Bard Professor Japheth Wood Receives 2021 MAA Award for Top Expository Mathematical Writing
Japheth Wood, director of quantitative literacy and continuing associate professor of mathematics at Bard College, is recognized for his article “Chords of an Ellipse, Lucas Polynomials, and Cubic Equations,” coauthored by Ben Blum-Smith and published by the American Mathematical Monthly. “We are thrilled to be recognized for this honor, and to now have our names associated with Paul Halmos and Lester Ford, as well as the long list of other excellent expositors who have been so lauded,” said Wood and Blum-Smith.
Bard Professor Japheth Wood Receives 2021 MAA Award for Top Expository Mathematical Writing
Japheth Wood, director of quantitative literacy and continuing associate professor of mathematics at Bard College, is recognized for his article “Chords of an Ellipse, Lucas Polynomials, and Cubic Equations,” coauthored by Ben Blum-Smith and published by the American Mathematical Monthly. “We are thrilled to be recognized for this honor, and to now have our names associated with Paul Halmos and Lester Ford, as well as the long list of other excellent expositors who have been so lauded,” said Wood and Blum-Smith.
The Bard Math Circle’s Creative and Analytical Math Program (CAMP) and founder Japheth Wood have been recognized with a 2020 Epsilon Award for Young Scholars Programs. The Epsilon Awards, given annually by the American Mathematical Society, support some of the most prestigious summer math enrichment programs in the United States.
American Mathematical Society Recognizes Bard Math Circle’s CAMP Program and Its Founder, Professor Japheth Wood
The Bard Math Circle’s Creative and Analytical Math Program (CAMP) and its founder, professor Japheth Wood, have been recognized with a 2020 Epsilon Award for Young Scholars Programs. The Epsilon Awards, given annually by the American Mathematical Society, support some of the most prestigious summer math enrichment programs in the United States.
CAMP is not “summer camp.” It is a nonresidential academic program for middle school students that features mathematics in a creative learning environment. CAMP started in August 2014 with initial funding from the Dolciani Math Enrichment Grant Program, and it has grown to become a popular late-summer treat for math kids in the Mid-Hudson Valley and beyond. Experienced educators and undergraduate math majors lead classes and activities that emphasize hands-on math, teamwork, and outside-the-box thinking.
This summer, CAMP was held online for the first time. During the first week in August, 49 middle schoolers and a staff of 15—including seven Bard math and computer science majors and two Bard math alumnae—got together via Zoom. “Since cyberspace shortened the distance between us, the Bard Math Circle received numerous applications from around the country,” says Wood. “We could see students’ excitement over running into old friends and connecting with new CAMPers in Zoom classrooms.”
This year’s CAMP theme was cryptography. Students explored cipher encryption (using a cipher wheel like the one at right), created artworks with encoded messages, made cryptograms, and more.
“Though [CAMP] wasn’t around during my student days at Bard, an amazing community has developed since,” says Bard alumna and CAMP senior instructor Erin Toliver ’00. “I love seeing the look on a student’s face when they’ve discovered a new pattern, found a different perspective, or made a new connection for a deeper understanding of this glorious world of mathematics.”
“What’s really distinguishing [our study} from a lot of the studies that are being quoted by the national press . . . and the Administration is that we look at the local connections inside of communities, and those are usually ignored by bigger studies,” Junge tells WAMC’s Hudson Valley Bureau Chief Allison Dunne.
Bard Assistant Professor of Mathematics Matthew Junge Talks with WAMC about National Science Foundation RAPID Grant to Study COVID-19 Forecasting Models
“What’s really distinguishing [our study} from a lot of the studies that are being quoted by the national press . . . and the Administration is that we look at the local connections inside of communities, and those are usually ignored by bigger studies,” Junge tells WAMC’s Hudson Valley Bureau Chief Allison Dunne. “Our study’s taking this opposite perspective of really finally modelling person-to-person connections that come up in our day-to-day lives, like who we socialize with, where we work, connections of that sort, and we ask how the disease spreads in this sort of zoomed-in picture.”
Bard College Professors Win National Science Foundation Rapid Grant to Develop Forecasting Models that Better Capture the Geographic and Social Complexity of the COVID-19 Pandemic
The National Science Foundation (NSF) has awarded Bard College professors Matthew Junge, mathematics, and Felicia Keesing, biology; and Grinnell College professor Nicole Eikmeier, computer science, a $60,000 grant to develop network models that—by more accurately incorporating social distancing measures—better capture the geographic and social complexity of the COVID-19 pandemic. Awarded through the NSF’s Rapid Response Research (RAPID) program, which provides support for urgent scientific research that responds to emergencies and unexpected events, the grant includes funding for salaries, publishing costs, and several undergraduate research assistants over a six-month period.
