Almost all of our math classes make use of the real numbers as well as subsets (the rational numbers, the integers, the natural numbers) and occasionally supersets (the complex numbers). John Horton Conway, in his research on game theory, came up with the notion of Surreal Numbers, an ordered field that contains the real numbers and much more, including positive numbers smaller than every positive real numbers (positive infinitesimals) and numbers bigger than every positive real number (positive infinite numbers). This talk will introduce the main concepts behind the Surreal Numbers, including their connection to game theory and how the real numbers are themselves defined.
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The games Projective SET and EvenQuads are both inspired by the famous SET game, but in different directions. The SET game is a model for the affine finite geometry AG(n,3), and Projective SET is so-named because it is a model for the projective finite geometry, PG(n,3). On the other hand, EvenQuads is a model for the affine finite geometry AG(n,2). Despite their apparent differences, there is an interesting way to play Projective SET within EvenQuads, and hence a mathematical connection between properties of the two, which are of interest in algebraic coding theory. In this talk, I will introduce the two games, show how to play one game within the other, and describe some of the mathematics involved in each. Time permitting, I will discuss some connections to coding theory.
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Given distinct planar points $A$ and $B$ and a real number $k$, called the _index_, Apollonius long ago showed that the locus of all points $P$ for which $k$ is the ratio of the distances from $P$ to $A$ and from $P$ to $B$ is a circle. The puzzle we present is this one: Given a circle $\mathcal Q$ in the hyperbolic disk whose diameter $CD$ lies along the real axis, how may we recover $\mathcal Q$ as a circle of Apollonius? That is, what are $A$, $B$, and $k$? The beauty of this puzzle is that $B$ is the hyperbolic center of $\mathcal Q$.
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We use the community version of Manim (created and popularized by Youtuber 3Blue1Brown) to animate mathematical concepts and theorems that are traditionally very difficult to convey. Examples include animations of the derivative, the $\varepsilon$-$\delta$ definition of the limit, and the fundamental theorem of calculus. If time permits, we will play with an interactive example where students can dynamically adjust animations of integrals.
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_EvenQuads_ is a _SET_-like card game published by the AWM whose goal is to find "quads", which are sets of four cards satisfying a particular pattern. The cards can be viewed as points in the finite affine geometry $AG(6,2)$, and a quad in the card game corresponds to a plane in $AG(6,2)$. An interesting puzzle is to consider what the largest number of quads is that we can possibly pack into a specified number of cards/points, if we are allowed to choose them however we wish. In this talk, we will explain the rules and geometric underpinnings of EvenQuads, and describe some current work and open questions about quad-packing.
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A simple closed space curve that is comprised of quarter circles of fixed curvature with continuous tangents is known as a Tangle, after the popular fidget toy. We show that all Tangles of a given length n (or n-Tangles) correspond to the solutions of a particular system of polynomial equations. Using the software platform Macaulay2, we prove the nonexistence of 5-Tangles and describe all 6-Tangles.
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As part of her 2025 MAA-SE plenary talk, Catherine Hsu introduced cards that represented elements of the group $S_2\wr S_3$ for a game similar to SET. We call these cards *Wreath cards* and pull out the 24 cards (the $\mathcal{R}$ deck) that correspond to the group of rotations of a cube. We propose a ``game" to express a drawn card from the $\mathcal{R}$ deck as a product with factors chosen from three designated generators for $\mathcal{R}$. The player is also challenged to physically manipulate a cube to demonstrate the product.
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