摘要:

Our aim is to present a completed form of Young's inequality. We will give an elementary analytic proof of this inequality by the application of the mean value theorem for integrals known from a first course in real analysis. Moreover, to facilitate understanding, the heuristic strategy of analogy, which is a constructive source of discovery, will be used.

ISSN:0020-739X    

DOI:10.1080/0020739940250201

出版商:Taylor & Francis Group    

年代:1994

数据来源: Taylor

摘要:

The authors have been developing functional programming units within the computer science BSc degree course at Warwick. In recent years there has been a shift away from a principally theoretical approach to the subject; functional programming is now taught using a ‘hands on’ experiential approach. This paper outlines the reasons for this change of emphasis and discusses some of the pedagogical issues raised.

ISSN:0020-739X    

DOI:10.1080/0020739940250202

出版商:Taylor & Francis Group    

年代:1994

数据来源: Taylor

摘要:

Within the time‐lag between acquiring the admission requirements and the actual gaining of admission into the system, students engage in differing sets of jobs/activities. These, in turn, affect the students’ performance at the tertiary level. In this paper, the combined effect of these jobs/activities and length of time‐lag on performance are assessed. Results show that spending a long period on any of the activities/jobs tend to reduce performance.

ISSN:0020-739X    

DOI:10.1080/0020739940250203

出版商:Taylor & Francis Group    

年代:1994

数据来源: Taylor

摘要:

Paradoxes, in any subject, have the interesting feature of making the subject come alive. They not only make students of the subject examine their theoretical models closely, but also provide insight and directions for exploring the subject further while making them aware of the limitations of the models they use. In this paper we examine several paradoxes that arise in incompressible flow theory with the intent of showing that the frequently used commonsensical arguments, such as, small causes produce small effects, symmetric causes produce symmetric effects, three‐dimensional phenomena have two‐dimensional and one‐dimensional counterparts, steady‐state behaviour can be studied by examining steady‐state equations etc., can actually be very naive arguments in some cases.

ISSN:0020-739X    

DOI:10.1080/0020739940250204

出版商:Taylor & Francis Group    

年代:1994

数据来源: Taylor

摘要:

The triangular numbers are generalized in a natural way and a discovery‐type approach is used to find properties of these numbers. The numbers are connected to the Pascal numbers and generalized combinations that arise are connected to the Stirling numbers of the first kind.

ISSN:0020-739X    

DOI:10.1080/0020739940250205

出版商:Taylor & Francis Group    

年代:1994

数据来源: Taylor

摘要:

The Special Science Programme was introduced into the Alvan Ikoku College of Education, Owerri, Nigeria, on account of the finding that students desiring to pursue Mathematics as an area of speciality in addition to associated physical or social science disciplines, in the Nigerian Certificate of Education programme, lacked one of the requisite entry qualifications in most cases ‐‐ that is a credit level pass in Mathematics in the West African School Certificate (WASC) examinations. It thus acquired the status of a remedial programme. Having lasted some years, it is the desire of the authors to appraise to what extent the objective for establishing the programme can be said to have been achieved. We have endeavoured to establish whether or not performance of students in the Special Science Programme (SSP) in mathematics reflected their performances in the Nigerian Certificates of Education (NCE) programme. Results of the students in the two programmes were correlated, applying the appropriate statistical tools. The recommendations reflected the findings as evident from the results of our hypothesis.

ISSN:0020-739X    

DOI:10.1080/0020739940250206

出版商:Taylor & Francis Group    

年代:1994

数据来源: Taylor

摘要:

A further investigation of the so‐called sub‐exponential series which was considered recently by Chorlton and Clarke, and also Glaister, is presented. Relevant connections with substantially more general results, available already in the mathematical literature, are also pointed out.

ISSN:0020-739X    

DOI:10.1080/0020739940250207

出版商:Taylor & Francis Group    

年代:1994

数据来源: Taylor

摘要:

The structure of polarity is examined while providing a glimpse into some of the features of n‐dimensional geometry. The optimization problem associated with minimizing the volume of a dual body is described and acts as a unifying theme for this material. First, we give a gentle (and quick) introduction to aspects of duality, including the notion of polar bodies, and their application to affine invariant points. A discussion of the difficulties associated with volume calculations in high dimensions is also given. Following this, we construct the polar of a general convex polytope and derive expressions for the polar volume of the simplex and cube.

ISSN:0020-739X    

DOI:10.1080/0020739940250208

出版商:Taylor & Francis Group    

年代:1994

数据来源: Taylor

摘要:

This paper reports on an international comparison of seventh graders’ conceptions of mathematics teaching. A questionnaire survey was made of the conceptions of a total of 200 pupils in Hungary and Finland. The main results were, as follows: The Finnish pupils were more in favour of calculation‐centred working, where the teacher is always in control of the learning process than their Hungarian counterparts. The Hungarian, in contrast to the Finns, placed greater emphasis on exact teaching methods which strive for understanding according to pupils’ capabilities, they also stressed computational aspects of mathematics, such as rapid performance, correct answers, the memorization of rules and a belief in the existence of proper procedures.

ISSN:0020-739X    

DOI:10.1080/0020739940250209

出版商:Taylor & Francis Group    

年代:1994

数据来源: Taylor

摘要:

Spreadsheets are essentially mathematical creations, nevertheless their use in mathematical education is very limited. Almost certainly students of mathematics spend more time using programming languages than spreadsheets. It is argued that many mathematical procedures are more easily and more visually represented on a spreadsheet than in a programming language. Three mathematical investigations are proposed which illustrate the transparent nature of a spreadsheet.

ISSN:0020-739X    

DOI:10.1080/0020739940250210

出版商:Taylor & Francis Group    

年代:1994

数据来源: Taylor