Junge, Bard assistant professor of mathematics and lead investigator on the project, says their project aims to develop network models and mathematical theory to test the robustness of some prominent models being used by governments to justify the extreme levels of intervention we are living through. One advantage of a network model, which tries to accurately describe the face-to-face interactions each individual in a society has and how an infection might spread, is that it is relatively easy to implement social distancing into the network.
“Mathematicians are fairly adept at modeling the natural evolution of epidemics, but most ‘off the shelf’ models were not built to describe the dramatic levels of intervention—business closures, travel limitations, and social distancing—that we are living through during the COVID-19 pandemic,” says Junge. “The grant brings together a biologist (Felicia), computer scientist (Nicole), and mathematician (myself) as well as a few undergrad research assistants to tackle this problem over the next six months. Felicia is an expert in infectious disease, Nicole in modeling real world networks, and I am experienced in network infection models.”
Matthew Junge, assistant professor of mathematics, comes to Bard from Duke University, where he served as William W. Elliott Research Assistant Professor. He received his doctorate in mathematics from the University of Washington, where he also earned MS, BS, and BA degrees. His areas of interest include probability, statistical physics, and mathematical biology. Junge’s research takes a probabilistic approach to particle systems from physics and biology, including models for chemical reactions, species proliferation, and epidemic outbreaks. He also studies random structures from classical mathematics and computer science, such as permutations and fragmented spaces.
Felicia Keesing, David and Rosalie Rose Distinguished Professor of Science, Mathematics, and Computing, has been on the Bard faculty since 2000. She has a B.S. from Stanford University and a Ph.D. from the University of California, Berkeley. Since 1995, she has studied how African savannas function when the large, charismatic animals like elephants, buffaloes, zebras, and giraffes disappear. She also studies how interactions among species influence the probability that humans will be exposed to infectious diseases. Keesing also studies Lyme disease, another tick-borne disease. She is particularly interested in how species diversity affects disease transmission.
Nicole Elkmeier is an assistant professor of computer science at Grinnell College. She has a PhD in Mathematics from Purdue University and a BA from in mathematics and computer science from Concordia College. Her research is in the field of Network Analysis, specifically focused on studying features of real data and constructing and analyzing graph models which maintain those features. A network, in this case, is a set of nodes (people, web pages, etc.) connected by edges (physical connection, collaboration, etc). She is interested in random graph models, which are used to study how well an algorithm may do on a real-world network, and for testing properties that may further improve algorithms. Her research is at the intersection of math and computer science.
The Algebra Project: Bard Alumna, Teacher Kate Belin on Using Math to Help Students Build More Ethical Communities
Kate Belin BA ’04, MAT ’05 teaches math at Fannie Lou Hamer Freedom High School, a small public school in the South Bronx that uses project-based learning. At Fannie Lou, she oversees the Algebra Project, a national initiative that connects math to students’ lived experiences. In this episode of the Ethical Schools podcast, Belin talks about the synergy between the Algebra Project and Fannie Lou, both of which have their roots in the history of the civil rights movement.
Mathematics Professor Matthew Junge Receives National Science Foundation Grant
Matthew Junge, Bard College Assistant Professor of Mathematics, has been awarded a grant from the National Science Foundation in the amount of $190,868 for research into multitype particle systems. The grant comes from the NSF's Division of Mathematical Sciences Probability Program.
Interacting particle systems with random dynamics are fundamental for modeling phenomena in the physical and social sciences. Such systems can be used to describe chemical reactions, as well as the spread of disease, information, and species through a network. These models often become more meaningful when multiple particle types are incorporated. For example, the celebrated First Passage Percolation model describes the spread of a single species through an environment; the incorporation of competing species enriches the model. This project seeks to study more realistic variants of well-known models for chemical reactions, epidemic outbreaks, and the spread of information as to deepen our understanding of important phenomena from across the sciences and further develop the mathematics that helps explain them. The project will involve the training of undergraduate students.
In summer 2020, Professor Junge will use a portion of the NSF grant to run a Tiny Mathematics Research Community at Bard that vertically connects undergraduates, graduates, postdoctoral researchers, and professors in a retreat-style research workshop.
