面积与等积变换

面积与等积变换是初中数学竞赛的基本内容,等积变换是解决面积问题的基本方法,这里我们将着重讨论面积与等积变换的有关问题。在初中,计算几何图形面积的基本公式有:     

旋转体的体积与侧面积计算教学中的一个问题

旋转体的体积与侧面积计算教学中的一个问题王燕生田载今（首都师范大学１０００３７）（人民教育出版社１００００９）旋转体的体积和侧面积计算，是定积分的重要应用之一，在高等数学的课程中，这是必学内容；新颁《全日制普通高级中学数学教学大纲（供试验用）》，也在...     

面积问题与面积方法

面积问题与面积方法黄启林（华南师大附中５１０６３０）在各级各类国内外数学竟赛试题中，有不少关于面积的问题，面积问题是几何中的一个重要问题．面积方法─—利用面积知识来求解或证明命题的方法，是几何证明的重要方法，几乎所有的平面几何定理都可以用面积方法来加...     

运用推理的几何计算问题教学的改进

1.问题的提出 　　运用推理的几何计算问题是上教版九年义务教育八年级第二学期第二十五章第三节的内容.运用推理的几何计算问题是教学的难点,特别是运用推理计算几何图形面积的若干方法,其中包含着分解与组合的数学思想,而且面积的可分性、可比性也是较难理解的环节,逻辑推理的能力要求较高.……     

一类旋转体积计算法

对极坐标表示的面积绕轴旋转的体积计算问题分别从积分元素法,P.Guldin定理及球坐标下三重积分计算,给出三种计算方法,本不仅导出了一类旋转体积的简单计算公式,而且其中的解题思想方法有助于学生提高解题能力和数学素养。     

一类旋转体体积计算法

对极坐标表示的面积绕轴旋转的体积计算问题分别从积分元素法、P.Guldin定理及球坐标下三重积分计算 ,给出三种计算方法 .本文不仅导出了一类旋转体体积的简单计算公式 ,而且其中的解题思想方法有助于学生提高解题能力和数学素养 .     

平面直角坐标系中三角形面积计算的“万能公式”

平面直角坐标系中三角形的面积计算问题一直以来是中考的常考题型,近几年的中考中又演变出了在函数背景下的三角形面积的最大值问题等,这类是初高中数学结合的问     

《应用数学与计算数学学报》征稿简则

《应用数学与计算数学学报》（Communicahon on Applied Mathematics and Computation）是由上海市教育委员会主管、上海大学主办的专业性学术期刊，创刊于1987年。刊物的办刊宗旨是反映应用数学与计算数学领域中的原创性研究成果，刊登有关应用数学与计算数学学术论文，及其在自然科学、工程技术、经济和社会等各领域的应用研究成果。     

浅议21世纪工科大学生的数学知识结构与数学素质培养

随着科学技术的不断发展，特别是现代计算机技术的飞速发展，数学在科学技术中的地位不断提高，国内外许多专家把数学科学、自然科学和社会科学并列为基础科学的三大领域。当今，在科学技术研究中，理论分析、实验分析和计算分析已成为三种最主要的研究方法，而其中理论分析和计算分析研究能力的培养，同工科数学的教学内容直接相关联，这就对工科人才的数学素质提出了更高的要求。     

高考命题交汇点的新宠——三视图与直观图

三视图是新课程中新增加的内容，对于这一部分内容，经常与立体几何中有关的计算问题交汇在一起进行考查，如面积、体积、角的计算等，考查学生的运算能力、空间想象能力和推理论证能力，是命制试题的良好素材．2008年山东、广东、海南、宁夏四地的高考数学《考试说明》与往年相比，出现了一些新变化，其中“三视图与直观图”是高考新增加的内容之一，     

The use of ROC for defining the validity of the prognostic index in censored data

The validity of a diagnostic marker can be summarised by using statistical measures either for the goodness of the fit like the deviance, measures of the explained variation like R² or the misclassification rate. Other intuitive measures are sensitivity and specificity in the case of binary response. In the absence of censored data the calculation of these measures is widely used. In the presence of censoring the estimation of time-dependent sensitivity and specificity is not well known. In this article we propose a new method for calculating ROC curves with censored data using the observed number of events and calculating the additional number of expected events for censored observations. The new method is illustrated with data for predicting mortality in patients surviving a myocardial infarction.     

