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Math - Wabash Summer Institute in Algebra (WSIA)

The Wabash Summer Institute in Algebra offered 12 undergraduate students an unprecedented opportunity to conduct algebraic research with top faculty on the campus of a private college during the summers of 2005, 2006, and 2007. (Its grant from the National Science Foundation expired after the 2007 session.)

See WSIM for the NSF-funded REU for 2008.

WHAT: The Wabash Summer Institute in Algebra (WSIA) is an eight-week research experience in abstract algebra for undergraduates. Participants will explore three diverse areas in abstract algebra and conduct original research in small teams in one of these areas. In addition, participants will engage in seminars designed to investigate the ethics of research. Select participants will present their results at the Joint Mathematical Meetings in San Diego in January of 2008.

WHO: WSIA is open to undergraduates who have coursework in mathematics up through and including a course in abstract algebra, though a course in linear algebra may suffice in exceptional cases. Participants must be a citizens or permanent residents of the United States or its possessions. WSIA is interested in attracting a broad and diverse group of participants with an emphasis on students from smaller colleges and universities. Female, minority and disabled students are especially encouraged to apply. (See identification of 2005 WSIA participants at bottom of page.)

WHEN: WSIA ran from June 6 to July 29 in 2005, June 5 to July 28 in 2006, and June 4 to July 27 in 2007.

WHERE: WSIA is hosted by Wabash College located in Crawfordsville, Indiana. Wabash College is located within an hour of downtown Indianapolis and within 30 minutes of Purdue University.

PURPOSE: The Wabash Summer Institute in Algebra is designed to introduce participants to the world of research mathematics in a collegial and cooperative environment and to encourage participants to explore the possibilities afforded by graduate studies in the mathematical sciences. In addition, WSIA seeks to provide the opportunity for participants to carefully examine and discuss the ethical considerations involved in conducting scientific research.

FORMAT: Participants will spend the first four weeks working together to explore three areas of abstract algebra as well as the ethics of scientific inquiry. During the remaining four weeks, participants will be divided into teams of four that will conduct original research into one of the three areas of algebra explored earlier. Each team will be guided by an experienced research leader, and teams will meet regularly to discuss their results.

STIPEND: Participants will receive a stipend of $2400 for the eight weeks and free lodging. In addition, travel expenses to and from Wabash College will be provided. Funding is provided by the National Science Foundation.


Mike Axtell is an Associate Professor of Mathematics at Wabash College. Prof. Axtell’s area of research is Commutative Ring Theory with a focus on the role played by zero divisors within the structure of rings. Prof. Axtell will focus on a structure that blends elementary graph theory with the study of zero divisors – namely the graph of zero divisors. This remarkably elegant structure has recently become a topic of active investigation within the Commutative Ring community. The broad goal of the investigation will be to learn more about the behavior of zero divisors in a ring by examining the structure of the zero divisor graph.

J.D. Phillips is Professor and Chair of Mathematics and Computer Science at Wabash College. Prof. Phillips works in a number of areas of algebra, with a particular emphasis on algebras with a single binary operation, e.g., quasigroups and loops, groups, distributive groupoids, semigroups, etc. In recent years he has used automated theorem provers and finite model builders in his research. Prof. Phillips will introduce students to some of these computational tools in investigating quasigroups and loops.

William Turner is an Assistant Professor of Mathematics and Computer Science at Wabash College. Prof. Turner’s area of research is Black Box Linear Algebra – a blend of algorithms, linear algebra and abstract algebra – whose aim is to improve a computer’s ability to answer questions related to linear algebra using exact arithmetic. Prof. Turner will introduce students to the world of Black Box Linear Algebra and will guide a team of students in exploring efficient preconditioners for these linear algebra problems, including exchange matrices for arbitrary radix switching networks.

David Neidorf is the director of the Integrated Studies Program at Middlebury College. In addition, David Neidorf is the director of Educational Programs, Bioethics-In-Action, Inc., a developer of curricular and pedagogical modules for non-partisan educational programs in the ethics of human biotechnology. Prof. Neiedorf will conduct a one-week workshop whose goals are to provide promising students a significant and formative exposure to the interface between work in mathematics and ethics, to ensure that participants are thoughtfully aware of their responsibilities as both professionals and citizens, and are alert to the tensions and conflicts between these two roles, and to empower the skillful discussion and resolution of concrete ethical problems through the examination of ethical case studies according to varying schema of conceptual evaluation.

Funding provided by the National Science Foundation

In group photo above: 2005 WSIA participants: Top row, left to right: Mike Lawlor (Wabash College), Mollie Kerrigan (Merrimack College), Michael McGowan (John Carroll University), Linda Scalici (Bucknell University), Chris Jackson (Wabash College), and Tristan Brand (Harvey Mudd College). Front row, left to right: Jacob Carson (Lafayette College), Catherine Crompton (Agnes Scott College), J.D. McKeel (University of Evansville), Josean Figueroa (University of Puerto Rico - Mayaguez Campus), Paige Rinker (Kalamazoo College), and Marie Jameson (Harvey Mudd College).