Professor Junge joined the Bard faculty this fall, coming to Annandale from Duke University, where he served as William W. Elliott Research Assistant Professor of Mathematics. He received his doctorate in mathematics from the University of Washington, where he also earned MS, BS, and BA degrees.
His areas of interest include probability, statistical physics, and mathematical biology. Professor Junge’s research takes a probabilistic approach to particle systems from physics and biology, including models for chemical reactions, species proliferation, and epidemic outbreaks. He also studies random structures from classical mathematics and computer science, such as permutations and fragmented spaces.
This semester, he is teaching Probability and Calculus I, as well as supervising a research project with two Bard undergraduate students. He also teaches in the Bard Prison Initiative, alongside Mathematics Program colleagues John Cullinan and Japheth Wood.
STEAM Explorers: Changing How Kids Think About Science and Math
By Sarah Wallock ’19
If you’re passing through the Reem-Kayden Center on a given Saturday afternoon, you may run into a group of middle school girls, chatting about math games and examining the origami designs that they just made in the Girls Math Club. Or, if you’re a patron of the Tivoli Library, you may come across a STEAM Workshop using soap and food coloring to make marbled milk paper and learn about how calcium affects saturation rates. Both programs are hosted by STEAM Explorers, an initiative of Bard’s Center for Civic Engagement (CCE) and Math Program. STEAM Explorers has two components: Bard Science Outreach and the Bard Math Circle. Together, they work to create experiences and design experiments that inspire wonder, spark curiosity, and challenge old ideas.
Sarah deVeer ’17 volunteered for STEAM Explorers as a Bard student; now, she runs the program as the science outreach coordinator. This year she has worked to expand the program beyond local partners in Red Hook, Rhinebeck, Kingston, and Tivoli to communities across the Hudson Valley such as in Beacon, Albany, and Hudson. Sarah also worked to revamp the curriculum, and to good effect: John Kemnitzer, the principal of Bulkeley Middle School in Rhinebeck, recently said that this year’s program was the best one yet.
Children participating in Bard’s STEAM Explorers program make marbled milk paper at the Tivoli Library. Photo by Sarah Wallock ’19.
“One aspect that I really love about Bard’s STEAM Explorers is that we don’t charge the schools or community for our programs,” says deVeer. “We offer these programs because we genuinely believe that Bard is a private institution operating in the public interest.” Working with six STEM fellows and 30 engagement mentors, STEAM Explorers collaborates with 12 partners in schools and community organizations throughout the Hudson Valley. DeVeer also coordinates science engagement efforts as part of Bard’s Citizen Science Program and Martin Luther King Jr. Day of Engagement. The most important part of discussing issues such as water quality and natural resource use with students, she notes, is how STEAM Explorers is “starting the conversation with the next generation.”
The Bard Math Circle was started in 2007 by mathematics students and faculty at Bard, to address the dearth of math enrichment opportunities in the Mid-Hudson Valley. It began with a monthly program at the Tivoli library, where the organizers brought puzzles, games, and toys that emphasized problem-solving skills and making math fun for all ages. Students attending the library programs reported doing better in their math courses at school because of their involvement with the project.
The Girls Math Club, led by Bard students, works on origami designs in the Reem-Kayden Center on Bard’s campus. Photo by Bari Bossis ’19.
From the outset, Bard undergraduates have been an integral part of the Math Circle, running and developing programs, leading hands-on workshops, and mentoring K-12 students. The Math Circle has expanded over time to include programs at several libraries, schools, and community centers; math contests and national math competitions; programs to empower girls in math; a Rubik’s Cube Club; special events for teachers and senior citizens; and the most popular program, a weeklong summer CAMP (Creative, Analytical Math Program) for middle schoolers, run primarily by Bard faculty, alumni/ae, undergraduates, and local high school volunteers who have taken part in Math Circle programs. One parent whose daughter participated in the Girls Math Club recently commented, “My child was always happy after meetings, and she liked the girls-only space to learn and explore.” Undergraduate leaders credit their involvement with the Math Circle as one of the highlights of their Bard experience. The majority of Math Circle student leaders choose to pursue a career in teaching after graduation.
STEAM Explorers started in 2010 as an effort to bring science and math to area students in new and creative ways. Bard Science Outreach fellows and Bard Math Circle faculty and volunteers work with more than 4,000 children and teens throughout the Hudson Valley each year. Partnering with local schools, they connect what students are learning in the classroom with real-world issues, especially those facing the Hudson Valley region.
