Bücher der Reihe Foundations for Undergraduate Research in Mathematics

This volume provides accessible and self-contained research problems designed for undergraduate student projects, and simultaneously promotes the development of sustainable undergraduate research programs.

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.

Building New Models: Rethinking and Revising ODE Model Assumptions: Paul J. Hurtado.- A Tour of the Next Generation Reproductive Number and the Next Generation of Researchers.- The Effect of External Perturbations on Ecological Oscillators: Eli E. Goldwyn.- Exploring Modeling by Programming: Insights from Numerical Experimentation: Brittany E. Bannish and Sean M. Laverty.- Simulating Bacterial Growth, Competition, and Resistance with Agent-Based Models and Laboratory Experiments: Anne E. Yust and Davida S. Smyth.- Agent-Based Modeling in Undergraduate Biology: A Few Examples: Alexandra Ballow, Lindsey Chludzinski, and Alicia Prieto-Langarica.- Network Structure and Dynamics of Biological Systems: Deena Schmidt.- What Are The Chances? -Hidden Markov Models: Angela B. Shiflet, George W. Shiflet, Mario Cannataro, Pietro Hiram Guzzi, Chiara Zucco, Dmitry A. Kaplun.- Using Neural Networks to Identify Bird Species from Birdsong Samples: Russell Houpt, Mark Pearson, Paul Pearson, Taylor Rink, Sarah Seckler, Darin Stephenson, and Allison VanderStoep.- Using Regularized Singularities to Model Stokes Flow: A Study of Fluid Dynamics Induced by Metachronal Ciliary Waves: Elizabeth L. Bouzarth, Kevin R. Hutson, Zachary L. Miller, and Mary Elizabeth Saine.

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.

Speaking directly to the growing importance of research experience in undergraduate mathematics programs, this volume offers suggestions for undergraduate-appropriate research projects in mathematical and computational biology for students and their faculty mentors. The aim of each chapter is twofold: for faculty, to alleviate the challenges of identifying accessible topics and advising students through the research process; for students, to provide sufficient background, additional references, and context to excite students in these areas and to enable them to successfully undertake these problems in their research.Some of the topics discussed include: ¿ Oscillatory behaviors present in real-world applications, from seasonal outbreaks of childhood diseases to action potentials in neurons¿ Simulating bacterial growth, competition, and resistance with agent-based models and laboratory experiments¿ Network structure and the dynamics of biological systems¿ Using neural networks to identify bird species from birdsong samples¿ Modeling fluid flow induced by the motion of pulmonary ciliaAimed at undergraduate mathematics faculty and advanced undergraduate students, this unique guide will be a valuable resource for generating fruitful research collaborations between students and faculty.

This volume provides accessible and self-contained research problems designed for undergraduate student projects, and simultaneously promotes the development of sustainable undergraduate research programs.