将数学建模思想融入大学数学教学全面提升教学质量——培养学员创新精神与创新能力的探索与实践

以加强数学建模课程建设,组织参加全国大学生数学建模竞赛为突破口,通过教学内容、教学方法、教学手段和培养模式的改革,引导学员参加科技创新活动,深化大学数学教学改革,培养学员的创新意识与创新能力.     

论大学开展数学建模教育

数学建模教育是围绕数学建模而进行的教学和实践活动 .开展数学建模教育可以培养学生的创新意识与创造能力 .因此 ,大学开展数学建模教育具有重要作用 .但是 ,开展数学建模教育一定要结合大学生的年龄特点、知识结构和智力水平 ,结合正常教学的教材内容 ,分层次逐步推进 .所以 ,大学生的数学建模能力应分阶段培养 ,建模题目也应划分不同层次 ,从而达到面向全体提高大学生数学素质的目的 .     

完善数学建模课程体系，提高学生自主创新能力

随着大学生数学建模竞赛的快速发展,全国大部分高校越来越认识到数学建模教学在大学生创新意识和实践能力培养中的重要作用,如何提高数学建模活动的成效成为普遍关注的问题。从数学建模课程的本质出发,尝试构建了较为完善的数学建模教学体系,达到数学建模教学贯穿大学生培养的全过程的教学理念。同时讨论了拓宽数学建模活动形式的途径和尚存在亟待解决的几个问题。     

第六届全国数学建模教学与应用会议纪要

<正>第六届全国教学建模教学与应用会议于1998年8月19日至22日在江西庐山召开.这次会议是在教育部高教司和中国工业与应用数学学会的领导下,由学会数学模型专业委员会和全国大学生数学建模竞赛组委会主办,并由南昌大学承办. 来自全国74所高等院校的110位代表出席了会议.中科院院士、南昌大学校长潘际銮教授和南昌大学汪茂湘处长还出席了大会开幕式.在开幕式上,俞文鱿教授首先代表学会数学模型专业委员会和全国组委会回顾了大学生数学建模竞赛活动开展以来在各方面带来的变化,指出这已成为大学生规模最大的一项课外科技活动.潘校长在致词中从高等院校教学中的一些问题谈到开展数学建模活动对于提高学生素质、能力和培养创造性的重要性,并介绍了江西文化教育事业,特别是南昌大学的发展及开展数模竞赛活动的概况.谭永基教授传达了中国工业与应用数学学会最近在成都召开的常务理事会和第五次代表大会中有关数学建模方面的内容,及将于2001年在北京召开的第十     

第七届全国数学建模教学与应用会议论文集将在本刊今年第5期发表

第七届全国数学建模教学与应用会议于2000年8月17日至20日在郑州举行，来自全国27省（市、自治区）205所院校的代表283人出席会议. 这次会议是在教育部高教司和中国工业与应用数学学会的领导下，由全国大学生数学建模竞赛组委会和中国工业与应用数学学会数学模型专业委员会组织、由中国人民解放军信息工程大学承办的，中科院院士、中国数学会副理事长丁伟岳教授出席了会议. 这次会议是1986年第一届会议以来出席人数最多的一次，特别是30岁左右的年轻人占大部分，而且第一次有中学教师参加，充分显示出我国从事数学建模教学与应用的队伍在不断壮大 从1989年，特别是1994年以来，在教育部的领导和指导下，我国数学建模教学与应用活动取得很大成绩，具体表现在：参加过国内外数学建模竞赛的大学生超过四万人，通过赛前准备、竞赛三天的拼搏和赛后继续三个阶段的努力，他们的能力普遍获得很大提高；培养出一大批年轻教师；推动了数学教学改革；推动了中学生数学知识应用活动；为进一步发展我国的应用数学事业提出了许多值得思考的问题. 这次会议也是为明年将在我国召开的第十届国际数学建模教学与应用会议作准备. 四天的会议安排了多项大会报告和分组报告. 这些报告经整理后将以论文形式在本刊2001年第5期发表. 分为“数学建模与数学教育”、“数学建模教学与竞赛”、“数学建模应用”、“数学建模方法”等专栏.     

