A traveling salesman problem is used to illustrate the key idea in a general proof of a reduction technique. It is reduced to a problem in propositional calculus. (MNS)

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 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)

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)

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)

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)

Presented are two exercises on the differential geometry of curves. A generalization dealing with smoothness conditions is given that relates the two exercises. Included are the definitions, theorems, propositions, and proofs. (KR)

Presented is a Poisson derivation using explicitly stated assumptions and exact functional equations. The assumptions are homogeneity, independence, and negligibility. Included are the derivations and proofs using L'Hopital's rule for each assumption. (KR)

Presented is an example of a question that can be used to investigate probability and random triangles. Included is the question, analysis, and procedure for solving the question. (KR)

Described is a decomposition theory from which the Cayley-Hamilton theorem, the diagonalizability of complex square matrices, and functional calculus can be developed. The theory and its applications are based on elementary polynomial algebra. (KR)