Seminar Series

Abstract: JPEG is the silent engine that built the visual internet. While we use it every day, few realize it is a sophisticated tapestry of physics, human biology, and advanced mathematics. By exploiting the glitches in human perception, JPEG compression throws away data we never even knew was there. In this talk, we’ll take a high-altitude flight over the JPEG pipeline—from the Discrete Cosine Transform to psychovisual modeling. Join me to discover how we transform massive raw data into portable files, and why you’ll never look at a .jpg the same way again.

Abstract: The Kevin Bacon game challenges players to find shortest paths from a given performer to Kevin Bacon where connections consist of actors who appeared together in a movie. In this talk, we'll investigate a single object, the sum-of-bits function, that could perhaps be a contender for the Kevin Bacon role in an analogous game played with mathematics. We'll see a variety of topics from the undergraduate math curriculum that can be connected via this idea. Exploring bridge objects like this the sum-of-bits function allows us and our students to see that there are often beautiful connections between seemingly separate and independent mathematical areas. Knowing of these connections can allow problem-solving techniques in one subfield to help with another.

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January 16 (1p MT)

Speakers: Eugene Boman (Pennsylvania State University) and Robert Rogers (State University of New York, Fredonia)

Zoom Link: msu.zoom.us/j/94740679958

Passcode: Cardano

Abstract: The history of mathematics provides innumerable stories of mathematicians both famous and infamous, discovering, nearly discovering, and failing to discover deep and important results. These tales of discovery and near discovery are compelling at a purely human level. So too are descriptions of the quirks, foibles, fortunes, and personalities of individual mathematicians. These stories constitute the heritage of mathematics and it is our heritage that makes mathematics a relatable, very human discipline. Our common heritage should be used as much as possible to forge connections with, motivate, and pique the curiosity of our students. But most textbooks, if they use our heritage at all, use it quite ineffectively. For example, short historical vignettes sometimes appear as marginal notes, a clear indication to the student that they can, and possibly should be ignored. Which is unfortunate.

For the first several millenia of human existence a large component of education consisted of stories told and heard around a campfire. As a result storytelling is deeply embedded in the human psyche as a means of learning.

But the best stories are not told linearly. Some start in the middle, foreshadow future outcomes, and refer to past events with which the listener (or reader) is not yet familiar in order to build suspense, interest, and curiosity.

We have written two textbooks (and we're working on a third) where we have explicitly used mathematical heritage as the frame for the topics being taught. In the course of writing these books we found that we could also present the progression of mathematical ideas itself as a story with a beginning, middle, and end. We will discuss our efforts to use story-telling techniques as an effective teaching mode in our textbooks and classrooms without sacrificing the mathematics itself. 

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February 13 (1p MT)

Speaker: James Sellers (University of Minnesota, Duluth)

Title: Leonhard Euler’s Groundbreaking Work on Integer Partitions

Abstract: In the mid-18th century, Leonhard Euler single-handedly began the serious study of integer partitions and made fundamental contributions to the area for the next few decades. In particular, he proved a remarkable result which says that the number of partitions of the integer n into distinct parts equals the number of partitions of n into odd parts. My goal in this talk is to discuss Euler’s impressive work on partitions, including snapshots of historical (original) publications of Euler, and then to describe numerous 19th, 20th, and 21st century results which spring from Euler’s original result. The talk will be self-contained and geared towards anyone with an interest in mathematics.

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March 13 (1p MT)

Zoom Link: msu.zoom.us/j/94740679958

Passcode: Cardano

Speaker: Dwight Anderson Williams II (Morgan State University)

Title: Navigating mathematical and political structures: A perspective on the works of Black researchers in theoretical mathematics

Abstract: This talk is a reflection on the influence of Black mathematicians and their works in shaping my present/early career as a research mathematician. The impact of primary sources, cited stories, and personal communication is gauged by three themes: institutional memory, subversion, and point-of-contact. The talk also features contributions by Black mathematicians toward promoting, progressing and preserving mathematical ideas central to my professional development, current research in the representation theory of Lie superalgebras, and dissemination of mathematics to graduate students.

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April 10 (1p MT)

Speaker: Dwight Anderson Williams II (Morgan State University)

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March 11 (2p MT)

Speakers: 

Zoom Link: zoom.us/j/96174161540

Passcode: none needed

Title: From Sound to Structure: Reification and Embodied Meaning–Making in Sonified Function Exploration; How blind students can learn about function behavior via sound

Abstract: The strong emphasis on multiple representations in mathematics education, particularly in research on functional thinking, poses epistemic challenges for learners with visual impairment, whose access to functions is often mediated through verbal descriptions or tactile graphics that constrain dynamic exploration and increase cognitive load. This study investigates how learners with visual impairments develop mathematical understanding through interaction with Audiofunctions, a software environment that sonifies function graphs, focusing on reification as an embodied process. Grounded in an ecological perspective and framed by the Body–Artifact Functional System (Shvarts et al., 2021), and perception–action loops, we analyze three in-depth cases selected from a larger sample of ten participants engaged in task-based interviews. We develop an analytical instrument structured around three phases: sensorimotor coordination, transition, and crystallization, based on the reification process proposed by Shvarts et al. (2024), to trace how learners' activity evolves from exploratory interaction with the artifact toward the direct perception of functional structures through auditory invariants. Across cases, learners progressively construct stable auditory mathematical mappings, using features such as pitch, noise, and spatialization to interpret variation, slope, and global behavior. Sonification becomes perceptually transparent, enabling sound to be interpreted as mathematical behavior rather than interface feedback, while reification emerges through the stabilization of auditory–motor coordination supported by embodied actions such as gestures and prior experiential repertoires. The findings position sonification as a generative representational system that supports the emergence of mathematical objects without reliance on visual representations or immediate symbolic formalization. By documenting how embodied interaction with accessible technology fosters meaningful engagement with functions, the study contributes to an ecological understanding of learning in inclusive mathematics education and offers implications for the design of perceptually rich digital environments that expand access to mathematical meaning.

January 29 - Feb 2: Mathematical Contest in Modeling (MCM/ICM) (All AMP)

https://www.comap.com/contests/mcm-icm

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