关键词： 小学数学   算法多样化   教学引导  

摘要： 算法多样化是数学教学的特点之一,“一题多解”是学生自我能力的体现,也是数学课堂对每个学生提出的一个更高的学习要求。在当前新课程标准全面推进的环境下,算法多样化也被逐渐重视起来。但是算法多样化不是一味地去追求题目的所有解法,而是在解法中寻求最合适的最优解。文章从算法多样化的实施意义、多样化引导以及在教学过程中生成多样化问题这三个方面来论述。

关键词： BOPPPS模型   高等数学   微课程   教学设计  

摘要： BOPPPS模式是加拿大教师技能培训中广泛采用的教学模型,以教学目标达成为核心,构建了引言、教学目标、摸底、参与式互动教学、检验评估和总结等确保课堂成功的六大要素。该教学模式实践性和可操作性强,为教师提供了一个指导课堂教学各个环节的理论体系,使得课堂教学的安排更加条理化、合理化。同时,全国高校数学微课程教学设计竞赛的成功开展加快了传统课堂教学改革的步伐。为了有效地将数学微课程竞赛先进理念及成果应用于课堂教学,不断深化教学改革、提高教学质量。文章以“第一型曲线积分的计算法”为例,探讨基于BOPPPS模型的高等数学微课程教学设计的方法。设计理念是:以学生为中心、以问题为导向的探究式教学;注重知识的认知过程,强调从已知到未知的自然过渡的互动式教学。

关键词： 笔算数学   邹立文   美国传教士   新式学堂   数学算法   陈省身   狄考文   侯仁之   比赛开始   广义相对论  

摘要： 命运的转折,常取决于外界一个微小的引诱或刺激。譬如说陈省身。小时候,父亲在杭州工作,他跟着祖母待在老家嘉兴。有一年,父亲返家过春节,给他带了一套礼物,是当时流行于新式学堂的《笔算数学》,分上、中、下三册,是美国传教士狄考文和中国学者邹立文合编的。回家当日,父亲觉得儿子还小,仅仅给他粗略讲了阿拉伯数字和数学算法。

关键词： 算法多样化   意义   思维   培养  

摘要： 在当今的小学数学教育中,算法多样化具有了更为广泛的内涵,为了更全面地认识算法多样化,了解其在小学数学教学中的重要意义,从而深入、有效地实施算法多样化。本文通过对新课程标准的研究,结合教育实践及多位教育专家在算法多样化方面的研究成果,阐述算法多样化在小学数学中的重要意义,探讨怎样从思维的角度出发,培养学生算法多样化的能力。

关键词： 数学表达式   犹豫模糊集   检索   相似度   相关排序  

摘要： 针对数学表达式符号种类繁多、结构复杂多变、语法语义丰富等特点,提出一种检索结果相关排序算法,利用犹豫模糊集在处理多特征、多隶属度模式方面的优势,计算数学表达式间的相似度,实现基于相似度的数学表达式检索结果的相关排序。通过归纳数学表达式的符号、结构、语法、语义方面的特征,建立数学表达式的相似度函数,对数学表达式检索系统中用户查询式与检索结果集中数学表达式之间的相似程度进行综合多视角的测量。实验结果表明,该算法能实现数学表达式检索系统结果数据的有序输出,有助于改善数学表达式检索系统的性能。

关键词： 经济标   数学模型   价格分   基准价  

摘要： 本文利用数学差值法模型设置招投标综合评分法的经济标运算方式,列举了经济标数学模型的主要格式,通过具体案例和不同算法计算采取不同数学格式后经济标得分的差异,从而得出经济标数学模型设计的不同影响中标趋势的结论。

关键词： 15A24   65F30   65H10  

摘要： The doubling algorithms are very efficient iterative methods for computing the unique minimal nonnegative solution to an M-matrix algebraic Riccati equation (MARE). They are globally and quadratically convergent, except for MARE in the critical case where convergence is linear with the linear rate 1 / 2. However, the initialization phase and the doubling iteration kernel of any doubling algorithm involve inverting nonsingular M-matrices. In particular, for MARE in the critical case, the M-matrices in the doubling iteration kernel, although nonsingular, move towards singular M-matrices at convergence. These inversions are causes of concerns on entrywise relative accuracy of the eventually computed minimal nonnegative solution. Fortunately, a nonsingular M-matrix can be inverted by the GTH-like algorithm of Alfa et al. (Math Comp 71:217-236, 2002) to almost full entrywise relative accuracy, provided a triplet representation of the matrix is known. Recently, Nguyen and Poloni (Numer Math 130(4):763-792, 2015) discovered a way to construct triplet representations in a cancellation-free manner for all involved M-matrices in the doubling iteration kernel, for a special class of MAREs arising from Markov-modulated fluid queues. In this paper, we extend Nguyen's and Poloni's work to all MAREs by also devising a way to construct the triplet representations cancellation-free. Our construction, however, is not a straightforward extension of theirs. It is made possible by an introduction of novel recursively computable auxiliary nonnegative vectors. As the second contribution, we propose an entrywise relative residual for an approximate solution. The residual has an appealing feature of being able to reveal the entrywise relative accuracies of all entries, large and small, of the approximation. This is in marked contrast to the usual legacy normalized residual which reflects relative accuracies of large entries well but not so much those of very tiny entries. Numerical examples

关键词： complex network   multilayer network   time-varying network   high order network   graph algorithms  

摘要： We present the algebraic representation and basic algorithms for MultiAspect Graphs (MAGs). A MAG is a structure capable of representing multilayer and time-varying networks, as well as higher-order networks, while also having the property of being isomorphic to a directed graph. In particular, we show that, as a consequence of the properties associated with the MAG structure, a MAG can be represented in matrix form. Moreover, we also show that any possible MAG function (algorithm) can be obtained from this matrix-based representation. This is an important theoretical result since it paves the way for adapting well-known graph algorithms for application in MAGs. We present a set of basic MAG algorithms, constructed from well-known graph algorithms, such as degree computing, Breadth First Search (BFS), and Depth First Search (DFS). These algorithms adapted to the MAG context can be used as primitives for building other more sophisticated MAG algorithms. Therefore, such examples can be seen as guidelines on how to properly derive MAG algorithms from basic algorithms on directed graphs. We also make available Python implementations of all the algorithms presented in this paper.