求解模型。     

Contextual approach in teaching mathematics: an example using the sum of series of positive integers

In this paper, a contextual approach to teaching Mathematics at the pre-university level is recommended, and an example is illustrated. A context in the form of a real common mathematical problem is presented to the students. Different approaches to tackle the problem (from topics within and outside the syllabus) can be elicited from students. The insight obtained from the various methods of solving the problem can be used to deepen students’ learnt concepts and to enhance concepts to be learnt later in the curriculum.