Described is automata theory which is a branch of theoretical computer science. A decomposition theorem is presented that is easier than the Krohn-Rhodes theorem. Included are the definitions, the theorem, and a proof. (KR)

Discussed is the use of magic squares as examples in a first year course in linear algebra. Four examples are presented with each including the proposition, the procedure, and a proof. (KR)

Presented is a method of interchanging the x-axis and y-axis for viewing the graph of the inverse function. Discussed are the inverse function and the usual proofs that are used for the function. (KR)

Discussed are the vital properties that an operator must have to be called a derivative and how derivatives work. Presented is an extension of the derivative that uses least squares to find the line of best fit. (KR)

Described is a way to illustrate cyclic and dihedral groups through symmetry using corporate logos and hubcaps. Examples of the different kinds of symmetry groups are explained in terms of Leonardo's Theorem. (KR)

Presented is a way of extending the list of rotation groups to include all finite subgroups of symmetries of the sphere, up to conjugation in its full group. Included is Klein's method for enumeration of the finite subgroups. (KR)

Presented is L'Hopital's rule for the evaluation of limits in the case when x goes to infinity using geometric concepts. Included are the rule, extensions, counterexamples, and a rule for sequences. (KR)

Discussed are the idea, examples, problems, and applications of convexity. Topics include historical examples, definitions, the John-Loewner ellipsoid, convex functions, polytopes, the algebraic operation of duality and addition, and topology of convex bodies. (KR)

This learning activity provides an overview of the problem of clean energy sources and examination of alternatives. Student activity, quiz with answers, related activities, and nine references are provided. (SK)

Interest in mathematics can often be generated by seemingly nonmathematical items. A card trick from a course in recreational mathematics for middle school students is described. It involves several important mathematical activities: problem-solving analysis, making a conjecture and testing it, discovering, and verbalizing. (MNS)

Discussed is an application of number theory to cryptology that can be used with secondary school students. Background on the topics is given first, followed by an explanation for use of the topic. (MNS)

The focus is on using mathematical concepts and operations to decode holiday messages. Worksheets are provided for levels one-two, three-four, five-six, and seven-eight. (MNS)

Presents an integrated math/science activity in which families work together at an activity station and design and make a track for a marble to travel down using rules attached to a board. (MKR)

Provides three activities that help develop library skills for elementary school students. One describes a riddle card game that reviews research book terms; one explains a book report activity; and one focuses on cooperative problem-solving activities to find titles by favorite authors. (LRW)

This article is a reproducible page for students in grades four through six. The stated objective is the student will organize information about unfamiliar animals and infer other information. Students read clues about five newly discovered species and use a chart to organize this information in a more meaningful way. (PR)