ISSN:0020-739X    

DOI:10.1080/0020739860170301

出版商:Taylor & Francis Group    

年代:1986

数据来源: Taylor

摘要:

Illuminating examples are proposed as a means of simplifying mathematical communication. Further formalization is then conceived as the next step in the process of exactification. The concepts of proof strategy and action proof are the decisive structural elements of illuminating examples.

ISSN:0020-739X    

DOI:10.1080/0020739860170302

出版商:Taylor & Francis Group    

年代:1986

数据来源: Taylor

摘要:

In this paper we establish inequalities between generalized means which include the well known result concerning the arithmetic, geometric and harmonic means. The results are derived using only sixth‐form mathematics such as implicit differentiation, analysis of stationary points for functions of one variable and evaluation of limits. As a by‐product of this work we establish the interesting inequality

ISSN:0020-739X    

DOI:10.1080/0020739860170303

出版商:Taylor & Francis Group    

年代:1986

数据来源: Taylor

摘要:

The selection of a statistical/mathematical software (SMS) system is complicated. The satisfaction derived from a system depends on many variables. This study analyses the influence of SMS predictor variables on satisfaction as determined by multiple regression. The null hypothesis, that multiple correlation coefficient is zero, is rejected. The alternative hypothesis is accepted. This study confirms the theories that suggest that SMS ease of operation, computer reliability, and ease of programming are the major determinants of computer user satisfaction. The factors identified were used in the design of an SMS Expert System based on Artificial Intelligence (ESAI).

ISSN:0020-739X    

DOI:10.1080/0020739860170304

出版商:Taylor & Francis Group    

年代:1986

数据来源: Taylor

摘要:

This paper modifies the usual meaning of regression from ‘minimizing the sum of squared distances’ to ‘minimizing the sum of square perpendicular distances’. With this modified definition, the best‐fit plane, circle, and sphere may be meaningfully considered.

ISSN:0020-739X    

DOI:10.1080/0020739860170305

出版商:Taylor & Francis Group    

年代:1986

数据来源: Taylor

摘要:

Variational principles, invented in analytical mechanics, has become a tool in various fields of physics, engineering and applied mathematics. Very often, in an introductory course of analytical mechanics, there is not time for the discussion of variational principles in other disciplines. Perfect fluids represent a simple system for which the usefulness of Hamilton's principle can be easily demonstrated. Moreover, the physical notion of Lagrange multipliers and the role of constraints can readily be discussed for such a system. From the educational point of view this example can also be used as an introduction to the discussion of variational principles in continuum mechanics.

ISSN:0020-739X    

DOI:10.1080/0020739860170306

出版商:Taylor & Francis Group    

年代:1986

数据来源: Taylor

摘要:

This paper presents some innovative teaching strategies and a careful organization of the subject‐matter of trigonometry so that (micro)computers may be utilized in trigonometry courses. A brief historical sketch of trigonometry is also given; this clarifies, justifies, and motivates our approach. A useful computer program for solving triangles on (micro)computers is given. This is an excellent instructional device but, more importantly, the teacher may use it as an aid (i.e., the teacher may analyse‐dissect it) while learning to write similar computer programs.

ISSN:0020-739X    

DOI:10.1080/0020739860170307

出版商:Taylor & Francis Group    

年代:1986

数据来源: Taylor

摘要:

This paper presents an account of an investigation into the teaching of mathematics to first‐year undergraduates reading for a degree in Economics at a polytechnic in the United Kingdom.

ISSN:0020-739X    

DOI:10.1080/0020739860170308

出版商:Taylor & Francis Group    

年代:1986

数据来源: Taylor

摘要:

The problem of deriving Euler angles from a proper rotation matrix illustrates how a reformulation of the matrix elements renders obvious the nature of the non‐uniqueness of the solution, and exposes the degenerate case that requires special treatment.

ISSN:0020-739X    

DOI:10.1080/0020739860170309

出版商:Taylor & Francis Group    

年代:1986

数据来源: Taylor

摘要:

To evolve an efficient system, educational activities need to be carefully coordinated, for which an abstract realization of the real system is essential. A transition model is one which describes the stocks and flows of students through an education system in terms of transition ratios. In this paper we describe one such model, which traces the flow of a cohort of students through the system. We note some consequences of the model and give some results of its application in Kenya.

ISSN:0020-739X    

DOI:10.1080/0020739860170310

出版商:Taylor & Francis Group    

年代:1986

数据来源: Taylor