代数教学中的模式直观

“模式直观”是另一种直观思维方式,在代数教学中是有教育价值的.“模式直观”的初步分类是:(1)常识性模式直观;(2)迁移性模式直观;(3)和谐性的模式直观;(4)符号性模式直观.     

关于超越数的一些性质

从教学及历史的角度给出超越数的一些性质.     

Chebyshev加速方法的收敛性分析

讨论用于线性代数方程组的迭代解法的Ｃｈｅｂｙｓｈｅｖ加速方法的收敛性．分别就基本迭代矩阵具有实特征值和复特征值两种情形进行分析，得到一种较深刻的结论，并提出了一种新的收敛速度概念     

同构、同态在比较两个代数体系时的作用

以近世代数理论为基础,给出了同构、同态在代数体系的讨论中所起的简化作用。     

关于不定方程x^2＋4^2n=y^3

利用代数数论的方法,证明了不定方程x^2＋4^2n=y^3其中n∈N,x≡1（mod2）,x,y∈Z）无整数解．     

二次虚代数整数环中的Euclid整环

唯一分解是整数环所具有的重要性质,当数系扩充到全体代数整数时,该性质将会消失。该文把整数环扩充到二次虚单纯代数整环,讨论了二次虚单纯代数整环的可既约分解性,进一步探讨了具有Euclid性质的整环,从而得到了二次虚单纯代数整环中能够实现唯一分解的一部分整环。     

Excel在辅助生产费用分配中的应用

利用Excel的强大功能,建立计算模型,可以快速实现辅助生产费用的分配。文章通过三个具体实例,详细地阐述了Excel在计划成本分配法、交互分配法、代数分配法中具体应用的方法,解决了既麻烦又低效的手工分配辅助生产费用的工作难题。     

Optimal parametrization in numerical construction of curve

The application of the optimal parametric continuation method to constructing a solution set curve for a system of nonlinear algebraic or transcendental equations depending on a parameter is considered. There are discussed two approaches to solving this problem—the use of iterative methods and reduction to an initial value problem for a system of ordinary differential equations. The algorithm suggested in this paper can also be used for finding an appropriate initial approximation when solving a system of nonlinear algebraic or transcendental equations not depending on a parameter by an iterative method.     

Learners’ Difficulties with Quantitative Units in Algebraic Word Problems and the Teacher’s Interpretation of those Difficulties

This study examines 8th grade students’ coordination of quantitative units arising from word problems that can be solved via a set of equations that are reducible to a single equation with a single unknown. Along with Unit-Coordination, Quantitative Unit Conservation also emerges as a necessary construct in dealing with such problems. We base our analysis within a framework of quantitative reasoning (Thompson, 1988; 1989; 1993; 1995) and a theory of children’s units-coordination with different levels of units (Steffe 1994) that both encompass and are extended by these two constructs. Our data consist of videotaped classroom lessons, student interviews, and teacher interviews. Ongoing analyses of these data were conducted during the teaching sequence. A retrospective analysis using constant comparison methodology was then undertaken during which the classroom video, related student interviews, and teacher interviews were revisited many times in order to generate a thematic analysis. Our results indicate that the identification and coordination of the units involved in the problem situation are critical aspects of quantitative reasoning and need to be emphasized in the teaching-learning process. We also concluded that unit coordination and unit conservation are cognitive prerequisites for constructing a meaningful algebraic equation when reasoning quantitatively about a situation.     

论无理数——对本学报2007年第6期同名论文的修订和补充

将完全k方数的概念由N推广到R^＋,从而得到一个引理,由之推出一系列有关无理数的命题．此外,关于√2^√2,2^√2,α^β为≠0,1的代数数,而β乃不为有理数的代数数）,e＋π,e·π,e^π,π^e,2^e与2^π的无理性的简单证明也分别在此给出．