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1.
关于线性代数课教学的两点看法   总被引:2,自引:1,他引:1  
就线性代数教学中解析几何与线性代数的互相渗透以及如何处理教材内容更新的问题,谈一些个人看法,欢迎批评指正.1解析几何与线性代数的互相渗透微积分,解析几何,线性代数之间的互相渗透体现了教材内容的“现代化”.正如文[1]所述,将解析几何与线性代数整合为一门课程已经得到不  相似文献   

2.
指出了线性代数课程建设中存在的一些问题,介绍了教育信息化背景下对线性代数课程教学内容的创新,阐述了将信息技术与线性代数课程的教学内容进行整合的有效办法。  相似文献   

3.
首先明确了《线性代数(非数学专业)》整体教学的目的和实践的过程,其次从学生构建《线性代数》知识、技能和思想方法的角度总结了《线性代数》整体教学实践的一些体会,最后指出《线性代数》整体教学应把握数学观念,更好地将启发式教学与问题解决结合起来.  相似文献   

4.
中外线性代数教材的比较与探讨   总被引:2,自引:0,他引:2  
将中外线性代数教材做了较系统的比较,包括教材内容、结构安排、习题配置等多个方面,并通过比较发现和分析美国等西方国家线性代数教材的优点和新理念,以达到交流互补,融合提高的目的.最后,在参考与借鉴的基础上,对我国线性代数教材建设和教学改革作了一些思考和探讨.  相似文献   

5.
解线性方程组是线性代数课程的最重要内容之一,目前工科线性代数的大纲和教材一般不包括不相容方程组,其实这部分内容具有广泛的应用.本文用微积分方法给出不相容方程组的最小二乘解以及极小范数最小二乘解,可供线性代数课程的教学改革作参考.建议待条件成熟时,将不相容方程组的最小二乘解纳入工科线性代数的教学大纲和教材.  相似文献   

6.
线性代数是一门较抽象的数学课程 .传统的线性代数教材通常是基于入门学科立论的准确和证明的严格来编写的 ,其抽象性跃然纸上 .但是 ,线性代数除其抽象性之外 ,还具有另外一个同样重要的特点 :实用性 ,它同微积分一样极富实用价值 .实际上 ,线性代数更适于将数学的两大因素——抽象和应用结合起来 .由于电子计算机的飞速发展和广泛应用 ,线性代数已成为越来越多的科技工作者必不可少的数学工具 ,为培养跨世纪高级工程技术人才 ,教好学好线性代数是十二分重要的 .基于这样的理由 ,我在线性代数教学中采取了一些不同于传统的教法 ,一方面力求…  相似文献   

7.
借助MATLAB软件将几何直观方法应用于矩阵特征向量的判定、二次曲线的绘制、二次型的分类和微分方程组动力学性质刻画等线性代数特征值问题教学之中,以实例说明几何直观在线性代数课程教学中的应用.  相似文献   

8.
提出了以能力培养为目标,以计算思维训练为手段的《线性代数》混合式教学改革与实践.首先,将计算思维引入线性代数教学过程,以计算思维训练驱动线性代数的现代教学和课程改革.其次,教师主体通过不断提升信息化教学能力,设计适合在泛在环境下碎片化学习的混合式教学过程,培养学生运用线性代数思维分析和解决专业问题的能力.问卷调查结果表明了实施混合式教学改革的有效性.  相似文献   

9.
韩瑞珠 《大学数学》2002,18(6):52-58
空间解析几何是以坐标法和向量法作为主要的研究工具 ,用代数方法来研究几何图形的几何学 ,而线性代数则是用矩阵和向量等工具来研究多变量之间的线性关系 .因此 ,空间解析几何与线性代数紧密相关 .事实上 ,几何为线性代数中许多概念和理论提供了几何背景或几何解释 ,而线性代数为几何问题的解决提供了有效的方法 .鉴于此 ,近年来 ,国内许多学校相继把线性代数和空间解析几何整合成一门课程 .据笔者所知 ,最早将线性代数与空间解析几何整合成一门课程的学校是清华大学 ,他们出版了两本教材 .其一是萧树铁教授在国家教委“面向 2 1世纪教学内…  相似文献   

10.
文中论述了一种针对计算机专业大学生的线性代数的课程教学改革模式,即,将程序设计融入线性代数的课程教学.通过课程引入,理论与实践相结合以及考核方案等方面,借助具体实例探讨了这种教学改革的方法.最后,根据教学反馈与调查研究,分析总结了计算机专业特色相结合的线性代数教学模式的结论与启示.  相似文献   

