This page is no longer being updated and remains online for informational and historical purposes only. The information is accurate as of the last page update.
For questions about page contents, contact the Communications Division.
Derek Smith, assistant professor of mathematics, is coauthor of an acclaimed book with John H. Conway, On Quaternions and Octonions: Their Geometry, Arithmetic, and Symmetry, published this year by A.K. Peters, Ltd.
“This is a beautiful and fascinating book on the geometry and arithmetic of the quaternion algebra and the octonion algebra,” states an article in Mathematical Reviews, a publication of the American Mathematical Society. “This slim book is most intriguing to read: It is an excellent exposition of very attractive topics, and it contains several new and significant results.”
“The reader is taken on a grand tour of some pretty deep algebraic arcana, with a good deal of history thrown in along the way, as well as plenty of motivation and examples,” notes a review by the Mathematical Association of America. “And it’s all done in an immensely entertaining way. By and large, the material in these pages is geared to evoke pleasure and surprise by means of a light and readable writing style, a profusion of examples, and a huge number of (very cool) calculations. The authors entertain and teach us while obviously indulging themselves in sheer fun (it already starts with their dedication on page v: this is not going to be another dry tome).”
“But in the second part of the book Conway and Smith go on to introduce and describe a subtle but pervasive phenomenon, ‘triality symmetry,’ which attests to their ideological goal of placing these algebras in a proper, deeper context,” the review continues. “So the book is both fun and deep.”
“The book has been written by two mathematicians. A great advantage is that it is written in a style that makes it easily accessible also to other scientists,” states a review in Acta Crystallographica Section A: Foundations of Crystallography, a publication of the International Union of Crystallography. “The main messages are clearly stated, not buried under technical details. The book is carefully written”
Smith also has shared his research through journal articles and conference proceedings, including an upcoming piece in International Journal of Theoretical Physics, an article published this year in Journal of Physics A, and others. He has given 14 talks at forums in the United States and abroad since 2000, and will present an invited paper next January at the Joint Meetings of the American Mathematical Society and Mathematical Association of America in Phoenix, Ariz.
He is mentoring Carrie Abildgaard ’04of North Haven, Conn., in her yearlong, independent research project on the mathematical underpinnings of economics. She is investigating the ideal frequency with which to rebalance an investment portfolio, using historical returns fromstock and bond indicesover the past 15 years as data. If successful, the project will allow Abildgaard, a varsity swimming captain who is pursuing both a B.S. degree in mathematics and an A.B. degree with majors in economics & business and Spanish, to graduate with honors in mathematics. She will present some of her findings in February at the Conference for Undergraduate Women in Mathematics in Nebraska.
“His door has always been open to me, whether it’s for a question about my academic schedule, another math class I am taking, or just to say hello,” she says. “Derek is excited to be working with meI believe that it is the small, undergraduate environment which allows professors to devote so much time and energy on the students.”
For the past two summers, Smith has conducted research with Ekaterina Jager ’05 (Tashkent, Uzbekistan), who is pursing a B.S. in electrical & computer engineering and B.A. in mathematics, on a geometry problem involving group theory that relates to the logic of quantum mechanics. They will submit an article coauthored with a third researcher to a research journal. Jager also will present her work in January at the Joint Meetings of the American Mathematical Society and the Mathematical Association of America in Phoenix, Ariz.
Smith conducted research on divisor theories of the integral quaternions and octonions with mathematics major Steve DiMauro ’02 (Hatboro, Pa) and students from other top institutions, which resulted in a coauthored paper that Smith presented on the group’s behalf this August in Prague, Czech Republic. In addition, DiMauro and three other students presented their findings at the American Mathematical Society Conference in San Diego, Calif., and two coauthored papers on the group project have been submitted for publication to mathematics journals. The collaboration was part of the National Science Foundation’s Research Experience for Undergraduates at Lafayette, a summer program taught by the College’s mathematics faculty.
Smith also mentored DiMauro in a yearlong, independent research project on combinatorial and economic games. DiMauro, who graduated summa cum laude with membership in Pi Mu Epsilon, the national mathematics honor society, presented his ideas at the Regional Student Mathematical Conference hosted by Moravian College and earned honors in mathematics for his work.
Lafayette students are mentored by Smith in taking the William Lowell Putnam Mathematical Competition, described by Time magazine as “the world’s toughest math test.” Last year’s team finished 24th among 476 institutions, best among Patriot League schools. It was paced by three seniors who scored among the top ten percent of the 3,300 competitors.
In addition, Smith advises the Mathematics Club, founded last spring, which sponsors events and weekly activities such as a Problem Group, a game hour, and preparation sessions for the mathematics GRE examinations.
Smith conducted research at the Institute for Defense Analyses in Princeton, N.J., last spring and at the National Security Agency in the summers of 1992 and 1995. He served as lecturer at Princeton from spring 1997 through spring 1998, as an instructor in its Summer Scholars Institute from 1996-98, and as a graduate instructor from spring 1996 through fall 1996. He was co-organizer of the Rutgers-Princeton Group Theory Seminar from 1996-97 and editorial assistant for Annals of Mathematics from 1998-99.
He earned a Ph.D. in mathematics from Princeton University in 1999, an M.A. in mathematics from Princeton in 1995, and a B.S. in applied mathematics from North Carolina State University in 1992, graduating as valedictorian.
Smith received a grant from Lafayette’s Academic Research Committee in 2000, a graduate fellowship from Princeton from 1992-97, and the John T. Caldwell Alumni Scholarship from North Carolina State from 1998-92. He received Lafayette’s Thomas Roy and Lura Forrest Jones Faculty Lecture Award in 2002-03.
Carrie Abildgaard ’04 presented honors research on investment portfolios under the guidance of Derek Smith, assistant professor of mathematics, at the Nebraska Conference for Undergraduate Women in Mathematics.