一种不打乱现行教学秩序的大学数学教育改革的试验——记五邑大学数学建模教学活动

叶其孝教授在《大学生数学建模竞赛辅导教材 (二 )》中说 :以大学生数学建模竞赛为主体的数学建模教学活动实际上是一种不打乱现行教学秩序的、规模相当大的大学数学教育改革的试验。五邑大学自 1 995年以来 ,每年有 1 0个队参加全国大学生数学建模竞赛 ,几年的教学实践使我们对叶其孝教授上面的说法深有体会。1　数学建模教学活动在学校党政领导下开展数学建模教学和其它教学活动一样 ,应该在学校党政的领导下开展。学校的领导表现在两方面 ,一是领导的指导性的工作 ,二是领导对数模教学工作的支持。学校党政对数学建模教学的领导在于他们…     

搞好教学改革 培养高素质人才

数学建模作为一门崭新的课程是八十年代初进入我国高校的.在学院各级领导的关心支持下,我院于1995年将数学建模教学作为数学课程教学改革的突破口,重点投入.数学建模教学规模不断扩大.内容充实、形式多样的讲座、培训受到学生热烈欢迎.1995年以来,共组建了22个队参加1995-1998年的全国大学生数学建模竞赛,有16个队获奖,其中获全国一等奖一项,全国二等奖一项,江西赛区一等奖四项,江西赛区二等奖五项,江西赛区三等奖七项,数学建模活动在我院的影响迅速扩大,对于数学教学改革的推动作用日益显著.     

全国大学生数学建模竞赛章程

<正>第一条 总则 全国大学生数学建模竞赛（以下简称竞赛）是国家教委高教司和中国工业与应用数学学会共同主办的面向全国大学生的群众性科技活动,目的在于激励学生学习数学的积极性,提高学生建立数学模型和运用计算机技术解决实际问题的综合能力,鼓励广大学生踊跃参加课外科技活动,开拓知识面,培养创造精神及合作意识,推动大学数学教学体系、教学内容和方法的改革.     

数学建模竞赛的做法与体会

我院自 2 0 0 0年正式参加全国大学生数学建模竞赛以来 ,学院非常重视 ,多次派有关教练员外出调研和学习 ,请院外专家来院作报告 ,拨出专款筹建数学建模实验室 ,率先在全院本科中开设数学建模必修课 .几年的探索实践中 ,我们不断总结经验 ,吸取教训 ,逐渐形成了自己独特的培训模式 ,收到了良好的效果 .参赛三年来 ,共获 2个全国一等奖 ,2个全国二等奖 ,6个赛区一等奖 ,4个赛区二等奖 .下面介绍一下我院在数学建模培训和竞赛中的一些做法、体会和收获 .1　健全组织　完善制度　使数学建模竞赛工作规范化一、组织健全 ,领导重视学院成立数学建…     

北京高校数学建模讨论班积极开展活动

<正>为了更好地推动高校数学建模教学和研究工作,北京数学会于1992年组织了“北京高校数学建模讨论班”,平均一个多月举行一次活动每次半天,都是占用星期日的上午,迄今已举行了10次活动,参加的学校和教师愈来愈多,现已有近30所院校、40多位教师参加过活动,讨论班的内容也愈来愈扎实、丰富多采,不仅报告数学建模的优秀实例,还报告数学建模及其教学国际会议会议录中有关论文,特别是结合学生的具体情况如何组织数     

Accelerated hybrid viscosity and steepest-descent method for proximal split feasibility problems

The purpose of this paper is to present an accelerated hybrid viscosity and steepest-descent method for solving proximal split feasibility problems (if solutions exist) in real Hilbert spaces. We obtain strong convergence of the sequence generated by our scheme under some suitable conditions on the parameters. In all our results in this work, our iterative schemes are proposed with a way of selecting the step sizes such that their implementation does not need any prior information about the bounded linear operator norm. Finally, we give numerical comparisons of our results with other established result to verify the efficiency and implementation of our new method.     

l-solutions and stability analysis of difference equations using the Kummer’s test

We address the p-summability and asymptotic stability properties in nonautonomous linear difference equations. We focus our discussion on two kind of difference equations. The first one is a first order system of linear nonautonomous difference equations, and our discussion involves the use of Kummer’s convergence test. The second one is a linear nonautonomous scalar higher order difference equation. In this case our discussion is based on a recently introduced transformation of a higher order system into a first-step recursion, where the companion matrices are well treatable from our point of view. We give insight on our ideas that are behind our methods, prove new results, and show applications.     

Explicit trace inequalities for isogeometric analysis and parametric hexahedral finite elements

We derive new trace inequalities for NURBS-mapped domains. In addition to Sobolev-type inequalities, we derive discrete trace inequalities for use in NURBS-based isogeometric analysis. All dependencies on shape, size, polynomial degree, and the NURBS weighting function are precisely specified in our analysis, and explicit values are provided for all bounding constants appearing in our estimates. As hexahedral finite elements are special cases of NURBS, our results specialize to parametric hexahedral finite elements, and our analysis also generalizes to T-spline-based isogeometric analysis. We compare the bounding constants appearing in our explicit trace inequalities with numerically computed optimal bounding constants, and we discuss application of our results to a Laplace problem. We finish this paper with a brief exploration of so-called patch-wise trace inequalities for isogeometric analysis.     

