Point-set topology is among the most abstract branches of mathematics in that it lacks tangible notions of distance, length, magnitude, order, and size. There is no shape, no geometry, no algebra, and no direction. Everything we are used to visualizing is gone. In the teaching and learning of mathematics, this can present a conundrum. Yet, this…

Symmetry is found in the visual arts, architecture and design of artefacts since the earliest time. Many natural objects, both organic and inorganic, display symmetry: from microscopic crystals and sub-atomic particles to macro-cosmic galaxies. Today it features strongly in higher mathematics such as Linear and Abstract Algebra, Projective and…

Infinity has contradictions arising from its nature. Since mind is actually adapted to finite realities attained by behaviors in space and time, when one starts to deal with real infinity, contradictions will arise. In particular, Cantorian Set Theory, for it involves the notion of "equivalence of a set to one of its proper subsets," causes…

Good quality scientific teaching depends on the ability of researchers to translate laboratory experiments into high school and undergraduate classes, bridging the advanced and basic science with common knowledge. A fast-growing field in biomedical sciences is oxidative stress, which has been associated to several diseases, including cancer and…

The process of protein biogenesis culminates in its correct targeting to specific subcellular locations where it serves a function. Contemporary molecular and cell biology investigations often involve the exogenous expression of epitope- or fluorescent protein-tagged recombinant molecules as well as subsequent analysis of protein-protein…

Describes two sets of activities designed to stimulate thinking skills and to bring some topological aspects into the mathematics curriculum. One set explores Mobius strips; the other set deals with tori. The activities are suitable for students in fourth through eighth grades. (JN)

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)

The problem of finding all topological spaces is considered. Two characterizations are presented whose proofs involve only elementary notions and techniques. The problem is appropriate for students in a beginning topology course after they have been presented with the Embedding Lemma. (DC)

Describes graph theory and topology and its use by a programmer analyst in his job. Contains reproducible student worksheets. (MKR)

Describes a journal-writing project involving the best route to travel from one place to another and presents some student responses. (MKR)

Described is a way to use knots to relate a three-dimensional object to a two-dimensional representation of the object. The results are used to produce an algorithm or rule to explain a general case. Included are examples, diagrams, procedures, and explanations. (KR)

This perfect bound teacher's guide presents techniques and activities to teach mathematics using origami paper folding. Part 1 includes a history of origami, mathematics and origami, and careers using mathematics. Parts 2 and 3 introduce paper-folding concepts and teaching techniques and include suggestions for low-budget paper resources. Part 4…

Magic motivates students to talk, and stimulates the affective domain. While watching magic, many people imagine how the effect is accomplished or how they might perform the trick if they were performing. This can be extended into an English lesson by using phrases such as, "If I were a magician, I could..." Total physical response…

Describes three components of a seminar in mathematical problem solving for preservice mathematics teachers: (1) a cognitive component that accents particular phases of problem solving; (2) an affective component that allows for observation of skillful problem solvers; and (3) an investigative component that provides for independent study and…