Mathematics

Ernest H. Volwiler Professor of Mathematics, Emeritus

Specialization

Game Theory and Social Choice Theory
Information-Based Complexity
Use of Technology (Mathematica) in Teaching Mathematics

Interests

Probability and Paradox
The Mathematics of Gambling 

Education

PhD Massachusetts Institute of Technology
BA Amherst College

Courses Taught

Mathematics 110/111: Calculus 
Mathematics 230: Abstract and Discrete
Mathematics 231: Linear Algebra
Mathematics 214: Differential Equations
Computer Science 434: Theory of Computation

Books

THE MATHEMATICS OF GAMES AND GAMBLING, 2nd Edition, Mathematical Association of America, New Mathematical Library Series, 2006

ANIMATING CALCULUS: MATHEMATICA NOTEBOOKS FOR THE LABORATORY, Windows & Macintosh Version (with Stan Wagon), TELOS/Springer-Verlag, 1997.

MATHEMATICA FOR MATHEMATICS TEACHERS, Front Range Press, 1996.

LEARNING BY DISCOVERY: A LAB MANUAL FOR CALCULUS, (co-written with four other authors), Volume 1, ACM/GLCA Resources for Calculus Collection, Math. Association of America, 1993.

THE MATHEMATICS OF GAMES AND GAMBLING, Mathematical Association of America, New Mathematical Library Series, 1981.

FUNCTIONAL ANALYSIS; A SHORT COURSE (New York and London, Intext Educational Publishers, 1974), Reprint Edition (New York, Krieger Publishing Co., 1980).

Articles

“The Lambert W Function and Undergraduate Mathematics,” in Essays in Mathematics and Statistics, edited by Vladimir Akis, ATINER, Athens, Greece, (2009):147-154.

“Projectile Motion with Resistance and the Lambert W Function,” The College Mathematics Journal, Vol. 35, November 2004, pp. 337-350 (with David Yuen)

“On Montero’s Comments Concerning the Coordinated Solution of Antov and Packel,” Homo Oeconomicus XX(4) (2004): 471-472 (with Dimitar Antov).

“The Coordinated Solution for Superadditive Games with Empty Core,” Homo Oeconomicus XX(4) (2004): 449-460 (with Dimitar Antov).

CHAOTIC ELECTIONS!: A MATHEMATICIAN LOOKS AT VOTING, by Donald Saari, MAA Online Review, July 2001.

“Permutations and Combinations,” in Handbook of Discrete and Combinatorial Mathematics, edited by Kenneth H. Rosen, (2000):96-107.

COMPLEXITY AND INFORMATION, by J. Traub and A. G. Werschulz, Complexity 4: (1999): 39-40.

“Symbolic Dynamics: A Mathematica(l) Window to Chaos,” in Proceedings of Sydney University 25 YEARS OF TECHNOLOGY Symposium, (1997):28-42.

“Rearrangement Patterns for the Alternating Harmonic Series,” Mathematica in Education (1994): (with Stan Wagon).

“Measures of Uncertainty and Information in Computation,” Information Sciences 65 (1992): 253-273 (with J. F Traub and Henryk Woniakowski).

“On the Value of ‘Expository Research’ for Mathematics Undergraduates,” in Models for Undergraduate Research in Mathematics, edited by Lester Senechal, M.A.A. Notes, No. 18 (1990): 73-76.

“Do Linear Problems Have Linear Optimal Algorithms?,” Siam Review 30 (1988): 388-403.

“Recent Developments in Information-Based Complexity,” Bulletin of Amer. Math. Soc., 17 (1987): 9-26 (with Henryk Wozniakowski).

“Information-Based Complexity,” Nature 327 (1987): 29-33 (with J. F. Traub).

“The Algorithm Designer versus Nature: A Game-Theoretic Approach to Info.-Based Complexity,” J. of Complexity 3 (1987): 244-257. 

