Feb 23, 2007
Introduction to logic and algebraic structures
Hideo Nagahashi
In this talk we introduce various logics and algebraic structures behind them.
A set {a, b} has four subsets {a}, {b}, {a, b} and { }. Similarly {a, b, c} has eight subsets. Starting from this simple example, we discuss propositional logic, its generalization and interesting applications. The talk is accessible to anyone who wants to have fun with logic puzzles.
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Mar 23, 2007
The Geometry of the Triangle as the algebra of the Cubic Equation
Anatole Grishin
We introduce the "Fermat-Steiner Point" by way of its recent stellar appearance in the world of high-tech communication.
We look into the prospects of using standard algebraic theory to examine the properties of the triangle. The Fermat-Steiner point constitutes one such property. The "fundamental theory of algebra" locates three points in the plane as the solution of a cubic equation. A novel graphing technique places all solutions of polynomial equations on a plane graph, the "Argand image" of the polynomial equation.
Some of this material constitutes unfinished "work in progress" ad both students and faculty are cordially invited to participate.
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