A Primer for Undergraduate Research

1. Front Matter

   Pages i-vii

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2. Coxeter Groups and the Davis Complex

   • Timothy A. Schroeder

   Pages 1-33

3. A Tale of Two Symmetries: Embeddable and Non-embeddable Group Actions on Surfaces

   • Valerie Peterson, Aaron Wootton

   Pages 35-59

4. Tile Invariants for Tackling Tiling Questions

   • Michael P. Hitchman

   Pages 61-84

5. Forbidden Minors: Finding the Finite Few

   • Thomas W. Mattman

   Pages 85-97

6. Introduction to Competitive Graph Coloring

   • C. Dunn, V. Larsen, J. F. Nordstrom

   Pages 99-126

7. Matroids

   • Erin McNicholas, Nancy Ann Neudauer, Colin Starr

   Pages 127-144

8. Finite Frame Theory

   • Somantika Datta, Jesse Oldroyd

   Pages 145-170

9. Mathematical Decision-Making with Linear and Convex Programming

   • Jakob Kotas

   Pages 171-191

10. Computing Weight Multiplicities

    • Pamela E. Harris

    Pages 193-222

11. Vaccination Strategies for Small Worlds

    • Winfried Just, Hannah Callender Highlander

    Pages 223-264

12. Steady and Stable: Numerical Investigations of Nonlinear Partial Differential Equations

    • R. Corban Harwood

    Pages 265-303

13. Back Matter

    Pages 305-313

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This highly readable book aims to ease the many challenges of starting undergraduate research. It accomplishes this by presenting a diverse series of self-contained, accessible articles which include specific open problems and prepare the reader to tackle them with ample background material and references. Each article also contains a carefully selected bibliography for further reading.

The content spans the breadth of mathematics, including many topics that are not normally addressed by the undergraduate curriculum (such as matroid theory, mathematical biology, and operations research), yet have few enough prerequisites that the interested student can start exploring them under the guidance of a faculty member. Whether trying to start an undergraduate thesis, embarking on a summer REU, or preparing for graduate school, this book is appropriate for a variety of students and the faculty who guide them. 

• Undergraduate Research
• Expository Articles
• Open Problems
• General Interest
• Recreational Mathematics
• matrix theory

“This book is a superb resource for students and faculty mentors embarking on undergraduate research in mathematics. Its focus is on topics and applications rarely covered in the traditional undergraduate math curriculum, offering novice researchers a sturdy jumping-off point to a broad array of research problems. … A valuable resource for students and faculty mentors interested in undergraduate research.” (V. K. Chellamuthu, Choice, Vol. 56 (2), October, 2018)

• Department of Mathematics, University of Portland, Portland, USA

  Aaron Wootton, Valerie Peterson, Christopher Lee

Aaron Wootton, Valerie Peterson and Christopher Lee are all current professors in the Mathematics department of the University of Portland.

Professor Wootton's research interests include Complex Algebraic Geometry: Defining equations for Riemann Surfaces, Quasiplatonic Surfaces and Dessins D'Enfants, Automorphism Groups of Compact Riemann Surfaces; Group Theory: Finite Groups (Group Actions and Structure Theory), Finitely Presented Groups; Geometric Group Theory: Discrete Groups (Fuchsian Groups and Fundamental Groups), Mapping Class Groups of Compact Connected Surfaces.

Professor Peterson's research interests include algebraic topology, metric and combinatorial geometry, geometric group theory, and the teaching and learning of mathematics.

Professor Lee's research interests include equivariant differential topology and geometry. In particular: Hamiltonian Lie group actions on (folded) symplectic and contact manifolds, symmetry in completely integrable systems, applications of (combinatorial and smooth) Morse theory, and singularities of differentiable mappings.

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