“Green Beards and Kindred Spirits: A Preliminary Mathematical Model of Altruism Toward Non-kin Who Bear Similarities to the Giver,” Ethology and Sociobiology 7 (1986): 107-115 (with Robert Glassman and Douglas Brown).

“A Stochastic Model of Committee Voting with Exogenous Costs: Theory and Experiments,” Behavioral Science 27 (1982): 43-56 (with Elizabeth Hoffman).

“Strategic Equilibria and Decisive Set Structures for Social Choice Mechanisms,” Mathematical Social Sciences 2 (1982): 373-382 (with Donald Saari).

“Semisimple Games, Enactment Power, and Generalized Power Indices,” International Journal of Game Theory 10 (1981): 137-146.

“Nonequilibrium Solutions for Legislative Systems,” Behavioral Science 25 (1980): 140-148 (with John Ferejohn and Morris Fiorina).

“A New Index of Power for Simple n-Person Games,” International Journal of Game Theory 7 (1978): 113-123 (with John Deegan, Jr.).

“Hilbert Space operators and Quantum Mechanics,” American Mathematical Monthly 81 (1974): 863-873.

“A Simplification of Gibson’s Theorem on Discrete Operator Semigroups,” Journal of Mathematical Analysis and Applications 39 (1972): 586-589.

“A Semigroup Analogue of Foguel’s Counterexample,” Proceedings of the American Mathematical Society 21 (1969): 240-244.

Invited Talks

2009 Keynote Speaker, M.A.A. Ohio Sectional Meeting, Kenyon College, “Recent Results on Projectile Motion and a Plug for Experimental Mathematics” 

2007 First International Conference on Mathematics and Statistics, Athens, Greece, “The Lambert W Function and Undergraduate Mathematics”

1999 Conference Speaker, ACM/GLCA Conf. on Undergraduate Mathematics

1998 Keynote Speaker, Eastern Pennsylvania/Delaware M.A.A. Meeting

1998 Keynote Speaker, Rose Hulman Institute of Technology 15th annual Undergraduate Mathematics Conference

1997 Keynote Speaker, Western Kentucky Univ. 17th Annual Math. Symposium

1996 Univ. of Sydney Conference on “25 Years of Technology”

1995 Oberwolfach Conference on “New Trends in the Teaching and Learning of Mathematics,” Oberwolfach, Germany (conference co-organizer)

1995 Claremont Colleges Conference on Technology in Education, Claremont, California

1980 International Econometric Society, Marseilles, France (by coauthor Elizabeth Hoffman)

Posters

1996 AMS Meetings, Orlando, ILI Poster Session on Laboratory Approaches to Calculus

1994 International Conference on Technology in Collegiate Mathematics, Poster Session on Mathematica Notebooks for Introductory Calculus

Awards and Honors

Phi Beta Kappa, 1963, Amherst College

Sigma Xi, 1963, Amherst College

NSF Graduate Fellowship, 1963-1966

NSF Research Grant, 1979-1981

NSF Research Grant, 1981-1983

Math. Assoc. of Amer. Book Prize, 1986

NSF Research Opportunity Award, Summer 1986

Ernest H. Volwiler Chair in Mathematics & Natural Sciences, 1987-present

Sears-Roebuck Award for Teaching Excellence Campus Leadership, 1989

NSF Instrumentation Laboratory Improvement Grant, 1991-1993

NSF Instrumentation Laboratory Improvement Grant, 1995-1997

On-Line Links

CHAOTIC ELECTIONS!: A MATHEMATICIAN LOOKS AT VOTING, by Donald Saari, MAA Online Review ( http://www.maa.org/publications/maa-reviews/chaotic-elections-a-mathematician-looks-at-voting), July 2001.

Projectile Motion with Resistance and the Lambert W Function, by Edward Packel and David Yuen, (2004), ( http://math.lfc.edu/~packel/PackelYuenProjectilePaper.pdf)