The Carl B. Allendoerfer Award
The Lester R. Ford Award
The George Polya Award
The Trevor Evans Awards
Daniel J. Velleman, Amherst College, and Gregory S. Call, Amherst College, receive the prestigious award in recognition for their article, "Permutations and Combination Locks," (Mathematics Magazine 68, 1995, 243-253). The citation notes . . .
The authors take a simple, practical problem and develop the mathematics clearly and thoroughly. The writing is lucid and brisk; the reader is swept along but is never disoriented. Both the solution to the problem and the exposition are models for how these things should be done.Judith V. Grabiner, Pitzer College, receives the prestigious award in recognition for her article, "Descartes and Problem-Solving" (Mathematics Magazine 68, 1995, 83-97). The citation notes . . .
Dan Velleman received his doctorate from the University of Wisconsin in 1980. He taught at the University of Texas and the University of Toronto before joining the faculty of Amherst College in 1983.
Greg Call did his graduate work at Harvard, receiving his Ph.D. in 1986. He taught for two years at Tufts University, before meeting and then joining Dan Velleman at Amherst College in 1988 where Greg is now an Associate Professor of Mathematics.
This article deals with a big subject in a fascinating way, and the writing is superb. The article is an excellent example of the insight we can gain from an historical view of mathematics. Professor Grabiner, a leading historian of mathematics, is currently the Flora Sanborn Pitzer Professor of Mathematics and Professor of Science, Technology & Society at Pitzer College, Claremont, California.
Martin Aigner, Freie Universität Berlin, receives the prestigious award in recognition for his article, "Turán's Graph Theorem" (The American Mathematical Monthly 102, 1995, 808-816). The citation notes . . .
In this article Martin Aigner gives us a delightful collection of proofs of this theorem, illustrating how widely differing methods can sometimes be used to achieve the same result. In the end, Aigner's article leaves us with a new appreciation for the unity of mathematics. Martin Aigner received his Ph.D. in Mathematics in 1965 from the University of Vienna. Since 1974 he has been a Professor of Mathematics at the Freie UniversitŠt Berlin.
Sheldon Axler, Michigan State University, receives the prestigious award in recognition for his article, "Down With Determinants!" (The American Mathematical Monthly 102, 1995, 139-154). The citation
notes . . .
In this paper, Sheldon Axler shows explicitly how an undergraduate course can analyze the structure of a complex matrix directly. [In] the end, we see how to obtain determinants from the structure theorems, and we have a clearer view of the whole subject. Sheldon Axler was a graduate student at Berkeley [and] currently he is a Professor at Michigan State University.
John F. Oprea, Cleveland State University, receives the prestigious award in recognition for his article, "Geometry and the Foucault Pendulum" (The American Mathematical Monthly 102, 1995, 515-522). The citation notes . . .
The article succeeds at many levels: it teaches us some differential geometry, and it demonstrates once again that physical processes are controlled by geometry. And, of course, we now understand the Foucault pendulum! [John Oprea obtained his] Ph.D. at Ohio State and a postdoc at Purdue, returning to his hometown in 1985 by taking a job at Cleveland State University.
John H. Ewing, American Mathematical Society, receives the prestigious award in recognition for his article, "Can We See the Mandelbrot Set?" (The College Mathematics Journal. 26, 1995, 90-99). The citation notes . . .
In today's world of sophisticated computers and abstract mathematicians, what makes a "good" drawing? [John Ewing] brings a fresh viewpoint to this topic, guides readers to the frontier of current research, and administers a healthy dose of skepticism. His lovely paper is one of those rare expository gems that entertains as it informs and seems to improve with each reading. John Ewing is currently the Executive Director of the American Mathematical Society, having served on the faculty of Indiana University from 1973-1995.
James G. Simmonds, University of Virginia, receives the prestigious award in recognition for his article, "A New Look at an Old Function, eiq" (The College Mathematics Journal. 26, 1995, 6-10). The citation notes . . .
All who value accessible and appealing introductory notes on fundamental mathematical ideas will enjoy this lively, lucid treatment of Euler's exponential function eiq. Both students and professors long for nuggets of exposition like this. James G. Simmonds received all of his post-secondary education from the Massachusetts Institute of Technology, [including] a Ph.D. in Applied Mathematics in 1965. He has been in the Department of Applied Mathematics at the University of Virginia since 1966.
Joel Chan, University of Toronto, receives the prestigious award in recognition for his article, "As Easy as Pi" (Math Horizons, Winter 1993, 18-19). The citation notes . . .
Joel Chan has a great deal of fun relating some of the long and fascinating history of computing pi. Today's computer-oriented readers can only wonder how Johann Dase (1844) could possibly have computer 200 digits of pi in his head, or wonder why anyone (Tomoyori in 1987) would memorize 40,000 digits of pi. Joel Chan is currently a mathematics and economics student at the University of Toronto.
Underwood Dudley, DePauw University, receives the prestigious award in recognition for his article, "Why History?" (Math Horizons, Nov. 1994, 10-11). The citation notes . . .
Underwood Dudley makes an eloquent case for the importance of history in the everyday teaching of mathematics. [By studying the history of mathematics,] we will understand mathematics as a human activity, one that has not always been done in quite the way it is done today, and one that may well be done somewhat differently in the future. Professor Dudley received his Ph.D in 1965 from the University of Michigan [and has taught] at DePauw University since 1967.
Joseph A. Gallian, University of Minnesota at Duluth, receives the prestigious award in recognition for his article, "Weird Dice" (Math Horizons, Feb. 1995, 30-31). The citation notes . . .
This is a beautiful article that combines an interesting mixture of ingredients, guaranteed to fascinate readers of all ages. Joseph A. Gallian received his Ph.D. from Notre Dame in 1971 [and] has been at the University of Minnesota, Duluth, since 1972.
Alan C. Tucker, State University of New York at Stony Brook, receives the prestigious award in recognition for his article, "The Parallel Climbers Puzzle" (Math Horizons, Nov. 1995, 22-24). The citation notes . . .
Two climbers begin their ascents from opposite ends of a mountain range. If both start at the same altitude, is there a way they can make parallel climbs, always staying at equal altitudes, until finally reaching the summit simultaneously? This article shows how a few very accessible ideas from discrete mathematics can answer this question affirmatively. While doing so, Alan Tucker shows us how it is possible for deft exposition to embody full mathematical rigor without seeming at all pedantic. Dr. Tucker obtained his Ph.D. in Mathematics at Stanford University in 1969 and has been at Stony Brook since 1970.