11.
关于数学分析在线性代数中某些应用的数学札记   总被引:3,自引:0,他引:3  
姚云飞  姚磊 《大学数学》2005,21(6):108-112
线性代数中有不少难度较高的问题,若从代数学内部系统出发处理起来,相当繁冗.但是若从另一角度出发,运用数学分析的方法去处理这些代数问题,可能有着事半功倍之效.为此,本文运用数学分析的有关知识和方法论证线性代数中的某些问题.供大家在教学时参考,不妥之处,敬请斧正.  相似文献   

12.
高等代数是大学本科数学专业一门重要的基础课程,但由于该课程的内容、思想的抽象性,传统的教学模式很难使大一的学生入门,也很难培养学生对高等代数的兴趣.若将其与解析几何、数学软件、数学建模等结合起来,并将其内容的先后顺序做适当的调整,能使其内容具体化、生动化.更易适应大一新生的学习方式.切实培养大学生的数学素质,提高教学质量.  相似文献   

13.
论述线性代数教材改革的必要性及其指导思想,主张线性代数教材建设应以矩阵为主线,以教育部颁发的硕士研究生人学考试线性代数部分的大纲为纲,结合教学现代化的现状,强调几何与代数相结合,重视代数学思想方法的渗透,化抽象为具体,同时在教学中还要引入数学建模的思想.  相似文献   

14.
Various approaches and standards for transferring mathematical objects between different computer programs in multimedia environment in the framework of the OpenMath project are described. The use of these standards might revolutionize the exchange of mathematical information caused by the development of computer algebra tools and telecommunication possibilities. The standards make it possible to create databases and easily save and use mathematical objects obtained in different applications, e.g., to exchange the data obtained in different computer algebra systems and place information on the Internet. Bibliography: 9 titles.  相似文献   

15.
Max-plus algebra, cost measures, and mathematical fear have proved useful tools in dynamic optimization. Indeed, the first two have even become a central tool in some fields of investigation such as discrete event systems. We first recall the fundamentals of max-plus algebra with simple examples of max-plus linear models, and simple consequences of that remark. We then introduce cost measures, the natural equivalent of probability measures in the max-plus algebra, and their fundamental properties, including the definition of the mathematical fear (the equivalent of the mathematical expectation), induced measures and conditioning. Finally, we concentrate on those aspects that are put in use in dynamical optimization and state a separation theorem which was first derived using these tools.  相似文献   

16.
Student group work represents a central learning setting within mathematics programs at the university level. In this study, a theoretical perspective on collaboration is adopted in which the differences between students’ interpretations of a mathematical concept are seen as an opportunity for individual restructuring processes. This so-called interactionist perspective is applied to student group work on linear algebra. The concepts of linear algebra at the university level are characterized by a versatility of different modes of expression and interpretation. For students of linear algebra, the flexible transitions between the different interpretations of linear algebra concepts usually pose a challenge. This study focuses on how students negotiate their different interpretations during group work on linear algebra and how transitions between interpretations might be stimulated or hindered. Video recordings of eight student groups working on a task that required flexible transition between interpretations of homomorphisms were sampled. The recordings were analyzed from an interactionist perspective, focusing on interaction situations in which the participating students expressed and negotiated different interpretations of homomorphisms. The analyses of students’ interactions highlight a phenomenon whereby differences in students’ interpretations remain implicit in group discussions, which constitutes an obstacle to the negotiation process.  相似文献   

17.
本文叙述了RMI原则的一些基本概念,例举了RMI原则在数学分析、线性代数、积分变换和概率论中的应用。  相似文献   

18.
Summary As an application of the Riemann-Hilbert (RH) problem to mathematical physics, the RH transformations are considered for a Galilean invariant nonlinear system. Algebraic RH transformation gives rise to new solutions from the old via a calculation in linear algebra. It is proved that the infinitesimal RH transformations form an infinite-dimensional Lie algebra without using a hierarchy of potentials.  相似文献   

19.
We obtain some necessary and sufficient conditions for the non-x-autonomy of the basic Lie algebra of a system of first-order linear differential equations with constant coefficients over the field of complex numbers. Using these results, we establish the x-autonomy of the basic Lie algebra of some systems of equations of mathematical physics.  相似文献   

20.
In this article we present a didactic proposal for teaching linear algebra based on two compatible theoretical models: emergent models and mathematical modelling. This proposal begins with a problematic situation related to the creation and use of secure passwords, which leads students toward the construction of the concepts of spanning set and span. The objective is to evaluate this didactic proposal by determining the level of match between the hypothetical learning trajectory (HLT) designed in this study with the actual learning trajectory in the second experimental cycle of an investigation design-based research more extensive. The results show a high level of match between the trajectories in more than half of the conjectures, which gives evidence that the HLT has supported, in many cases, the achievement of the learning objective, and that additionally mathematical modelling contributes to the construction of these linear algebra concepts.  相似文献   

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