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Darin Stephenson's Undergraduate Research

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Math 231-232 Book About Me

Hope College mathematicians have been doing research with undergraduate students since the early 1990s. Therefore, undergraduate research is a longstanding part of the culture in our mathematics department. This page details the projects students have undertaken under my direction, and the resulting publications and presentations.

  • Summer 1998: Geoffrey Dietz and Ryan Higginbottom

  • Summer 1999: Andrea Douglass, Scott Mihalik and Courtney Fitzgerald

  • Spring 2001: Lee Kiessel and Brian Yurk

  • Summer 2001: Abigail Reck, Stephanie Wankier and Lee Kiessel

  • Summer 2003: Andrew Wells, Erika Frugoni and Nina Miller

  • Summer 2005: Shova KC and Anna Madras

  • Summer 2008: Jill Immink, HHMI Science Education Scholar

  • Summer 2008: Victoria Elandt, Nicholas James, Kathryn Johnson and Zachary Mitchell (project co-directed with Dr. Stephanie Edwards)

  • Summer 2012: Laura Ballard and Erica Budge

  • Summer 2017: Sarah Seckler and Russell Houpt (project co-directed with Dr. Mark Pearson)

Details about the students involved, the project, and related papers and talks are given below.


  • Summer 1998: Geoffrey Dietz and Ryan Higginbottom
    • Paper: Quantum 3-spaces which embed weighted quantum planes, Rocky Mountain Journal of Mathematics 35 (2005), 415-444.
    • Presentation: 1999 Joint Mathematics Meetings in San Antonio, TX.
    • Support: NSF-REU grant
    • Geoffrey Dietz graduated from the University of Dayton, and completed his PhD in commutative algebra at the University of Michigan. He is now a member of the mathematics faculty at Gannon University.
    • Ryan Higginbottom graduated from Bucknell University, and completed his PhD in algebraic topology at the University of Virginia. He is now a member of the mathematics faculty at Washington and Jefferson College.

  • Summer 1999: Andrea Douglass, Scott Mihalik and Courtney Fitzgerald
    • Paper: Expected areas of randomly generated triangles of fixed perimeter, Pi Mu Epsilon Journal, 11, No. 7, 2002, pp. 365-371.
    • Presentation: 1999 Hope College Mathematics Colloquium.
    • Presentation: 1999 PEW Undergraduate Research Conference, Chicago, IL.
    • Presentation: 2000 Joint Mathematics Meetings in Washington, DC.
    • Support: NSF-REU grant
    • Andrea (Douglass) Shaeffer graduated from Hope College and is a financial analyst.
    • Courtney (Fitzgerald) Slade graduated from Niagara University. She also attended the MASS program at Penn State University, and currently is a Math Editor for a publishing company.
    • Scott Mihalik graduated the University of Michigan and works in health care as a cardiovascular disease specialist.

  • Spring 2001: Lee Kiessel and Brian Yurk
    • Research in growth of algebras as an independent study course.
    • Presentation: 2001 MAA Annual Meeting, Michigan Section.
    • Lee Kiessel graduated from Hope College and completed a PhD in medical physics at the University of Wisconsin. He now works as a physics radiology consultant.
    • Brian Yurk graduated from Utah State University with a PhD in mathematical biology. He is now a faculty member at Hope College.

  • Summer 2001: Abigail Reck, Stephanie Wankier and Lee Kiessel
    • Paper: Noncommutative quadratic algebras with 2 generators (jointly with Darin Stephenson and Bryan Yurk).
    • Presentation: 2001 Hope College Mathematics Colloquium.
    • Presentation: 2002 Joint Mathematics Meetings in San Diego, CA.
    • Support: NSF-REU grant
    • Lee Kiessel graduated from Hope College and completed a PhD in medical physics at the University of Wisconsin. He now works as a physics radiology consultant.
    • Abigail (Reck) Brandsen graduated from Grand Valley State University.
    • Stephanie Wankier graduated from Utah State University, and is now teaching junior high school mathematics in Utah.

