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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

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 on related graphs, submitted, 2014.
    • Presentation: 2008 SUMMR Conference at Michigan State University.
    • Support: NSF-REU grant.
    • Laura Ballard is currently a student at Syracuse University.
    • Erica Budge graduated from Hope College and is working in insurance in Michigan. University.