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In addition to my textbooks, the most recent of which is Mathematics for the Management,
Life and Social Sciences, with John Costello and Spenser Gowdy
(McGraw Hill, Inc., 1997), I am involved in research in improving
instruction in the undergraduate mathematics curriculum. My most
recent articles appear in Primus and in monographs
published by the Mathematics Association of America, MAA Notes;
for example, the MAA Notes: Assessment in Mathematics.
A general repository Math Archives
contains several of my works
appearing in national and international proceedings of conferences.
My latest book, Interactive Calculus with Applications (2005, Brooks/Cole)), was completed with Dr. Jean Marie McDill, California
Polytechnic State University, Department of Mathematics. Hubert
Hohn, Massachusetts College of Art, produced the software for the project
in conjunction with Jean Marie McDill, John Cantwell, Richard Wilmore and me. This research was supported, in part, by
the National Science Foundation. You may view sample screen shots of the tools by connecting to
Jean Marie McDill's web page. A partial listing of the contents appears below.
My current project is to develop new interactive probabilistic models. I plan to develop interactive computer tools
and a monograph on models of probabilistic phenomena using theoretical probability. During the summer,
I began to develop the design for the tools, layout story boards, and introductory sample models. Probability is a powerful
theory whose applications are ever expanding. The concepts of probabilistic models and statistical inference are central
ideas and essential tools in science, social science, business and economics. The main goals of the reform movement
in mathematics include making theoretical mathematics more conceptual, to involve the reader more fully in problem solving,
conjecturing and analyzing, and to take advantage of modern technology in both content and pedagogy. Some basic probabilistic models,
such Poisson processes and bivariate normal distributions, become more readily accessible if one has a visual image of the concept. Concepts, not techniques, are
central to any mathematical process. Computer algebra systems (CAS) now replace hand calculations.
Computer graphics facilitate illustrating the central features of a model, and can foster visualization, understanding, and experimentation.
Combining symbolic manipulation, concept development, and a graphical viewpoint can be very time-consuming without the use of technology.
| List of Available Kits |
| Function Kit |
Asymptotes, Families, The Modeler, Compound Interest |
| Derivative Kit |
Tangent Line Slopes, Tangent Line Zoom, Definition of the Derivative, Inverse Functions, Concavity |
| Economic Kit |
Cost Curves, Cost, Revenue and Profit, Price Elasticity of Demand, Inventory Costs, Supply and Demand Dynamics |
| Geometric Optimization Kit |
Optimal Volume from a Square, Optimal Volume with Postal Constraints |
| Integration Kit |
Accumulation, Numerical Integration and Riemann Sums, Definite Integral, Lorentz and GINI Indices, Surplus |
| Diferential Equations Kit |
Exponential Growth, Growth of an Annuity, Limited Growth, Logistic Growth, Gompertz Growth, Allee Effect, Exponential Growth (Moore's Law) , Limited Growth (Movie Revenue), Logistic Growth (World Population) |
| Functions of Two Variables Kit |
Partial Derivatives, Level Curves (Cobb Douglas), Level Curves (Parabolic Hill), Level Curves (Parabolic Dale) |
| Series Kit |
Maclaurin Surge Function, nth Taylor Polynomial |
| Linear Regression Kit |
Motor Vehicle Productivity (Linear), National Health Expenditures %GNP (Linear), Direct Mail Expenditures (Linear), National Health Expenditures (Exponential) |
| Partial Derivative Kit |
Partial Derivatives, Level Curves, Constraints (Linear and nonlinear), |
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