If a mathematics department has a capstone course, how does undergraduate
research figure into that capstone requirement? What challenges are involved when
instituting undergraduate research as part of the capstone experience? These were
the central questions for discussion in the undergraduate research as a capstone
requirement breakout session at the 2012 Trends in Undergraduate Research in the
Mathematical Sciences conference. In short, there is not one design that will
satisfy the needs and goals of every mathematics program, but a department
seeking to implement undergraduate research as a capstone requirement may
benefit from the experiences of other departments. This article discusses the
common objectives of a capstone in mathematical sciences and presents several
successful models that incorporate undergraduate research in a capstone
experience. The challenges and questions associated with each model are also
discussed.