集合问题的解题策略

有些集合问题,直接考虑并不易解决,如果改变考虑问题的角度,就可以把问题合理转化,得到简单易行的解法.下面介绍几例.一、灵活应用补集思想解题有些集合问题,从正面处理较难,一是解题思路不明朗,二是需要考虑的因素太多,要分多种情况讨论,运算量大,且讨论不全又容易出错.如用补集思想考虑其对立面,可以达到化繁为简的目的.     

用“补集”的观点理解“命题的否定”

多年的教学中,我发现学生对"命题的否定"中一些常用词语的否定只是死记硬背、一知半解,致使在解决问题的过程中常常因为记忆的失误而把结论搞错.究其原因是学生对一些词语的否定理解起来有困难.如果我们在平     

善用几何性质解决二次曲线问题

笔者发现,很多学生解决二次曲线问题时,常忽视对图形几何性质的研究,从而陷入繁杂的代数运算当中,即只着重数,而忽视形,不能真正实现数与形的结合.从数学解题追求解法简捷和思维优化的角度看,对学生能力的发展是不利的.限于篇幅,仅举以下几例,希望一线师生能从中得到一些启示.     

“学生算错,‘我’的责任”——由“三位数乘两位数”计算错因分析引发的思考

运算能力是一个人最基本的数学能力之一。《数学课程标准》要求学生＂掌握必要的运算技能＂。随着课程改革的深入实施,学生的创造性思维、发散性思维得到了长足的发展,但不可否认的是学生的运算能力反而削弱了,为什么会这样？本文拟就＂三位数乘两位数＂计算错因分析,从教师的角度谈谈自己的思考。     

一“语”激起千层浪

在课堂中,往往因为教师独具匠心的设计或者不经意间的一句问话,收到意想不到的效果。案例一:引导知识再创造如教学加法运算律时,课前,我认为学生从一年级开始就接触加法计算,对加法积累了较多的感性认识,有了这样的     

FARMER: A novel approach to file access correlation mining and evaluation reference model

File semantic has proven effective in optimizing large scale distributed file system. As a consequence of the elaborate and rich I/O interfaces between upper layer applications and file systems, file system can provide useful and insightful information about semantic. Hence, file semantic mining has become an increasingly important practice in both engineering and research community. Unfortunately, it is a challenge to exploit file semantic knowledge because a variety of factors could affect this information exploration process. Even worse, the challenges are exacerbated due to the intricate interdependency between these factors, and make it difficult to fully exploit the potentially important correlation among various semantic knowledges. This article proposes a file access correlation miming and evaluation reference (FARMER) model, where file is treated as a multivariate vector space, and each item within the vector corresponds a separate factor of the given file. The selection of factor depends on the application, examples of factors are file path, creator and executing program. If one particular factor occurs in both files, its value is non-zero. It is clear that the extent of inter-file relationships can be measured based on the likeness of their factor values in the semantic vectors. Benefit from this model, FARMER represents files as structured vectors of identifiers, and basic vector operations can be leveraged to quantify file correlation between two file vectors. FARMER model leverages linear regression model to estimate the strength of the relationship between file correlation and a set of influencing factors so that the “bad knowledge” can be filtered out. To demonstrate the ability of new FARMER model, FARMER is incorporated into a real large-scale object-based storage system as a case study to dynamically infer file correlations. In addition FARMER-enabled optimize service for metadata prefetching algorithm and object data layout algorithm is implemented. Experimental results show that is FARMER-enabled prefetching algorithm is shown to reduce the metadata operations latency by approximately 30%–40% when compared to a state-of-the-art metadata prefetching algorithm and a commonly used replacement policy.     

小学阶段如何开展有效的计算教学

新课改以来,我们在看到了数学课堂内发生喜人变化的同时也看到了另外一种现象：由于课改后对计算教学的目标进行了适当调整,降低了计算教学的要求,因此,学生进行计算练习的量少了,学生的计算能力下降了,具体表现为计算的正确率下降、口算速度变慢、简便运算方法不够灵活等等。针对这种情况,我们应清醒地反思自己的教学,每个年段都必须重视计算教学,避免使计算教学偏离课标要求。     

几个常用的求极限的方法

几个常用的求极限的方珐高等数学是理工科类学生必修的一门学科,高等数学中最重要的内容是微积分学,而微积分中最重要的基本概念之一就是极限,微积分中的一些基本概念都要用极限概念来表达,并且微积分的运算和性质也都要用极限的运算性质来论述。因此,学好极限是学习高等数学的关键所在。     

关于实数集合的可列与不可列

本文先指出了两种证明实数集不可列的方式的不合理性,然后通过一种新的构造方式,证明了实数集可列。     

既快又准分解因式

把一个多项式化成几个整式的积的形式,这种变形叫做把这个多项式分解因式。分解因式在整式运算的基础上进行的,它是分式化简、解二次方程等的基础,是中考中的重点章节之一。下面就常见方法进行分析：