Knot theory has been inspirational to algebraic and geometric topology. The principal problem has been to ascertain whether two links are equivalent. New methods have been discovered which are effective and simple. Considered are background information; the oriented polynomial; the Jones polynomial; the semioriented polynomial; and calculations,…

Offering mathematics majors the opportunity to engage in current, real-world applications can be an important enhancement to their undergraduate course curriculum. Instead of focusing on the traditional topic areas in pure and/or applied mathematics, one may structure a seminar course for senior mathematics majors by concentrating on a specific…

This paper presents a method of encoding geometric line-drawings in a way which allows sets of such drawings to be interpreted as formal languages. A characterization of certain geometric predicates in terms of their properties as languages is obtained, and techniques usually associated with generative grammars and formal automata are then applied…

Fractal geometry is explored, with sections on snowflakes and flow snakes, Mandelbrot's definition of fractal, and other fractals. (MNS)

Definitions and examples are given for the concepts of neighborhood, exterior, interior, and boundary points, closed and open regions, and boundedness of point sets. (DT)

The TSS (Topological Screens System) for substructure search was applied to the CAS Registry file making it searchable on-line. The TSS screens and the use of the screen indexes are described. Statistics on screen assignment are provided, and the strengths and weaknesses of the system are discussed. (Author/NH)

Permanent models of soap bubble configuration can be made by using a new plastic art medium. (MM)

The basic ideas of the theory of manifolds is illustrated using elementary geometry. (MM)

Topics discussed include: reasons for strategies; the use of a hierarchy of spaces from topological to Euclidean in teaching; structural strategies; pedagogical strategies; and mathematical strategies. (MP)

Describes the effect, method, and mathematics of the following magic tricks which can be used in introducing mathematics lessons: the Ninth Card, Fibonacci Revealed, the Case of the Missing Area, I've Got Your Numbers, and the Card That Turns Inside Out. (MKR)

Quantitative algebraic and qualitative topological models can be used in the quest for simple explanations in the field of teaching and learning. The examples described cover such diverse topics as teacher anxiety and classroom control, process-product studies, aptitude-treatment interactions, the pace of instruction, the size of classes, and…

In a series of activities involving map coloring, students can discover various combinatorial theorems including Euler's formula. (SD)

Reported are studies which investigate children's understandings of concepts of symmetry and topology, area measure, limit and function, and logical inference. In each case, the mathematical concepts are analyzed in terms of their conceptual foundations. Tasks were created or adapted for testing the subconcepts at appropriate grade levels from K…