© 2017

A Primer for Undergraduate Research

From Groups and Tiles to Frames and Vaccines

  • Aaron Wootton
  • Valerie Peterson
  • Christopher Lee


  • A pioneering text providing state-of-the-art resources for faculty looking to mentor in undergraduate research and students looking to participate

  • Contains a wide range of topics, not normally addressed by the undergraduate curriculum, appropriate for student-faculty exploration that are from pure and applied math

  • A completely self-contained and accessible text with pre-requisites, specific open problems, directions for new research and a carefully selected bibliography included in every chapter

  • Equips readers to tackle the many challenges of starting undergraduate research


Table of contents

  1. Front Matter
    Pages i-vii
  2. Timothy A. Schroeder
    Pages 1-33
  3. Michael P. Hitchman
    Pages 61-84
  4. Thomas W. Mattman
    Pages 85-97
  5. C. Dunn, V. Larsen, J. F. Nordstrom
    Pages 99-126
  6. Erin McNicholas, Nancy Ann Neudauer, Colin Starr
    Pages 127-144
  7. Somantika Datta, Jesse Oldroyd
    Pages 145-170
  8. Pamela E. Harris
    Pages 193-222
  9. Winfried Just, Hannah Callender Highlander
    Pages 223-264
  10. Back Matter
    Pages 305-313

About this book


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

Editors and affiliations

  • Aaron Wootton
    • 1
  • Valerie Peterson
    • 2
  • Christopher Lee
    • 3
  1. 1.Department of MathematicsUniversity of PortlandPortlandUSA
  2. 2.Department of MathematicsUniversity of PortlandPortlandUSA
  3. 3.Department of MathematicsUniversity of PortlandPortlandUSA

About the editors

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.

Bibliographic information

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“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)