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Publications

Statistics Toolbox User’s Guide

Documentation for MathWorks, Inc. Statistics Toolbox software, 2006-2008.

o MATLAB Fundamentals & Programming Techniques

o Advanced MATLAB Programming Techniques

o MATLAB for Building Graphical User Interfaces

o MATLAB for Financial Applications

o MATLAB for Signal Processing

o MATLAB for Image Processing

o MATLAB-Based Optimization Techniques

o Statistical Methods in MATLAB

Texts and lab manuals developed for MathWorks, Inc. Training Services, 2001-2006.

Book Review: *Fragments of Infinity: A Kaleidoscope of Math and Art* by Ivars Peterson

The American Mathematical Monthly, 110, pp. 248-254, March 2003. Relationships between art and mathematics.

The American Mathematical Monthly, 108, pp. 785-796, November 2001. Investigates the larger historical currents leading up to and away from the proliferation of geometric models in 19th century mathematics education.

*Teaching Engineering Problem Solving with Mathcad and the Web*

With Philip Pritchard. Proceedings of the 2001 Annual Conference of the American Society for Engineering Education (Albuquerque), ASEE, 2001. Invited presentation at the First International Meeting of the ASEE (Berlin), 2001. Describes a Web-based introduction to engineering problem solving using Mathcad, addressing student difficulties with mathematical aspects of the engineering design process.

*Reform Now, Before It's Too Late!*

The American Mathematical Monthly, 108, pp. 126-143, February 2001. Comparisons of mathematics education reform 100 years ago and today.

o Exploring
Precalculus

o Introduction to Mathcad

o Mathcad *in Action*

Web-based instructional materials developed for MathSoft, Inc., 1999-2001. Appeared on the MathSoft Learning Site and StudyWorks Online.

*Calculus Student Descending a Staircase*

Problems, Resources and Issues in Mathematics Undergraduate Studies (PRIMUS), Volume IX, no. 2, pp. 133-138, June 1999. Student attitudes in reform calculus courses.

Arts and Sciences ASpect, Salem State College, Issue 6, p. 7, May 1999. Aspects of the digital culture, inside and outside the classroom.

Precalculus: Functions Modeling Change

With Eric Connally, Deborah Hughes Hallett, Andy Gleason, et al.; John Wiley & Sons, Inc., 1999. Preliminary Edition. Precalculus text and manuals; companion to the Harvard Consortium calculus materials.

Catalogue of Mathematical Models, Department of Mathematics, University of Arizona, 1998. Introductory essay for the Department's catalogue of historical mathematical models. Describes the models and the evolution of education reforms that produced them.

*Effective Design of Computer-Based Instructional Materials*

Proceedings of the Eleventh Annual International Conference on Technology in Collegiate Mathematics (New Orleans), Addison-Wesley, 1998. Describes an interactive Web-based text that summarizes principles of effective educational interface design from studies in psychology, skills-training, education, art and design.

*Web-Based Learning Materials: Design, Usage and Resources*

With Michael Colvin, Lester Coyle, Donald Hartig, Lawrence Moore, Charles Patton, David Smith and Frank Wattenberg. Proceedings of the International Conference on the Teaching of Mathematics (Samos, Greece), pp. 71-73, John Wiley & Sons, Inc., 1998. Describes work to develop the Connected Curriculum Library, a Web-based library of interactive modules on topics in mathematics and the applied sciences.

o Design Principles for Interactive Texts

o Principes de Design Pour Les Textes Interactifs (VF)

With Julie Jacobs. Web-based text developed for Duke University's Connected Curriculum Project under a grant from the National Science Foundation in association with the Mathematical Association of America's Interactive Mathematics Texts Project, 1994-1998. Translated to French by Sébastien Rock for the Réseau d’Enseignement Francophone à Distance du Canada, 2001. Interface design of computer-based educational materials. Demonstrates the findings of empirical studies from psychology, skills training, education, art and design.

*Centers of Triangles of Fixed Center: Adventures in Undergraduate Research*

Mathematics Magazine, vol. 70, no. 4, pp. 252-262, October 1997. Using technology to motivate original student research in accessible areas of mathematics. Also contains some new results on the geometry of plane triangles.

*Design, Development, and Use of Web-Based Interactive Instructional Materials*

With Michael Colvin, Lester Coyle, Donald Hartig, Lawrence Moore, David Smith and Frank Wattenberg. Proceedings of the Tenth Annual International Conference on Technology in Collegiate Mathematics (Chicago), Addison-Wesley, 1997. Considerations of the human-computer interface in the design of computer-based instructional materials for mathematics.

*Discovering Differential Equations in Optics*

With Richard Thompson. The College Mathematics Journal, vol. 28, no. 3, pp. 217-223, May 1997. Using technology to motivate methods in differential equations, through problems in geometric optics.

*Experiments in Lavatory Dynamics*

Journal of Undergraduate Mathematics and Its Applications (UMAP), pp. 5-10, spring 1998. Appeared originally as *Hydraulics in an Unlikely Place*, Newsletter of the Consortium for Ordinary Differential Equations Experiments (CODEE), pp. 8-10, summer 1996. Featured on National Public Radio. Student modeling projects for a course in ordinary differential equations.

*The Computerized Pump: A Lab-based Calculus with Precalculus*

College Mathematics at the Entry Level, Lester Senechal, ed., New England Consortium for Undergraduate Science Education (NECUSE), 1992. Describes a "calculus with precalculus" course for women with weaker mathematical backgrounds developed at Mt. Holyoke College under a grant from the Charles Dana Foundation.

The Connected Curriculum Project

With Michael Colvin, Lester Coyle, Donald Hartig, Lawrence Moore, David Smith and Frank Wattenberg. Web-based instructional materials developed under various grants from the National Science Foundation, 1992-present. Interactive computer projects, modules, and texts on topics in precalculus, calculus, differential equations, linear algebra, engineering mathematics and mathematical finance.

o The Calculus Reader, v. III;

o Project CALC Laboratory Manual, v. III

With David Smith, Lang Moore, et al.; D.C. Heath & Co., 1992. Text and lab manual for the multi-variable component of the NSF-funded *Project CALC* laboratory calculus program, based at Duke.

*Relative Computability and Abstract Degree Structures*

Ph.D. dissertation; Duke University, 1991. Joe Shoenfield, advisor. An axiomatic treatment of degree theory, a part of recursive function theory that attempts to classify mathematical problems according to their relative computational difficulty.

In Preparation

*The Natural Religion of Mathematical Modeling*

Examines the historical foundations and philosophical assumptions underlying popular presentations of mathematical modeling in the undergraduate curriculum.

*Discrete Analogues of Linear Chain Reductions*

Modifications of a continuous PDE technique, used for describing discrete Leslie models in population dynamics.

*An Axiomatic Approach to Computational Degrees*

Results in degree theory, set in an axiomatic framework based on fundamental classes for reduction and domain.