A Project-Based Guide to Undergraduate Research in Mathematics

1. Front Matter

   Pages i-xi

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2. Folding Words Around Trees: Models Inspired by RNA

   • Elizabeth Drellich, Heather C. Smith

   Pages 1-28

3. Phylogenetic Networks

   • Elizabeth Gross, Colby Long, Joseph Rusinko

   Pages 29-61

4. Tropical Geometry

   • Ralph Morrison

   Pages 63-105

5. Chip-Firing Games and Critical Groups

   • Darren Glass, Nathan Kaplan

   Pages 107-152

6. Counting Tilings by Taking Walks in a Graph

   • Steve Butler, Jason Ekstrand, Steven Osborne

   Pages 153-176

7. Beyond Coins, Stamps, and Chicken McNuggets: An Invitation to Numerical Semigroups

   • Scott Chapman, Rebecca Garcia, Christopher O’Neill

   Pages 177-202

8. Lateral Movement in Undergraduate Research: Case Studies in Number Theory

   • Stephan Ramon Garcia

   Pages 203-234

9. Projects in (t, r) Broadcast Domination

   • Pamela E. Harris, Erik Insko, Katie Johnson

   Pages 235-262

10. Squigonometry: Trigonometry in the p-Norm

    • William E. Wood, Robert D. Poodiack

    Pages 263-286

11. Researching in Undergraduate Mathematics Education: Possible Directions for Both Undergraduate Students and Faculty

    • Milos Savic

    Pages 287-302

12. Undergraduate Research in Mathematical Epidemiology

    • Selenne Bañuelos, Mathew Bush, Marco V. Martinez, Alicia Prieto-Langarica

    Pages 303-324

This volume provides accessible and self-contained research problems designed for undergraduate student projects, and simultaneously promotes the development of sustainable undergraduate research programs. The chapters in this work span a variety of topical areas of pure and applied mathematics and mathematics education. Each chapter gives a self-contained introduction on a research topic with an emphasis on the specific tools and knowledge needed to create and maintain fruitful research programs for undergraduates. Some of the topics discussed include:
• Disease modeling
• Tropical curves and surfaces
• Numerical semigroups
• Mathematics Education
This volume will primarily appeal to undergraduate students interested in pursuing research projects and faculty members seeking to mentor them. It may also aid students and faculty participating in independent studies and capstone projects.

• Undergraduate research in mathematics
• Phylogenetic networks
• Tropical Geometry
• Numerical Semigroups
• Squigonometry
• Mathematical Epidemiology
• Tilings
• combinatorics

“The book at hand provides readers with workable, tangible, and sustainable examples of topics and areas for undergraduate mathematics students in the areas of combinatorics, number theory, graph theory, analysis, mathematics education, and applied mathematics (mathematical biology). … This reviewer highly recommends high-impact practices: mentored undergraduate research, capstone projects, and collaborative work. In this volume, mathematics instructors and undergraduates will find deep possibilities for summer projects, senior theses, and capstone seminars.” (Jennifer R. Bowen, The UMAP Journal, Vol. 44 (1), 2023)

• Mathematics, Williams College, Williamstown, USA

  Pamela E. Harris

• Mathematics, Florida Gulf Coast University, Fort Myers, USA

  Erik Insko

• Mathematics, University of Portland, Portland, USA

  Aaron Wootton

Pamela E. Harris is an Assistant Professor of Mathematics at Williams College in Williamstown, Massachusetts.

Erik Insko is an Associate Professor of Mathematics at Florida Gulf Coast University in Fort Myers, Florida.


Aaron Wootton is a Professor of Mathematics at the University of Portland in Portland, Oregon.

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