Corinne Manogue and Tevian Dray
Corinne Manogue and Tevian Dray are both Professors of Mathematics and Physics at Oregon State University, where they are working on an NSF supported Vector Calculus Bridging project. They are distinguished mathematical physicists, who have published numerous joint papers in scientific journals, primarily in relativity theory and string theory. Their recent research has focused on the description of the fundamental particles using non-associative algebra.
They team-taught two special topics courses (described below), that met during the entire semester. In addition, they gave a convocation talk, participated in the math and physics departmental seminars, and met with interested students and faculty.
PHY(MAT)-295.01: Octonions in Mathematics and Physics
This cross-listed course met Tuesday and Thursday from 10:00-10:50 a.m. It dealt with octonions and their application to physics. The octonions are a generalization of the familiar real and complex number systems, but their algebra is both non-commutative and non-associative, so the linear algebra of the octonions is both fun and interesting. This algebra appears to be closely related to deep physics, such as the existence of supersymmetry (string theory).
Although the formal prerequisites of this course were light, and the course started at the beginning, it was challenging and fast-paced. It was aimed at intermediate to advanced students in mathematics or a physical science. Prerequisites: MAT 215 required, PHY 232 recommended.
MAT-295.02: Vector Calculus for Mathematicians and Other Scientists
This course met Monday and Wednesday from 2:15-3:05 p.m. The course was highly interactive and emphasized the underlying geometry. It was designed to bridge the gap between the different ways that mathematicians and other scientists use vector calculus. The course also developed the calculus of line and surface integrals and covered the fundamental theorems of Gauss and Stokes, as well as introduced differential forms as time permitted. Prerequisite: MAT 133.
Schedule of Seminars and Convocation
- Corinne gave a Physics seminar entitled "Rolling Relativistic Quantum Balls Uphill" on September 17, 2002.
- Beginning Tuesday, September 24, 2002, Tevian and Corinne started a series of seminars entitled "The Octonions". These seminars were conducted every Tuesday for a total of six to seven talks.
- On September 26, 2002, Tevian and Corinne gave a joint Math/CS and Physics faculty seminar entitled "Some Differences between Mathematics and Physics".
- Their joint convocation presentation on "What Does Geometry Tell Us About the Universe" was given on October 31, 2002.
- Corinne gave a presentation in several classes at the middle school November 8th, 2002 on "Black Holes".
- On Tuesday, November 12, 2002, Tevian gave the Physics seminar entitled, "The Rotating Quantum Vacuum". Additionly, he gave the Mathematics/Computer Science seminar entitled, "The Octonionic Eigenvalue Problem".
- "Using Technology to Visualize Derivatives of Vector Fields" was the Math/CS seminar given by Tevian on December 4, 2002.
- Tevian and Corinne jointly organized a lunchtime discussion on December 12, 2002, "Entitled What Works and What Doesn't". Also, they gave a duplicate of their convocation talk "What Does Geometry Tell Us About the Universe" at Grinnell High School.