During the month of January, Science Outreach fellows worked with six different school districts to host a Day of Science. The CCE outreach team conducted science experiments around the theme of Hudson River watershed health, from off-campus events at Chancellor Elementary in Rhinebeck and Smith Intermediate School in Hudson, to on-campus events for local middle school students. Bard students led activities that showed the importance of local aquifers to the ecosystem. Participants tested the salinity of the river water, played a PCB board game, explored pH filters, and demonstrated water conservation through interactive activities.
STEAM Explorers works to provide real-world applications in all its experiments, like dissecting owl pellets to classify rodent skeletons and building marshmallow towers to learn effective design and construction mechanisms. “My favorite experiment was when we played with owl pellets!” says Junnaria, a sixth-grade student in Perfect Ten, an after-school program in Hudson that empowers and mentors young girls. “It was so cool finding all the bones of the animals! This [experiment] has made me more curious about nature and biology.” Melissa, a seventh grader from Perfect Ten, comments, “I really liked the marshmallow tower. It showed me how to plan measurements for buildings. It’s cool to find out that math and science are in everything, even marshmallows.”
Antonio Gansley-Ortiz ’18, a science outreach engagement mentor, reflects on how his work with the STEAM Explorers continues to influence him: “In April while out having dinner with [another mentor], I ran into one of my middle school students. She recognized us and pointed us out to her parents. The entire family then came over and thanked us for the experience. They also mentioned the student hadn’t stopped talking about her excitement with science. That moment was incredibly fulfilling. I want to help provide that positive experience to other students in the community.”
STEAM Explorers Initiatives
Day of Science brings eighth graders from local school districts to the Bard campus to engage with Bard science fellows, faculty, and undergraduates in a series of themed science stations.
Girls Math Club for middle school girls run by Bard female math majors.
Math Circle Library Programs include puzzles, games, and fun math activities for upper elementary and middle school students.
Rubik’s Cube Club teaches kids how to master the Rubik’s Cube.
Science Fairs connect Black Student Organization fellows and volunteers to mentor local students preparing to enter school science fairs.
Science for Kids brings in-school, hands-on science experiments to K-5 students by using household products in new ways.
Science Saturday brings children and families together with Bard students at local libraries and community centers to participate in science enrichment activities.
STEM Night Out invites young students throughout the Hudson Valley to an evening of fun, hands-on scientific experiments led by science fellows and Bard first-year students.
Adam Lowrance, Vassar College Hegeman 1024:00 pm – 5:00 pm EDT/GMT-4 Take off your shoelaces, tie them up, and fuse the two ends together to form a continuous lace without ends. Now you have a mathematical knot. Two knots are the same if you can move, bend, and stretch one until it looks exactly like the other. Now take a flashlight and point it at your knot. The shadow of your knot on the wall is called a knot diagram or a knot projection.
One common way to study knots is via their invariants, quantities that are associated with the knot that do not change regardless of how the knot is presented. One such invariant is the Jones polynomial. In this talk, we define the Jones polynomial of a knot and discuss what the Jones polynomial tells us about a knot.
Thursday, May 20, 2021
Join our graduating seniors in presenting their research! Main Commencement Tent5:30 pm – 7:00 pm EDT/GMT-4 Please see the abstract booklet below for full descriptions of students' research.
Ismar Volić, Wellesley College Online Event3:00 pm – 4:00 pm EDT/GMT-4 Simplicial complexes are versatile objects in the intersection of graph theory, combinatorics, topology, and geometry. While mathematicians have always appreciated the fact that simplicial complexes are extremely powerful in spite of being easy to define and relatively easy to work with, their usefulness in real-world applications has increased dramatically just in the last decade or so.
In this talk, I will first discuss the definition and the basic constructions that can be performed with simplicial complexes, toggling back and forth between combinatorics and topology. I will then give an overview of some of their recent applications in signal processing, neuroscience, data analysis, and social sciences. I will in particular describe ongoing work by several undergraduates at Wellesley College in which certain types of political systems and their interactions are modeled by simplicial complexes.
This talk should be accessible to anyone who has had some exposure to combinatorics (basics of combinations and permutations).
Mona Merling '09, University of Pennsylvania Online Event3:00 pm – 4:00 pm EDT/GMT-4 To avoid misleading anyone, this talk will not be about the sociology of topologists! "Social choice" is a model for decision making in economic, social, and political contexts. For example: suppose that each person gets to vote on their favorite location where they would like to place a statue on an island. Is there a fair way based on these votes to choose the location? This will turn out to be a topological, even a homotopical, problem, depending on the topology of the island. In this talk we will explore social choice models and answer the question about when they exist using algebraic topology.
