This article explores an application of combinations, geometric series, and elementary probability that arises in a Biblical setting. Describes examples of the applications such as the use of "urim and thummin." (YP)

Presents an example from the combinatorial theory of partially ordered sets. Discusses algorithms of on-line antichain partitioning problems, a topic in discrete optimization. (YP)

Presents an approach to Vieta's formula involving pi and infinite product expansions of the sine and cosine functions. Indicates how the formula could be used in computing approximations of pi. (MVL)

Presents frequently occurring patterns of repeating decimals. Provides a method for completing a repeating decimal with a long period from only a portion of the string. Gives several theorems with proofs. (MVL)

Illustrates how heuristics can provide a psychological narrative of Hippocrates' and Archytas' thinking on the duplication of the cube. Four general heuristic techniques were used. (YP)

Describes properties of Fibonacci numbers, including the law of recurrence and relationship with the Golden Ratio. Discussed are some applications of the numbers to sewage of towns on a river bank, resistances in electric circuits, and leafy stems in botany. Lists four references. (YP)

This paper reports on the views of school and college students in the 14-18 age range on mathematics and its applications. The findings relate to the perceived relevance of mathematics and to choices for sixth form study.

In the department of mathematics of the Lulea University of Technology in Sweden, a dynamic model for the education of doctoral students and guidance of supervisors in research groups has been developed and applied for several years now. Presently groups in mathematics as well as a group in mathematics education are working according to this model…

In this article and part 2, the author focuses on how an individual appropriates notions from the socially-sanctioned body of knowledge called mathematics. Specifically, the author is concerned with how students, to a greater or lesser extent, internalise mathematical ideas that exist in the social world (on the chalkboard, in textbooks, in the…

Item analysis of a mathematics preknowledge test given to physics students revealed that significant differences existed on certain items between groups of students who had followed different mathematics syllabuses. (MLH)

Inversions are transformations of geometric figures, under which straight lines may be mapped to circles, and conversely. The use of such mapping allows development of a unified method of solution for many of the problems of elementary geometry, especially those concerning constructions and "pencils" of curves. This book discusses the inversion…

THIS STUDY RELATED TO DISCOVERY METHODS OF TEACHING AND LEARNING WAS CONCERNED WITH TWO MAJOR QUESTIONS. FIRST, CAN "WHAT IS LEARNED" THROUGH MATHEMATICAL DISCOVERY BE IDENTIFIED AND TAUGHT BY EXPOSITION WITH EQUIVALENT RESULTS. SECOND, HOW DOES "WHAT IS LEARNED" DEPEND ON PRIOR LEARNING AND ON THE NATURE OF THE DISCOVERY…

Part I of this guide develops sets and set operations: listing and describing sets, characteristics of sets, universal empty sets, unions and intersections of sets, properties under set operations, differences and complements of sets, Venn diagram interpretations, set notation, ordered pairs, Cartesian products, and equivalent sets. Part II deals…

Presented are a suggested program and the course outlines for the pregraduate preparation of research mathematicians. The program set forth is designed for the first four years of a sequence of formal course study leading to the Ph.D. in a total of seven years. The proposed program of pre-graduate mathematical studies falls into two parts:…