  • Summer 2003: Andrew Wells, Erika Frugoni and Nina Miller
    • Paper: Counting quadratic forms of rank 1 and 2, Pi Mu Epsilon Journal 12 (2009), No. 11, 613-622.
    • Presentation: 2003 Undergraduate Research Mini-conference at Central Michigan University.
    • Presentation: 2003 Michigan Undergraduate Mathematics Conference at Grand Valley State University.
    • Support: NSF-REU grant
    • Erika Frugoni graduated from Loyola-Marymount University in 2004, and received her PhD in mathematics from the University of Colorado-Boulder.
    • Nina Miller graduated from Valparaiso University in 2004, and is working for an educational publishing firm in South Carolina.
    • Andrew Wells graduated from Hope College in 2005, and received his PhD in mathematics from Iowa State University. He is currently an Assistant Professor at East Central University in Oklahoma.

  • Summer 2005: Shova KC and Anna Madras
    • Paper: Randomly generated triangles whose vertices are vertices of a regular polygon, Rose-Hulman Undergraduate Mathematics Journal 7, No. 1, 2006.
    • Presentation: 2005 Michigan Undergraduate Mathematics Conference at University of Michigan-Flint.
    • Presentation: 2005 Undergraduate Research Mini-conference at Grand Valley State University.
    • Support: NSF-REU grant
    • Shova KC graduated from Hope College and completed a Master's degree in survey methodology at the University of Maryland, College Park. She now works as a survey statistician for the National Opinion Research Center in Chicago.
    • Anna Madras graduated from Drury University and is teaching high school mathematics in Missouri.

  • Summer 2008: Jill Immink
    • Created a booklet of Maple labs and projects for the Math 231-232 Multivariable Mathematics sequence, in use during the 2008-09 academic year.
    • Created exercises for the Math 231-232 book being developed by Darin Stephenson.
    • Created learning assessments for the Maple labs and projects.
    • Explored ways to connect the topics of linear algebra and difference equations to the high school curriculum.
    • Presentation: 2008 SUMMR Conference at Hope College.
    • Funding: Howard Hughes Medical Institute Science Education Scholarship.
    • Jill Immink graduated from Hope College with a degree in mathematics, and is now teaching high school.

  • Summer 2008: Nicholas James, Zachary Mitchell, Kathryn Johnson and Victoria Elandt
    • Paper: Lights Out on Finite Graphs, Involve 3 (2010), No. 1, 17-32.
    • Presentation: 2008 SUMMR Conference at Hope College.
    • Presentation (by Zachary Mitchell): 2008 Michigan Undergraduate Research Conference at University of Michigan-Dearborn. This talk won an award for second place in the competition for "Best Talk" at the conference.
    • Support: NSF-REU grant and Hope College funds.
    • Victoria Elandt graduated from University of Wisconsin-Stevens Point.
    • Nicholas James graduated from the University of Florida, and is pursuing mathematics graduate work at Cornell University.
    • Kathryn Johnson graduated from Hope College and completed a graduate program in library sciences. She is now a reference librarian.
    • Zachary Mitchell is a graduated from Hope College and is pursuing graduate work in mathematics at Texas A&M

  • Summer 2012: Laura Ballard and Erica Budge
    • Paper: Lights Out for Graphs Related to One Another by Constructions, to appear.
    • Presentation: 2012 SUMMR Conference at Michigan State University.
    • Support: NSF-REU grant.
    • Laura Ballard is a student at Syracuse University.
    • Erica Budge graduated from Hope College and is working in insurance in Michigan.

  • Summer 2017: Sarah Seckler and Russell Houpt
    • Worked in developing software to use machine learning algorithms to determine bird species from bird song samples.
    • Sarah and Russell each made presentations at the 2017 SUMMR Conference at Grand Valley State University.
    • The presentation "What Bird Was That? Feature Extraction of Recorded Bird Songs for Neural Networks" by Sarah Seckler at the 2017 MathFest in Chicago won a Pi Mu Epsilon Outstanding Speaker Award.
    • The presentation "Name that Bird! Using Neural Networks to Identify Bird Songs" by Russell Houpt at the 2017 MathFest in Chicago won the Janet L. Andersen Award given for outstanding presentations in mathematical biology.
    • A poster presentation "Name That Bird: Using Neural Networks to Classify Recorded Bird Songs" by Russell Houpt at the 2017 Joint Mathematics Meetings in San Diego, CA, won an award for being in the "Top 15%" of posters in Biomathematics.
    • Support: Hope College.
    • Sarah and Russell are students at Hope College.