A general method is given for determining an efficient problem-solving process for a given type problem. An application of the method is then described in an experiment involving teaching indefinite integration. (MP)

Four of the author's favorite calculus word problems are presented. These aid students in recognizing and applying concepts in contexts unlike those in typical textbook problems. (MNS)

The symposium is seen to create an opportunity for students to understand the way mathematics is actually used in their own fields and to understand both their own potential as mathematics users and inherent difficulties in modeling. The symposium acts as a capstone for a two-semester, introductory calculus course. (MP)

Discussed is the tendency of students to equate the concepts of continuity and connected graphs based on their lack of an understanding of such concepts as limit points, closed sets, and connected sets. Included is a theorem with three lemmas with their proofs. (KR)

Discussed is the problem of inscribing a rectangle of maximum area in a given right triangle. Answered is whether there is an advantageous orientation and whether a corner of the rectangle of maximum area can lie on the midpoint of a leg of the triangle. (KR)

Presented is a example that shows why a certain technical lemma is necessary for a valid proof of Galois Theory. The usual proof of Galois' Theory is included as well as one using the lemma. (KR)

Presented is an alternate way to derive R from Taylor's Theorem without involving the (n + 1)st derivative of f. Included is the procedure for estimating the bounds of R. (KR)

Developed is a condition, expressed in terms of an index, that ensures that a quasinormal subgroup is normal. The arguments suggest a variety of exercises for a course in group theory or Galois theory. Included are the definitions, lemmas, and proofs. (KR)

Presented are activities that help students understand the idea of a vector field. Included are definitions, flow lines, tangential and normal components along curves, flux and work, field conservation, and differential equations. (KR)

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)