S曲线与产业结构调整

高新技术革命是当今社会变革当中的热点之一,它影响着国民经济的方方面面,文章从高新技术的一个独特现象——Ｓ曲线出发,分析了这一现象在产业结构调整中的表现,并结合我国经济的现状,提出了我国企业面对这次革命的应有对策     

Clustering Categorical Data via Ensembling Dissimilarity Matrices

We present a technique for clustering categorical data by generating many dissimilarity matrices and combining them. We begin by demonstrating our technique on low-dimensional categorical data and comparing it to several other techniques that have been proposed. We show through simulations and examples that our method is both more accurate and more stable. Then we give conditions under which our method should yield good results in general. Our method extends to high-dimensional categorical data of equal lengths by ensembling over many choices of explanatory variables. In this context, we compare our method with two other methods. Finally, we extend our method to high-dimensional categorical data vectors of unequal length by using alignment techniques to equalize the lengths. We give an example to show that our method continues to provide useful results, in particular, providing a comparison with phylogenetic trees. Supplementary material for this article is available online.     

q-Rook Monoid Algebras, Hecke Algebras, and Schur–Weyl Duality

When we were at the beginnings of our careers, Sergei's support helped us to believe in our work. He generously encouraged us to publish our results on Brauer and Birman–Murakami–Wenzl algebras, results which had in part, or possibly in total, been obtained earlier by Sergei himself. He remains a great inspiration for us, both mathematically and in our memory of his kindness, modesty, generosity, and encouragement to the younger generation. Bibliography: 19 titles.     

举办《应用数学学校》和参加数学应用数学建模竞赛的实践和思考

通过开展应用数学教学活动和开办《应用数学学校》的多年实践 ,我校学生结合实际学习和应用数学知识的意识和能力不断提高 ,在上海市数学知识应用竞赛和美国大学生数学建模竞赛中连续取得好成绩 ,为了争取把这项工作做得更好 ,我们作了进一步思考和打算     

Explaining modal intuition

The paper defends causal explanationism concerning our modal intuitions and judgments, and, in particular, the following claims. If a causally explainable mirroring or “pre-established harmony” between our mind and modal reality obtains, we are justified in believing it does. We do not hold our modal beliefs compulsively and blindly but with full subjective and objective justification. Therefore, causal explanation of our modal beliefs does not undermine rational trust in them. Explanation and trust support each other. In contrast, anti-explanationists (from Kant, through neo-wittgensteinians to T. Nagel and J. Pust), claim that causal explanation of intuitions and judgments undermines rational trust in them. They especially target causal explanation in terms of pre-established harmony between our mind, shaped by causal processes, and the underlying modal structure of reality. The paper argues against them. The argument builds upon the claim that the appeal to modal facts is indispensable for systematization and explanation of non-modal ones. Therefore, we should assume that modal facts exist and are not disjoint and isolated from actual facts. The modal structure of the universe intervenes in the non-modal reality. Causal processes indirectly carry information about deep modal structure. Any (reasonable candidate) causal explanation of our intuitional modal beliefs should start from this indirect contact with and information about modal facts. Therefore, if our intuitional modal beliefs are true and causally explainable (by a factual, non-modal explanans), they are true in virtue of the deep underlying modal structure. They are sensitive to modal reality and track it. We can come to know this fact, and thus strengthen our spontaneous trust in our modal intuitions.     

Mathematics teacher educators’/researchers’ collaboration with teachers as a context for professional learning

This paper describes our joint activity as mathematics teacher educators and academic researchers in collaborating with both experienced and novice teachers in two contexts: an emergent community of inquiry into mathematics teaching and its development; and a research methods course, offered as part of a mathematics education Master’s program, aspiring to initiate participating teachers into research practice through inquiry. Adopting an Activity Theory (AT) perspective, we analyse our activity, identifying its nature and transformations that frame our professional learning. The results indicate that our professional learning is the outcome of a continuous process of becoming aware of our own activity and its transformation in relation to that of the teachers.     

Basic modelling of uncertainty: young students’ mental models

This paper focuses on a research programme that aims to explore students?? mental models when acting within elementary situations of uncertainty before stochastics have been addressed in school. In order to frame our research, we begin by reporting briefly on the recent history of research in stochastics education. Then, we discuss the main aspects of our theoretical foundation concerning the research programme. Afterwards we restrict our discussion to an exploratory study aiming to further develop our theoretical framework, describing the development of tasks representing situations of uncertainty and the method of the exploratory study involving students of grade 4 and grade 6. Finally, from the perspective of theory development, we discuss the results of analysing students?? solutions gained through quantitative analysis of tests and qualitative analysis of written rationales and of interviews. We conclude our paper with a discussion of our research results and potential future research questions.