摘要:

The paper compares the syllabus content of written examination papers in mathematics at, or near, the level of the British General Certificate of Education Advanced Level, taken in 20 countries. All the papers are compared on the basis of a broad system of classification. A subset of 12 papers is then subjected to a detailed comparison, using a more refined classification. The technique of cluster analysis is used to identify groups of papers that exhibit certain similarities.

ISSN:0020-739X    

DOI:10.1080/0020739910220101

出版商:Taylor & Francis Group    

年代:1991

数据来源: Taylor

摘要:

Despite the close association between q‐differences and derivatives, ‘basic’ functions are ignored by numerical analysts and engineers. By examining a particular q‐difference equation we reveal a little of the interesting relations and important results that are being discarded. The two solutions developed for the equation differ by a periodic function, a result which seems not to have been previously recognized. The introduction of this periodic function permits a much fuller development of the theory.

ISSN:0020-739X    

DOI:10.1080/0020739910220102

出版商:Taylor & Francis Group    

年代:1991

数据来源: Taylor

摘要:

This paper discusses the problem of mathematics deficiency in students entering the technologies, some schemes to overcome this deficiency and the move into computer‐enhanced learning in this area, especially computer‐managed learning (CML), with the possible extension into a computerized unified national system of bridging mathematics in Australia.

ISSN:0020-739X    

DOI:10.1080/0020739910220103

出版商:Taylor & Francis Group    

年代:1991

数据来源: Taylor

摘要:

This paper is concerned with finding and enumerating symbols to represent all circulant tournaments with n vertices up to isomorphism. A formula giving the exact number of such symbols is known for n prime and the derivation of this formula is reviewed. That result is then developed to produce a formula for the case where n is the product of two distinct primes and for giving an upper bound when n is the product of two identical primes. Some general techniques for testing isomorphism are also described. The paper describes a simple application of Burnside's lemma suitable for inclusion in an undergraduate course.

ISSN:0020-739X    

DOI:10.1080/0020739910220104

出版商:Taylor & Francis Group    

年代:1991

数据来源: Taylor

摘要:

This paper details the immediate results that a corporate gift of $600 000 had on a university summer programme designed for high‐ability pre‐college students.

ISSN:0020-739X    

DOI:10.1080/0020739910220105

出版商:Taylor & Francis Group    

年代:1991

数据来源: Taylor

ISSN:0020-739X    

DOI:10.1080/0020739910220106

出版商:Taylor & Francis Group    

年代:1991

数据来源: Taylor

摘要:

For several years now the Northern Ireland Further Mathematics Project has run two‐day workshops for sixth‐formers to promote mathematical investigations or mathematical modelling. This paper outlines a mathematical modelling problem investigated by three members of the teachers’ group while the sixth‐formers were working on their own problems. It addresses a topical question ‐‐ the minimizing of water pollution in an industrial complex.

ISSN:0020-739X    

DOI:10.1080/0020739910220107

出版商:Taylor & Francis Group    

年代:1991

数据来源: Taylor

摘要:

In the solution of the classical Gambler's Ruin problem against an infinitely rich adversary, the determination of the roots of the polynomial associated with the difference equation and their corresponding coefficients in the solution are, in general, difficult to describe. A special case of this ruin problem is studied in which the roots and coefficients can be specifically and compactly written.

ISSN:0020-739X    

DOI:10.1080/0020739910220108

出版商:Taylor & Francis Group    

年代:1991

数据来源: Taylor

摘要:

A comparison is made between van Hiele levels of development in geometry and the structure of learning outcomes (SOLO) taxonomy. It is hypothesized that if the correspondence between van Hiele levels and SOLO levels is tenable, then the latter may be used as an operational scheme for characterizing a posteriori the learning outcomes in geometrical tasks without going through the process of identifying van Hiele level indicators by empirically deriving them for a multitude of geometrical tasks. This is particularly relevant since the construct validity of the SOLO taxonomy has been established. A logical comparison and an illustrative example reveal a high degree of similarity between the two sets of levels.

ISSN:0020-739X    

DOI:10.1080/0020739910220109

出版商:Taylor & Francis Group    

年代:1991

数据来源: Taylor

摘要:

The well‐known Frobenius method is a very useful tool for finding two independent solutions of a linear, second‐order differential equation about a regular singular point. However, in its usual form the method is not suitable for computer use. The present paper presents an adaption of the method that can be used on a computer.

ISSN:0020-739X    

DOI:10.1080/0020739910220110

出版商:Taylor & Francis Group    

年代:1991

数据来源: Taylor