Abstracts of Invited Talks
Games played on Hypercubes and their relation to certain graph-theoretic parametersAbstract: We explore the connections between certain 2-player games played on either the vertex set or the edge set of the n-dimensional hypercube, and certain graph parameters of the hypercube. Examples of these parameters: minimum size of a maximal matching, minimum size of an independent dominating set, and maximum size of a “balanced” independent set (where “balanced” in a bipartite graph means that there are equal numbers from the two parts of the bipartition).
The French and Indian War, Nyctaginaceous Shrubs, Mathematics and other Triangular Tales
Abstract: We begin by recounting the adventures of a mathematician, soldier, and explorer who was a student of D'Alembert and wrote an impressive sequel to L'Hôspital's "Analyse des Infiniment Petits." His exploits will lead us into the realm of number theory where we investigate the properties of some well-known and not so well known triangles.
The Use of Animation in the Teaching of Multivariate Calculus and Differential EquationsAbstract: We will demonstrate and discuss how we use computer animation in both multivariate calculus and ordinary differential equations. In particular, we will demonstrate how we construct animations using a combination of Mathematica, Quicktime, and Martin Kraus’s LiveGraphics3D java applet.
The Ageless Fascination of Geometric Dissection
Abstract: Geometric dissection is the mathematical art of cutting figures into pieces that can be rearranged to form other figures, using as few pieces as possible. Each dissection problem can be viewed as a puzzle, and many, such as the dissection of a regular octagon to a square, have elegant solutions. I will examine a selection of remarkable dissections, employing a variety of solution methods. I will highlight the colorful history of these problems, which originated many centuries ago and have flourished since their appearance in the mathematical puzzle columns of turn-of-the-century newspapers.
This talk should be accessible to anyone who has had a course in high school geometry and thought that regular hexagons were rather pretty.
The Lighthouse Theorem and Morley, but not MalfattiAbstract: Exploration of Morley’s theorem leads to the Lighthouse theorem. Attempts to apply it to the Malfatti problem have failed, but reveal a remarkable chain of ramifications of the original theorem.
Is Monopoly a Math Game? Developing Puzzles and Games that are Both Educational and Commercially Successful.Abstract: Mathematical games and puzzles are wonderful for stimulating the imagination and generating more serious interest in the fields of math and science. But watch out! If a game is too explicitly “educational” or doesn’t look fun enough, it can bomb in the market and end up not helping anyone.
In this talk, the speaker will share some serious and lighthearted observations about puzzle and game design, and strategies that a game development company needs to consider to maximize the success of a “math” type game or puzzle.
The Christie Lecture
Math from Fun & Fun from MathAbstract: An autobiographical history of combinatorial games, along the paths of Bouton, Sprague, Grundy, Smith, Berlekamp and Conway. Some simple games which turn out to be not so simple, and which lead to a lot of mathematics and a lot of fun.
Calculus BooksAbstract: Calculus books we have had with us ever since L'Hôspital published the first in 1696. Over the years they have increased in number (around 500,000 are sold every year) and weight. This talk, in preparation for which its author inspected eighty-nine separate and distinct calculus books, will examine what they have contained and now contain, especially about L'Hôspital's Rule and about applications. Seven important conclusions will be drawn and a moral message presented.
Geometric Dissections Now Swing and TwistAbstract: A geometric dissection is a cutting of a geometric figure into pieces that can be rearranged to form another figure. Some dissections can be connected with hinges so that the pieces form one figure when swung one way, and form the other figure when swung another way. These dissections have remained as mathemagical as they first seemed almost a century ago when the English puzzlist Henry Dudeney exhibited a hinged dissection of an equilateral triangle to a square. This talk explores two fundamental ways to hinge dissections of 2-dimensional figures such as regular polygons and stars. The first way uses “swing hinges”, which allow rotation in the plane. The second relies on “twist hinges”, which allow one piece to be turned over relative to another, using rotations by 180 degrees through the third dimension. I will introduce a number of novel techniques for designing both types of dissections. This talk should be accessible to anyone who has had a course in high school geometry and can swing on a swing or turn a knob on a door.
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