摘要:

Several investigations on cubic polynomials are presented. The studies reported here deal with certain relationships which hold between the roots of the general cubic equation and other appropriate parameters derived from the same polynomial. Each section is organized in a monotonic sequence; that is, statement, demonstration and verification.

ISSN:0020-739X    

DOI:10.1080/0020739920230201

出版商:Taylor & Francis Group    

年代:1992

数据来源: Taylor

摘要:

This study presents a summary of perceptions expressed by students in response to university courses in calculus and differential equations that featured implementation of a discovery learning pilot programme. The programme used multi‐stage, multi‐task ‘projects’, with extended periods allocated for completion and requiring formal written reports of solutions. Project assignments included both independent and group work.

ISSN:0020-739X    

DOI:10.1080/0020739920230202

出版商:Taylor & Francis Group    

年代:1992

数据来源: Taylor

摘要:

The National Policy of Education (revised 1981) professes a functional literacy dimension to educational attainments in the Federal Republic of Nigeria. Consequently, obvious and unavoidable steps were adopted by government for the purposes of ensuring the realization of this functional literacy element in the system. One such step bordered on the revision/restructuring of school curricula at the appropriate levels.

ISSN:0020-739X    

DOI:10.1080/0020739920230203

出版商:Taylor & Francis Group    

年代:1992

数据来源: Taylor

摘要:

This article describes how a biological modelling technique, originally applied to random cell division in a plane, may be adapted as a mathematical model for the generation of a set of random polygons. The mean number of sides of a randomly chosen polygon from this set is then determined and found to be 4.

ISSN:0020-739X    

DOI:10.1080/0020739920230204

出版商:Taylor & Francis Group    

年代:1992

数据来源: Taylor

摘要:

For mathematics students in schools and universities in Papua New Guinea, English is usually a second (or third or fourth) language. Often, the difficulties that these students have with mathematical questions arise not because they have problems with the required mathematical operations but because they have problems with reading English. This seems to be the case even at tertiary level. Research on other second language learners seems to show that inadequate lexical knowledge is very often the origin of poor reading comprehension.

ISSN:0020-739X    

DOI:10.1080/0020739920230205

出版商:Taylor & Francis Group    

年代:1992

数据来源: Taylor

摘要:

In this paper it is suggested that an effective way to teach the introductory management science/operations research course is to tie together techniques in solving some fairly complex, realistic problems. A multistage process of analysis called the combined‐methodologies approach (CMA) is proposed. A queueing design problem is given as an example. Its solution requires the use of simulation, regression analysis, and goal programming. The particular techniques applied under CMA are specific to the situation under study. The authors believe the approach will increase student interest and address some criticisms of MS/OR instruction in universities.

ISSN:0020-739X    

DOI:10.1080/0020739920230206

出版商:Taylor & Francis Group    

年代:1992

数据来源: Taylor

摘要:

Newton's laws and coded sequences are used to explore sport mathematically. Track and field athletics, American, association, Gaelic and rugby football, golf, rowing, skating, snooker and hockey, among others, provide illustrations. Mathematical considerations include classical mechanics; linear and angular momentum, work, impulse, kinetic and gravitational energy, simple harmonic motion, friction, rolling, rotating frames, Euler angles and projectiles.

ISSN:0020-739X    

DOI:10.1080/0020739920230207

出版商:Taylor & Francis Group    

年代:1992

数据来源: Taylor

摘要:

Solutions of Fermat's last equation are expressed in terms of Wright's generalized hypergeometric function. Some of the properties of these solutions are discussed and an equivalent form of Fermat's conjecture is given in terms of them.

ISSN:0020-739X    

DOI:10.1080/0020739920230208

出版商:Taylor & Francis Group    

年代:1992

数据来源: Taylor

摘要:

In the course of a research project now in progress, two pairs of externally similar but essentially different problems were presented to 7th‐12th grade students. In each pair, one problem related to infinity and the second to the paniculate nature of matter. The first pair pertained to a process of successive division (of a line segment and a copper wire respectively). Students were asked to judge whether each process will come to an end. For the second pair students were asked to compare the number of points/atoms in two differently sized line segments/copper wires. Our data show most students unable to differentiate between the two theoretical frameworks (mathematics vs. science). A substantial number of students hold a generalized finite viewpoint and solve all problems from this perspective. With age and/or instruction students lose this finite perspective and respond to the problems according to their external features. Successive division in both mathematics and science triggered ‘infinite’ responses whereas both comparison problems yielded finite responses.

ISSN:0020-739X    

DOI:10.1080/0020739920230209

出版商:Taylor & Francis Group    

年代:1992

数据来源: Taylor

摘要:

This expository article presents a concise but up‐to‐date account of pre‐Robinson treatment of infinitesimals. It is reiterated that, though the application of infinitesimals appeared in earlier works, it was fully vindicated in the works of Newton, Leibniz, the Bernoulli brothers and Euler. It is noted that, despite Berkeley's scepticism and absence of precise logical foundation, the mathematics of infinitesimals did continue to flourish, both in applicative and foundational domains, until the final setting of the system of real numbers on axiomatic foundation in the nineteenth century when mathematicians could see ‘clearly’ that the existence of infinitesimals led to inconsistency. Subsequently a completely new foundation of calculus based on the concept of ‘limit’ and its ‘epsilon‐delta’ definition (in terms of ordinary real numbers) was led by Cauchy and Weierstrass. A host of problems which reflected the need for more ‘sensitive’ numbers than the Cauchy‐Weierstrass foundation purported is presented. Finally, it is noted that prior to Robinson's work in 1960, in which he reinvented the method of infinitesimals called ‘non‐standard’ analysis in order to exploit the powerful newly developed formal language theory, the concept of infinitesimals remained as borne out of necessity only.

ISSN:0020-739X    

DOI:10.1080/0020739920230210

出版商:Taylor & Francis Group    

年代:1992

数据来源: Taylor