JMU Math & Stat: Experimental Mathematics Lab

Welcome to the JEM Lab

Originally known as the JMU Math MakerLab, the JEM Lab offers opportunities for experimental and exploratory research in mathematics to students who are early in their undergraduate careers. To this date more than 60 undergraduates and 8 faculty mentors have completed collaborative mathematical research projects in the JEM Lab.

About the JMU Experimental Mathematics Lab

The JEM Lab is an experimental laboratory space founded in 2013 by Dr. Laura Taalman in the Department of Mathematics & Statistics at James Madison University. In 2021 the JEM Lab became a member of Geometry Labs United, a consortium of technology research labs at national and international research universities. The JEM Lab is proud to be the first and only Geometry Lab at a primarily undergraduate institution.

Computational exploration

Students who work in the JEM Lab leverage a wide variety of computational tools and resources to explore mathematics. Past projects have used software such as Mathematica, MATLAB, Knot Plot, Seifert View, and the Online Encyclopedia of Integer Sequences to conjecture and test mathematical ideas; this year's main project will use Processing. To visualize mathematical objects we use 3D design software such as OpenSCAD, Fusion 360, Meshmixer, TopMod, and Grasshopper. To share our designs we use the 3D/VR platform Sketchfab.

JEM Lab students are usually first-year or second-year undergraduates, with no previous experience with any mathematical or design software packages, and that is how we like it! Everyone in the JEM Lab learns what they need to learn, when they need to learn it.

3D printing

The JMU Experimental Mathematics Lab started out as a 3D printing MakerLab. Over time our 3D modeling and printing capacity has increased significantly, though funds from the JMU College of Science & Mathematics, the JMU Department of Mathematics & Statistics, and a small equipment sponsorship from 3D printing company Ultimaker. Our equipment now includes a multi-material dual-nozzle 3D printer, a large-nozzle 3D printer, a small off-site loan printer, and a resin printer with post-processing station. We also explore laser cutting and fiber arts such as crochet, knitting, and weaving. Students in the JEM Lab are able to produce physical mathematical visualizations with fine detail, multiple colors, and/or in large size.

Many of our student projects cultimate in the production of 3D visualizations of mathematical objects. Understanding, designing, and then actually producing such visualizations is a way for early undergradate students to pursue their own creative mathematical explorations. In addition, the resulting visualizations support outreach projects and inspire new students to ask questions and get involved with JEM Lab projects.

Current and recent projects

Crochet & Code (Dr. Taalman)
Cameron Barb, Kae Birch, Jared Gonzalez, Claire Jones, Josh Makela, Abigail McClennan, Lauren Wiermanski
Menger Slices and Volume by Shells (Dr. Taalman)
Carolyn Angelillo (senior Lab Tech for the JEM Lab)
Firefly Synchronization (Dr. Oh and Dr. Thelwell)
Dhanshree Atre, Gerardo Cruz Mejia, Rafael Dietsch, Izzy Dionne, Treya Gunn, Bryce Jennings, Janefer Lobo Funez, Ellona Macmillan, Carolina Moscote Rodriguez, Juan Resendiz-Perez, Sahara Sania, Micari Turner, Trey Vaughn (the 2022 Haynes Scholars), and Carolyn Angelillo (senior Lab Tech for the JEM Lab)
Stick Knot Conformations (Dr. Arnold and Dr. Taalman)
Alexis Alston, Bryce Anderson, Brevin Bugauisan, Mikiela Campbell, Eliana Diaz-Aceituno, Marvin Fuentes, Amaya Hamilton, Jada Marie Herrera, James Love, Jordan Milton, Valeria Moscote Rodriguez, Derrell Plair, Sukriti Sharma, Jayme Stevenson, Chayse Tucker, Jasmine White, and Jada White (the 2021 Haynes Scholars), and Carolyn Angelillo (senior Lab Tech for the JEM Lab)
Intrinsically Knotted Graphs (Dr. Lucas and Dr. Taalman)
Seeking future students!

Past Projects

Past student projects in the JEM Lab have covered a wide range of topics, under the mentorship of faculty mentors Laura Taalman, Steven Lucas, John Bowers, Rebecca Field, Caroline Lubert, Minah Oh, and Eva Strawbridge:

Spatial Graphs
Hannah Critchfield, Abigail Eget, Benjamin Flint, William Nettles, and Becky Wild
Submitted research paper: Ideal Spatial Graph Configurations
Interactive visualizations and downloadable models: Catalog of 3D-Printable Spatial Graphs
Optimized Tritangentless Knots
Abigail Eget, Harley Meade, and William Nettles
Published research paper: Optimizing Morton's Tritangentless Knots for Rolling
Rocket Exhaust Trench Modelling
Lyndon Swarey
Collaboration with Dr. Caroline Lubert's Aeroacoustics Lab
Praxinoscope Knot Isotopy
Jonathan Gerhard
With support from a $1000 Education grant from Shapeways
Ars Geometrica Seminar
Xiang Chen, Quincy Mast, and Adam Slattum
Collaboration with Dr. John Bowers' Ars Geometrica Lab
Strongly Regular Graphs
Jonathan Gerhard
Blog post at Mathematical ADD: Visualizing the difference between Rook and Shirkhande graphs
Spiral Knot Determinants
Charlie Kim and Ryan Stees
Published research paper: Sequences of Spiral Knot Determinants
Knot Conformations
Jonathan Gerhard, Gregory Houchins, Kirill Korsak, Taylor Meador, and Patrick Moran
Descriptions and downloadable models: 3D-printed Conformations of Knots Through 7 Crossings
Multi-material 3D Printing
Zev Woodstock
Experimental hardware with the 3D Systems CubeX Trio
C-elegans Worm Locomotion
Jeff Kopsick
JMU article about this project: Cross-disciplinary locomotion study
Finite Element Method
Brock Crook
Final REU Report: Finite Element Methods for the Poisson Equation and its Applications
Afinia Engineering and 3D Prototyping
Brandon Lancaster and Ryan Moneymaker
Original MakerLab blog: jmumakerhome.blogspot.org

Courses and Programs

Some of the student projects in the JEM Lab take place through informal independent study, and some run as listed semester courses. The JEM Lab also supports student work in other semester research courses. The following JMU courses and research programs have been supported by the JEM Lab:

Spring 2023: Haynes Scholars Research Seminar: Firefly Synchronization
Spring 2022: Haynes Scholars Research Seminar: Minimal Stick Knot Conformations
Fall 2017, Spring 2018: Ars Geometrica Seminar: 3D Graphs and Discrete Geometry
Fall 2017 - MATH 297: Spatial Graphs and 3D Printing
Spring 2017 - Ars Geometrica Seminar: Pushing 3D Printing Boundaries
Spring 2017 - MATH 297: Homotopy and 3D Printing
Spring 2014, Fall 2014, Spring 2015 - Honors Thesis: Spiral Knots
Spring 2014 - MATH 297: Knot Theory and 3D Printing
Fall 2013, Spring 2014 - Star Student Program: Multimaterial 3D Printing
Summer 2013 - Internal Math/Stat REU: 3D Printing Laboratory
Spring 2013 - MATH 167: Mathematical 3D Fabrication
Summer 2012 - Internal Math/Stat REU: Knot Determinant Patterns