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Mathematics research opportunities for undergraduate students have grown significantly in recent years, but accessible research topics for first- and second-year students with minimal experience beyond high school mathematics are still hard to find. To address this need, this volume provides beginning students with specific research projects and the tools required to tackle them. Most of these projects are accessible to students who have not yet taken Calculus, but students who know some Calculus will find plenty to do here as well. Chapters are self-contained, presenting projects students can pursue, along with essential background material and suggestions for further reading. Suggested prerequisites are noted at the beginning of each chapter. Some topics covered include:
- games on graphs
- modeling of biological systems
- mosaics and virtual knots
- mathematics for sustainable humanity
- mathematical epidemiology
Mathematics Research for the Beginning Student, Volume 1 will appeal to undergraduate students at two- and four-year colleges who are interested in pursuing mathematics research projects. Faculty members interested in serving as advisors to these students will find ideas and guidance as well. This volume will also be of interest to advanced high school students interested in exploring mathematics research for the first time. A separate volume with research projects for students who have already studied calculus is also available.
List of contents
Games on Graphs.- Mathematics for Sustainable Humanity--Population, Climate, Energy, Economy, Policy, and Social Justice.- Mosaics and Virtual Knots.- Graph Labelings: A Prime Area to Explore.- Acrobatics in a Parametric Arena.- But Who Should Have Won? Simulating Outcomes of Judging Protocols and Ranking Systems.- Modeling of biological systems: from algebra to calculus and computer simulations.- Population Dynamics of Infectious Diseases.- Playing with Knots.
About the author
Eli Goldwyn is Assistant Professor of Mathematics at the University of Portland. His research is focused on using mathematics to better understand and manage natural populations.
Sandy Ganzell is Professor of Mathematics at St. Mary's College of Maryland. His research covers knot theory, topology of 4-manifolds, and combinatorial game theory.
Aaron Wootton is Professor of Mathematics at the University of Portland. His research interests include complex algebraic geometry, group theory, and geometric group theory.
Report
"The volumes are an interesting blend of resource and textbook. Taken as a whole, the primary audience for each volume is mathematics instructors who are looking for a resource for independent inquiry projects for students. ... An instructor who is interested in creating opportunities for secondary and early undergraduate students to engage in self-directed exploration and inquiry in mathematics will find the volumes of this set a strong addition to their professional resources." (Duane Graysay, MAA Reviews, March 30, 2024)