The purpose of this talk is to serve as an advertisement for algebraic topology and basic category theory. I will not assume any background other than calculus (in particular the notion of continuity so that I can give an intuition about topology). Familiarity with abstract algebra will help, but I will err on the side of defining what a group is, and I will give a crash course in category theory.
Hala Nelson, James Madison University Online Event3:00 pm – 4:00 pm EDT/GMT-4 Today's popular AI is mostly software, algorithms, and big data processing. Mathematics powers most of these AI techniques that are rapidly integrated into every aspect of our society and are useful for a vast array of applications. AI agents only understand numbers, more specifically, blobs of zeros and ones. In this talk we will use undergraduate mathematics to make an AI agent process our natural language, recognize what she sees, and make intelligent decisions. We will work out simple examples that have wide applications in the Artificial Intelligence sphere. This is an extremely undergraduate friendly talk and you only need to have calculus and linear algebra backgrounds.
Florian Frick, Carnegie Mellon University Online Event1:30 pm – 2:30 pm EDT/GMT-4 How do you fairly divide rent among roommates, a necklace among thieves, or a pizza between friends? Such questions of fair division can often be understood with the tools of geometry and topology — even for those problems that are not geometric to begin with. We will discuss how to do this, and why topology is useful for problems that appear to be unrelated to topology. In particular, we will explore a relation between fairly splitting a necklace and inscribing shapes into curves. No prior knowledge of topology is needed, and this talk is available to all who are familiar with some linear algebra or multivariable calculus.
Galen Dorpalen-Barry '15, University of Minnesota Online Event3:00 pm – 4:00 pm EDT/GMT-4 In 1943, J. L. Woodbridge of Philadelphia submitted the following problem to American Mathematical Monthly: “Show that n cuts can divide a cheese into as many as $(n+1)(n^2 - n + 6)/6$ pieces.”
This question and its solution are deeply connected to the study of collections of lines in $mathbb{R}^2$, planes in $mathbb{R}^3$, and more generally hyperplanes in $mathbb{R}^n$. We will explore the solution and a more general version: given n (hyper)planes in a real, d-dimensional vector space, how can we figure out the number of chambers of an arrangement of hyperplanes, without necessarily being able to see and count them?
There are many wonderful solutions to this question. We present one provided by the Varchenko-Gel’fand ring, which is the ring of functions from the chambers of the arrangement to the integers with pointwise addition and multiplication. Varchenko and Gel’fand gave a simple presentation for this ring, which can be computed using simple facts about linear algebra.
We will assume very little background but expect that the audience is familiar with linear independence and dependence. We will give a ring-theoretic solution to this problem, so it may be helpful (but not necessary) to be familiar with quotient rings.
Ethan Bloch, Bard College Online Event3:00 pm – 4:00 pm EDT/GMT-4 In this talk we discuss the interplay between curvature and the distance between points on polyhedra. We start by discussing the curvature of polyhedra, which is concentrated at the vertices, and we then consider the question of whether or not a shortest path between two points on a polyhedron can pass through a vertex. We then discuss an attempt, not yet successful, at finding a polyhedral analog of Myers' Theorem for smooth surfaces, which relates positive curvature to distances between points. Along the way we consider some questions about the unfolding of polyhedra (for example, unfolding a cardboard box so that it is flat). This talk is open to all.
Lauren Rose, Bard College Online Event3:00 pm – 4:00 pm EDT/GMT-4 Generalized splines on a graph G with edge weighted by ideals a commutative ring R are R-vertex labelings such that if two vertices share an edge in G, the vertex labels are congruent modulo the edge ideal. When R is a principal ideal domain, we introduce collapsing operations that reduces any simple graph to a single vertex and carries along the edge ideal information. This corresponds to a sequence of surjective maps between the associated spline modules, and leads to an explicit construction of an R-module basis in terms of the edge ideals. We also solve an interpolation problem, i.e., given a partial vertex labeling, when can it can be extended to a generalized spline?
Pablo Soberón, Baruch College Online Event3:30 pm – 4:30 pm EST/GMT-5 Given a family of convex sets in R^d, how do we know that their intersection has a large volume or a large diameter? A large family of results in combinatorial geometry, called Helly-type theorems, characterize families of convex sets whose intersections are not empty. During this talk we will describe how some bootstrapping arguments allow us to extend classic results to describe when the intersection of a family of convex sets in R^d is quantifiably large. The work presented in this talk was done in collaboration with undergraduate students.