Parametric differentiation and integration

Parametric differentiation and integration under the integral sign constitutes a powerful technique for calculating integrals. However, this topic is generally not included in the undergraduate mathematics curriculum. In this note, we give a comprehensive review of this approach, and show how it can be systematically used to evaluate most of the famous improper integrals in analysis. Students in mathematics and science would benefit from an exposure to this wonderful method.     

Mathematics university teachers' perception of pedagogical content knowledge (PCK)

Teaching mathematics in university levels is one of the most important fields of research in the area of mathematics education. Nevertheless, there is little information about teaching knowledge of mathematics university teachers. Pedagogical content knowledge (PCK) provides a suitable framework to study knowledge of teachers. The purpose of this paper is to make explicit the perception of mathematics university teachers about PCK. For this purpose, a phenomenological study was done. Data resources included semi-structured interviews with 10 mathematics university teachers who were in different places of the mathematics university teaching experience spectrum. Data analysis indicated a model consisting of four cognitive themes which are mathematics syntactic knowledge, knowledge about mathematics curriculum planning, knowledge about students' mathematics learning and knowledge about creating an influential mathematics teaching–learning environment. Besides, it was found out that three contextual themes influenced on PCK for teaching mathematics in university levels which were the nature of mathematics subjects, university teachers' features and terms of learning environment.     

高等数学CAI中的质疑与自测方法

本文针对高等数学的特点，介绍了一种计算机辅助教学（ＣＡＩ）的质疑与自测方法，并就智能化评改的实现作了一些探讨。     

An analysis of history of mathematics research literature in Turkey: the mathematics education perspective1

Research in history of mathematics gained momentum in the past two decades in Turkey. The present paper aims to describe the patterns in the history of mathematics research in Turkey and to analyse the research in Turkey using a mathematics education framework. The qualitative paradigm and a case study design are used in the study. The obtained data were analysed by using the document analysis technique with the help of a content analysis. The study group which is comprised of twenty-two postgraduate theses at master's or doctoral level were purposefully selected from the higher education council postgraduate theses database. Findings indicate a dearth of research in the area and that most of the theses are done in the area of mathematics education. Moreover, the focus, in general, was on attitudinal variables, and cognitive aspects seemed to be ignored.     

Variations on seven points: An introduction to the scope and methods of coding theory and finite geometries

We use a simple example (the projective plane on seven points) to give an introductory survey on the problems and methods in finite geometries — an area of mathematics related to geometry, combinatorial theory, algebra, group theory and number theory as well as to applied mathematics (e.g., coding theory, information theory, statistical design of experiments, tomography, cryptography, etc.). As this list already indicates, finite geometries is — both from the point of view of pure mathematics and from that of applications related to computer science and communication engineering — one of the most interesting and active fields of mathematics. It is the aim of this paper to introduce the nonspecialist to some of these aspects.To Professor Günter Pickert on the occasion of his 65th birthday     

A class of autoregressive models for predicting the final claims amount

We treat one of the main problems of insurance mathematics, i.e. the problem of calculating loss-reserves, and investigate a general class of autoregressive models for predicting the final claims amounts of a collection of risks.     

例谈数形结合在高数解题中的应用

通过微分中值的等式证明、求渐近线方程、定积分中的换元法、几何图形的描绘以及曲线积分的计算等例题,说明将代数运算或证明与几何直观相结合给解高等数学问题带来的好处．     

Principal Components Along Quiver Representations

Quiver representations arise naturally in many areas across mathematics. Here we describe an algorithm for calculating the vector space of sections, or compatible assignments of vectors to vertices, of any finite-dimensional representation of a finite quiver. Consequently, we are able to define and compute principal components with respect to quiver representations. These principal components are solutions to constrained optimisation problems defined over the space of sections and are eigenvectors of an associated matrix pencil.