高职线性代数课程的模块化设计

在高职教育快速发展的背景下,为适应高职各专业对线性代数基础课的多元化需求,需对该课程内容、教学方法和手段进行全新设计。文章提出了以线性方程组求解为主要目标、矩阵及其初等变换为主流方法、融入建模思想和信息技术的教学模块设计方案,并论述了各主要模块在高职教学中的特征与设计思路。     

线性代数教学中关于向量组线性相关性概念的引入与延伸

线性相关性理论是线性代数中的重要内容,本文对教学中向量组的线性相关性的概念的引入,定义的延伸与拓展进行了研究,并分析了其在后续课程最优化和小波分析课程中的应用,拓展了知识面,开阔了学生视野.     

提高自考线性代数教学效果的几点突破

《线性代数》是高等院校一门重要的公共基础课,内容具有很强的抽象性,逻辑性,内在联系性。本文研究了自考课程《线性代数（经管类）》助学中要注意的教学重难点以及教学内容的内在联系,旨在帮助自考学生掌握线性代数课程,提高学习效率和自考考试成绩。     

引入MATLAB软件工具提高线性代数教学应用水平

线性代数课程内容应用水平低的原因在于其教学内容偏重理论、教学手段相对滞后、缺乏与工程实际及专业课的联系.要改变这一状况可采取如下措施：补充应用实例,完善课程体系;进行专业调研,与专业紧密结合;编写新教材;使学生掌握MATLAB软件工具的使用方法.     

线性空间的直和分解思想的地位和作用

论述了线性空间的直和分解思想在数学中和在学生学习过程中所处的地位;并论述了直和分解思想对学习本课程和后继课程以及对培养学生思维能力方面所起的重要作用．     

Success in Algebra Among Community College Students

College algebra is a required course for most majors, but is viewed by many as a gatekeeper course for degree completion by students. With almost half a million students taking college algebra each year, faculty are experimenting with new course lengths of time that might result in higher success, completion, and retention rates for college algebra students. This article reports on a study of the traditional 16-week versus an 8-week course length in college algebra at a two-year Metropolitan Community College (MCC) in the United States. The study was to determine which course length of time, 8 weeks or 16 weeks, results in a higher proportion of students successfully completing the college algebra course. Also investigated were success rates among ethnicities, genders, and age groups. The study included 231 students in college algebra. Data were analyzed on four sections of the traditional 16-week courses and four sections of 8-week courses. In this study, success was measured as earning a grade of A, B, or C in the course. Understanding more about course lengths of time for college algebra can aid in increased understanding of time as a factor and, ultimately, may determine if students are more successful in 8-week or 16-week courses of instruction.     

《线性代数》教学中对于“第一节课”的体会及思考

线性代数课程与其他数学公共课程相比,具有自身的特点,当前部分研究也针对教学中的突出问题进行了探讨。文章结合近年的教学实践体会及新教学计划中线性代数课程的地位,对线性代数教学中"第一节课"的内容设计进行了探讨。     

《线性代数》课程教学改革的实践与思考

《线性代数》在自然科学与社会科学的各个领域发挥着越来越重要的作用,但大学里的课堂教学与现实中的实际应用存在着一定的脱节。本文从线性代数课程的教学现状出发,提出了在教学内容、教学方法及教学手段上进行改革的一些建议。     

跨学科类比法在线性代数教学中的应用

针对线性代数教学的抽象与沉闷的现状,结合当前大学生的时代特性与兴趣特性,文章将以一个教学实例为对象,尝试使用跨学科类比法,并以此为突破口,试图探索生活化的＂去数学化＂的新型教学。     

关于线性代数课程教学的一些思考

结合线性代数课堂教学,从优化教学内容、加强方法引导、抓好基础知识、渗透思想方法、采用多媒体辅助教学五个方面阐述了在线性代数课程教学中的一些思考。     

提高线性代数课堂教学效果的几点体会

线性代数是理工科重要的基础课程,结合教学实践以及一些思考,从线性代数的课程主线、概念教学、技能培养、思想方法等方面,就如何提高线性代数课程教学效果的谈几点体会。     

工科线性代数的教改与创新

传统的线性代数教学内容偏重理论、教学手段滞后,阻碍了工科学生对线性代数知识的掌握和应用。文章基于数学建模思想引出概念教学法并借助计算机Matlab软件,对教学内容的设计和教学手段进行改革和创新,激发工科学生学习线性代数的兴趣,提高其理论联系实际和实践动手能力。     

线性方程组理论在高等代数中的应用

在高等代数的研究中一般常用矩阵作为研究工具,该文系统地从多项式、矩阵、广义逆矩阵、线性空间、欧氏空间等五个方面的应用,说明线性方程组理论也是研究高等代数的强有力的工具．在线性空间的的讨论中不但给出了替换定理的一个推广,而且应用线性方程组的知识给出了线性空间中的替换定理的一个新证法,进而推出了一个新结论,并得到了一些有实用价值的应用．     

Applications,MATLAB and linear algebra as a unifying vehicle for the engineering-oriented syllabus

The paper considers the negative effects of the degeneration of the mathematics syllabus for engineering-oriented students into a collection of unconnected recipes, and presents a modernization of a linear algebra course to serve as a tool for the unification of the syllabus into a single transparent picture. The modernization is centred on the use of operator language as enabled by the incorporation of MATLAB-based applications into the theoretical part of the course.     

关于Cayley-Hamilton定理的连续论证法

Cayley-Hamilton定理是线性代数中的一个重要结论.对该定理从不同角度入手的证明也多种多样.为丰富线性代数的这部分理论,首先对有限维向量空间某些结果的论证进行了改进,然后利用矩阵数值分析的连续论证法,给出了Cayley-Hamilton定理的另一种新证明.     

新建本科院校线性代数课程教学的一些思考

本文论述了新建本科院校线性代数课程教学中存在的问题,以及我们在教学中从教学大纲、教学计划、考核方式等方面所做的探索和改革。     

Instructional television and student attitudes toward teacher,course, and medium

Summary and conclusions Semantic Differential data were obtained from 234 ninth graders who had just completed an algebra course which included a televised lecture presenting a new approach to the subject matter, and from 269 pupils who had had algebra taught in the usual way.     

也谈线性相关与线性无关

通过类比线性代数学中的关于线性相关与线性无关的定义及其性质给出函数组的线性相关与线性无关的一个新性质及二个推论．     

Exploring Personality Profiles with Matrices

We present a short-term class project used in an introductory linear algebra course, designed to engage students in matrix algebra. In this activity, students responded to a survey of their pop culture tastes. Using the survey responses, they worked to design a series of matching algorithms, using matrices, with the goal of matching the students in the class to the person whose tastes most closely aligned with their own. The class then explored various ways of testing the quality of the match. Topics covered along the way included: symmetric matrices, vector products, and numerical interpretation of qualitative data.     

Incorporation of Computer Algebra into an Undergraduate Course in Open Channel Hydraulics

Modern computer algebra systems have wide-ranging mathematical capabilities and user-friendly interfaces, which make them ideal tools for research and education. To demonstrate the applications of computer algebra for teaching, this paper reports on its successful incorporation into a senior, undergraduate, civil engineering course in open-channel hydraulics. Computer algebra is particularly useful for this course, since many hydraulics problems are non-linear and have traditionally required laborious solution techniques. The advanced capabilities of computer algebra systems also make them ideal tools for the design of hydraulic structures.