摘要:

In this paper a report is given on a study comparing the traditional method of instruction with an individualized type of instruction for a beginning mathematics course. A description is given of the individualized method, and how it addresses some of the problems associated with the entry level course is indicated. An analysis of the data seems to indicate a significant difference in the two methods for students with a weak background, which is favourable to the individualized method.

ISSN:0020-739X    

DOI:10.1080/0020739830140101

出版商:Taylor & Francis Group    

年代:1983

数据来源: Taylor

摘要:

The paper deals with the necessary and sufficient conditions of optimality for a convex programming problem which is the deterministic equivalent of the stochastic transportation problem. The optimality conditions are derived without using the Lagrange multipliers method.

ISSN:0020-739X    

DOI:10.1080/0020739830140102

出版商:Taylor & Francis Group    

年代:1983

数据来源: Taylor

摘要:

The computation of a minimal Steiner tree for a general weighted graph is known to be NP‐hard. Except for very simple cases, it is thus computationally impracticable to use an algorithm which produces an exact solution. This paper describes a heuristic algorithm which runs in polynomial time and produces a near minimal solution. Experimental results show that the algorithm performs satisfactorily in the rectilinear case. The paper provides an interesting case study of NP‐hard problems and of the important technique of heuristic evaluation.

ISSN:0020-739X    

DOI:10.1080/0020739830140103

出版商:Taylor & Francis Group    

年代:1983

数据来源: Taylor

摘要:

The computer language APL is explored as a pedagogical approach for teaching econometrics. Typical econometric techniques are presented in standard notation, and equivalent APL expressions are developed. A computer implementation of these expressions is discussed and demonstrated with examples. This approach reduces the difficulties of transferring and translating theoretical ideas into practical forms useful for applied work. The major innovation of this approach is that in a classroom setting theoretical ideas and their computer implementation can be discussed using a uniform set of notation.

ISSN:0020-739X    

DOI:10.1080/0020739830140104

出版商:Taylor & Francis Group    

年代:1983

数据来源: Taylor

摘要:

Mathematics teaching is a complex task involving interactions between people. Good teaching requires an awareness of the human aspects of the problem. In particular it is necessary to regard mathematics as an activity of human minds rather than a set of immutable truths.

ISSN:0020-739X    

DOI:10.1080/0020739830140105

出版商:Taylor & Francis Group    

年代:1983

数据来源: Taylor

摘要:

This article considers and evaluates the use of filling forms in mathematics education. The aim is the testing of the problem‐solving ability of the student. Related to other testing schemes, the filling form appears to be useful in the early phase of learning, when the subject must learn a given method and perhaps, organized work. For final tests, however, the filling forms are not proposed. An example illustrates the method.

ISSN:0020-739X    

DOI:10.1080/0020739830140106

出版商:Taylor & Francis Group    

年代:1983

数据来源: Taylor

摘要:

The interest in applying Walsh functions in electrical and electronic engineering has resulted in a proliferation of notations and definitions. This paper is an attempt to summarize some of the features and applications of these functions as an aid to staff and students.

ISSN:0020-739X    

DOI:10.1080/0020739830140107

出版商:Taylor & Francis Group    

年代:1983

数据来源: Taylor

摘要:

It is shown that the Second Mean Value Theorem for Integrals can be used to construct an infinite family of means, some of which were until now unknown and some of which were until now obtained only as limits of other means.

ISSN:0020-739X    

DOI:10.1080/0020739830140108

出版商:Taylor & Francis Group    

年代:1983

数据来源: Taylor

摘要:

In this article, which is in criticism of a previous paper by Eric Blaire in this journal, I suggest that one's perspective of mathematics teaching is a logical consequence of one's epistemological commitment in relation to mathematical knowledge, and not merely one of expediency in response to societal pressures, or of pedagogical convenience. I suggest that from a consideration of the schools of thought in philosophy of mathematics, two distinct movements emerge. These are the Euclidean programme, an attempt to base mathematics on firm foundations, and the quasi‐empirical programme, the recognition that mathematics progresses heuristically, and through the re‐transmission of falsity. As a consequence, two teaching perspectives can be identified, knowledge‐centred and problem‐solving respectively. In describing these styles, I criticize the former and propose that the latter can initiate substantial changes and advances for school mathematics programmes.

ISSN:0020-739X    

DOI:10.1080/0020739830140109

出版商:Taylor & Francis Group    

年代:1983

数据来源: Taylor

摘要:

The main theorem on permutations is proved by decomposing the permutation into disjoint cycles. This enables the theorm to be introduced before homomorphisms, and thus used to motivate them.

ISSN:0020-739X    

DOI:10.1080/0020739830140110

出版商:Taylor & Francis Group    

年代:1983

数据来源: Taylor