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Mathematics Research for the Beginning Student, Volume 1

Accessible Projects for Students Before Calculus

  • Textbook
  • © 2022

Overview

Editors:
  1. Eli E. Goldwyn

    1. Mathematics, University of Portland, Portland, USA

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  2. Sandy Ganzell

    1. Mathematics & Computer Science, St. Mary’s College of Maryland, St. Mary’s City, USA

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    You can also search for this editor in PubMed   Google Scholar

  3. Aaron Wootton

    1. Mathematics, University of Portland, Portland, USA

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    You can also search for this editor in PubMed   Google Scholar

  • Focuses on mathematics research topics suitable for students who have not yet taken calculus
  • Equips students with the tools needed to begin their own mathematics research projects, with or without faculty advisors
  • Provides substantial background material and recommendations for further reading in each chapter

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Table of contents (9 chapters)

  1. Front Matter

    Pages i-ix
    Download chapter PDF

  2. Games on Graphs: Cop and Robber, Hungry Spiders, and Broadcast Domination

    • Joshua Carlson, Pamela E. Harris, Peter Hollander, Erik Insko
    Pages 1-19

  3. Mathematics for Sustainable Humanity: Population, Climate, Energy, Economy, Policy, and Social Justice

    • Jue Wang
    Pages 21-56

  4. Mosaics and Virtual Knots

    • Sandy Ganzell
    Pages 57-79

  5. Graph Labelings: A Prime Area to Explore

    • Elizabeth A. Donovan, Lesley W. Wiglesworth
    Pages 81-111

  6. Acrobatics in a Parametric Arena

    • Therese Shelton, Bonnie Henderson, Michael Gebhardt
    Pages 113-136

  7. But Who Should Have Won? Simulating Outcomes of Judging Protocols and Ranking Systems

    • Ann W. Clifton, Allison L. Lewis
    Pages 137-171

  8. Modeling of Biological Systems: From Algebra to Calculus and Computer Simulations

    • Alexander Dimitrov, Giovanna Guidoboni, William Hall, Raul Invernizzi, Sergey Lapin, Thomas McCutcheon et al.
    Pages 173-226

  9. Population Dynamics of Infectious Diseases

    • Glenn Ledder, Michelle Homp
    Pages 227-285

  10. Playing with Knots

    • Allison Henrich
    Pages 287-318
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Keywords

About this book

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.


Editors and Affiliations

  • Mathematics, University of Portland, Portland, USA

    Eli E. Goldwyn, Aaron Wootton

  • Mathematics & Computer Science, St. Mary’s College of Maryland, St. Mary’s City, USA

    Sandy Ganzell

About the editors

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.

Bibliographic Information

  • Book Title: Mathematics Research for the Beginning Student, Volume 1

  • Book Subtitle: Accessible Projects for Students Before Calculus

  • Editors: Eli E. Goldwyn, Sandy Ganzell, Aaron Wootton

  • Series Title: Foundations for Undergraduate Research in Mathematics

  • DOI: https://doi.org/10.1007/978-3-031-08560-4

  • Publisher: Birkhäuser Cham

  • eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)

  • Copyright Information: The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2022

  • Hardcover ISBN: 978-3-031-08559-8Published: 25 November 2022

  • Softcover ISBN: 978-3-031-08562-8Published: 25 November 2023

  • eBook ISBN: 978-3-031-08560-4Published: 24 November 2022

  • Series ISSN: 2520-1212

  • Series E-ISSN: 2520-1220

  • Edition Number: 1

  • Number of Pages: IX, 318

  • Number of Illustrations: 108 b/w illustrations, 103 illustrations in colour

  • Topics: Mathematics, general, Mathematics Education

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