关键词： 数学分析   算法设计   教学   应用  

摘要： 为提高程序算法设计的质量,探索将数学分析引入算法设计教学中。研究表明,数学分析的应用越深入,则设计的程序算法质量越高;程序设计教学中应加强数学分析的应用。

关键词： 小学   数学   算法   多样化  

摘要： 算法多样化是数学新课程标准的重要理念之一，由于学生生活背景和思考角度不同，所使用的方法必然是多样的，教师应尊重学生的想法，鼓励学生独立思考，提倡计算方法的多样化。

关键词： PageRank   随机过程   静态分布  

摘要： 介绍了网页等级算法的基本思想和数学背景,根据随机过程静态分布存在性的条件得出了经典PageRank的计算方法,并对网页等级算法的利弊作了分析。同时针对经典PageRank中算法上的缺陷,提出了一种改进方法。

关键词： Economics   Evolutionary game theory   Genetic algorithm   Long-run behavior   Social modeling  

摘要： We present a mathematical analysis of the long-run behavior of genetic algorithms (GAs) that are used for modeling social phenomena. Our analysis relies on commonly used mathematical techniques in the field of evolutionary game theory. We make a number of assumptions in our analysis, the most important one being that the mutation rate is positive but infinitely small. Given our assumptions, we derive results that can be used to calculate the exact long-run behavior of a GA. Using these results, the need to rely on computer simulations can be avoided. We also show that if the mutation rate is infinitely small the crossover rate has no effect on the long-run behavior of a GA. To demonstrate the usefulness of our mathematical analysis, we replicate a well-known study by Axelrod in which a GA is used to model the evolution of strategies in iterated prisoner's dilemmas. The theoretically predicted long-run behavior of the GA turns out to be in perfect agreement with the long-run behavior observed in computer simulations. Also, in line with our theoretically informed expectations, computer simulations indicate that the crossover rate has virtually no long-run effect. Some general new insights into the behavior of GAs in the prisoner's dilemma context are provided as well. [ABSTRACT FROM AUTHOR]

关键词： MATHEMATICAL programming   ESTIMATION theory   ALGORITHMS   LEAST squares   NUMERICAL analysis  

摘要： Although the weighted least of squares technique is an efficient and well-established power system state-estimation procedure, a number of alternative estimation approaches have been proposed in the technical literature. This study presents and compares the most-common estimators formulating them as mathematical programming problems. The numerical accuracy and computational efficiency of the different estimators are analysed using an illustrative case study. [ABSTRACT FROM AUTHOR]

关键词： 课堂教学   程序设计   有效教学   绿色教学  

摘要： 绿色教学,是课堂教学追求高效益与高质量的统一,是追求让课堂唤醒学生的参与意识、学习兴趣、思维热情,真正还课堂以生命的激情与活力,实现课堂的有效教学。在必修三模块《算法初步》的课堂教学中遵循绿色教学的课堂教学特点,把课堂还给学生,把创造还给教师,把世界引进教室,让学生在课堂中多分析、多操作、多体验,在操作中学,在学中操作,真正实现有效教学,让学生学有所获。

关键词： Monte-Carlo方法   e值   Newton-Leibniz公式  

摘要： Monte-Carlo方法是一种以概率统计理论为指导的非常重要的数值计算方法,基于Monte-Carlo方法计算定积分的算法是较常见定积分近似计算方法。本文针对计算数学常数e(自然对数的底)值的问题,选择一个特殊定积分分别用Monte-Carlo方法和Newton-Leibniz公式进行计算,通过对这两个计算结果进行比较分析,从中得到数学常数e计算方法。实验结果表明,该算法具有实效性,且有较好的准确率和时间效率。