摘要:

This paper uses a number of examples to show how probability problems can be solved with the aid of flow graphs. This method has been used with great success by R. A. Howard in his recent work on dynamic probabilistic systems. The approach in this article is somewhat different from Howard's, as the use of flow graphs here is combined with the collective marks method. The problems solved have to do with renewal processes in discrete and continuous time.

ISSN:0020-739X    

DOI:10.1080/0020739730040401

出版商:Taylor & Francis Group    

年代:1973

数据来源: Taylor

摘要:

In this paper we present and discuss two basic ideas which have arisen in the researches of the American writer‐philosopher L. R. Hubbard into the field of study. These ideas are stated as simple assertions, followed by brief discussions of their applications. The assertions are:

ISSN:0020-739X    

DOI:10.1080/0020739730040402

出版商:Taylor & Francis Group    

年代:1973

数据来源: Taylor

摘要:

This paper explores the growth of mathematical studies in recent times and suggests future patterns that may occur in mathematical curricula. It is proposed that courses in the History and Methods of Mathematics, Mathematical Engineering (rather than Engineering Mathematics) and Mathematics and Education should be used to widen the curriculum choices for the mathematical student of the future. Finally, in illustrating the application of mathematics to the study of Noise and Vibration it is shown that, in such an investigation, mathematics cannot be an end in itself but can be greatly helped by a knowledge of other physical disciplines.

ISSN:0020-739X    

DOI:10.1080/0020739730040403

出版商:Taylor & Francis Group    

年代:1973

数据来源: Taylor

摘要:

Certain classical experiments in genetics provide interesting ratios amongst the offspring population which relate to the pattern of the inheritance of the parents’ features. In this paper these ratios are analysed.

ISSN:0020-739X    

DOI:10.1080/0020739730040404

出版商:Taylor & Francis Group    

年代:1973

数据来源: Taylor

摘要:

This paper demonstrates one way to approach mathematical remediation with dignity for faculty and students alike. It illustrates specific ways in which student deficiencies can be improved while simultaneously developing creative, significant and stimulating approaches to teaching basic mathematical concepts. In order to aid students who have not mastered even the addition and multiplication of rational numbers, examples will be provided to show how these deficiencies can be improved within mathematical formats that lead naturally to the principles of algebra, progressions, powers and roots, symbolism, number theory, probability theory, linear programming, information theory, etc. An integral part of this approach to mathematical remediation involves the selection of appropriate research problems by the students.

ISSN:0020-739X    

DOI:10.1080/0020739730040405

出版商:Taylor & Francis Group    

年代:1973

数据来源: Taylor

摘要:

This paper supports the view that search for the applicative standpoint in mathematical education has yet to be sufficiently exploited. Mathematical propositions are considered to have both an ‘internal’ and ‘external’ role and thus a system of ‘potential models’ is evolved. Despite the stress on the applicative nature of the subject it is argued in conclusion that the position in the body of the paper is compatible with the synthetic apriority of mathematics.

ISSN:0020-739X    

DOI:10.1080/0020739730040406

出版商:Taylor & Francis Group    

年代:1973

数据来源: Taylor

摘要:

In this paper I discuss some of the historical and philosophical aspects of mathematical education, especially in foundational subjects where many of the principal issues seem to lie. Historical examples are chosen from the calculus, mathematical analysis, set theory and logic, but the philosophical points discussed also apply to other branches of mathematics.

ISSN:0020-739X    

DOI:10.1080/0020739730040407

出版商:Taylor & Francis Group    

年代:1973

数据来源: Taylor

摘要:

This paper presents a number of carefully selected examples, designed to indicate the proposed approach for the high school mathematics course, under the auspices of the Comprehensive School Mathematics Program (CSMP) in the U.S.A. The problems chosen deal with dynamic processes, and flowgraphs are used to reveal the logical structures of the situations examined. The flowgraphs lead naturally to solutions by means of computer programs.

ISSN:0020-739X    

DOI:10.1080/0020739730040408

出版商:Taylor & Francis Group    

年代:1973

数据来源: Taylor