The study of continued fractions goes back to Indian mathematicians in the 6th century. They came back into fashion in Europe in the 1600’s and were studied extensively in 18th and 19th centuries. They find their way into modern mathematics through their use in computing modular forms and computer recognition of rational numbers. In this talk, I will introduce continued fractions and discuss some of their modern applications.
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During this interactive session, we will begin with a team strategy game followed by an error-correcting code with a corresponding link to hypercubes. Participants will explore how the game, code and cubes are connected to each other through examples and questions that arise. Come engage yourself with some contemporary mathematical topics that will be accessible regardless of the mathematics courses you have taken.
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Navigating academia as an outlier—whether due to background, research interests, teaching philosophy, or identity—can be both challenging and rewarding. In this talk, I will share the challenges I have faced, as well as insights from my unique journey, reflecting on the strategies that helped me not only persist but also thrive in environments where I did not always fit the mold. Drawing from experiences in teaching, research, and mentoring, I will discuss the power of authenticity, resilience, and community-building in shaping my identity as a mathematician. Whether you find yourself feeling like an outlier or simply want to support those who do, this talk will provide practical takeaways for overcoming obstacles, embracing unique perspectives, and fostering a supportive community that values diversity and inclusion. Join me as we explore how the challenges of being an outlier can become a powerful catalyst for growth and success.
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Mathematicians love SET. On the surface, this classic game is a con test of pattern recognition, but it also presents an interesting way to visualize the geometry of a torus over a finite field. In this talk, we will discuss some of the mathematics connected to SET and then explore several new versions of the game, including one arising from projective geometry and one arising from non-abelian groups. In particular, we will see how these non-abelian variations on SET can give intuitive visualizations of abstract group structures.
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In this talk, I explore the tension between mathematical rigor and perfectionism, particularly how the fear of failure can hinder their engagement with rigorous mathematical thinking. Drawing on Imre Lakatos' book Proofs and Refutations, which describes a dialectical process of conjecture, proof, and refutation, I argue that just as historical developments in mathematics emerge through a cycle of failure and refinement, our students develop their own rigorous thinking through their experiences of failure. As a result, a large barrier to developing mathematical cognition stems from a rise in maladaptive perfectionism. I will discuss pedagogical strategies, including course structure and historically motivated problems, to help students navigate the discomfort of not knowing and cultivate genuine mathematical rigor.
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*“When I use a word, it means just what I choose it to mean — neither more nor less.” - Humpty Dumpty* Creating new words can clarify mathematical communication and logic, especially when forging new pathways. In this session, a few new words will help us approximate rationality in a purely geometric context. These proofs will not use high-powered tools, so leave your slithy toves at home. Instead, we will rely on geometric constructions, proportional reasoning, tiling, dissection, and proof by descent. We will determine whether 3, 4, 5, 6, and 9 are “grational,”as defined below. We will use the stealth of geometry to sneak up on number theory, such as proving all perfect squares are grational. Define a nice-gon to be a regular polygon with integer side lengths in Euclidean geometry. A nice n-gon is a nice-gon with n sides. An integer n is grational if and only if there exists a nice n-gon such that its area equals the sum of areas of n congruent nice n-gons. Open questions about grationality will follow you home and may inspire your next mathventure. What would grationality look like with higher values or with higher dimensions? How is grationality related to rationality? Might grationality be related to the work of Hippasus of Metapontum, described by Plato?
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