Undergraduate Research

(or how to assign intractable open questions to undergraduates)

Overview

1. What kinds of projects are we discussing?

2. How do such projects fit into the faculty workload and student curriculum?

3. How do we define successful for undergraduate research projects?

4. Tips, tricks, and logistics.

Kinds of projects

See math.scranton.edu/monks/pubs.html for details.

Student Publications

• C. Farruggia, M. Lawrence, B. Waterhouse; The Elimination of a Family of Periodic Parity Vectors in the Problem, Pi Mu Epsilon Journal, 10 (4), Spring (1996), 275-280 (1996 Richard V. Andree award winner)

• Fusaro, Marc, A Visual Representation of Sequence Space, Pi Mu Epsilon Journal, Pi Mu Epsilon Journal 10 (6), Spring 1997, 466-481 (1997 MAA EPADEL section student paper competition winner and 1997 Richard V. Andree award winner)

• Joseph, J.; A Chaotic Extension of the Function to , Fibonacci Quarterly, 36.4 (Aug 1998), 309-316 (1996 MAA EPADEL section student paper competition winner)

• Fraboni, M.;Conjugacy and the Conjecture (1998 MAA EPADEL section student paper competition winner)

• Kucinski, G.; Cycles for the Map on the Gaussian Integers, to appear, Pi Mu Epsilon Journal

• Riggi, C.; Hutchinson Operators in , honor's thesis, Spring 2001

• Yazinski, J.; Pseudoperiodicity of the Conjugacy Function (in preparation)

A Side Benefit - Faculty publications

• Monks, K.; minus the , Discrete Mathematics and Theoretical Computer Science, 5, no. 1, (2002), 47-54

• Monks, K. and Yazinski, J.; The Autoconjugacy of the Function , Discrete Mathematics, 275, (2004) pp 219-236

• Monks, K.; A Category of Topological Spaces Classifying Acyclic Set Theoretic Dynamics, in preparation

Other undergraduate projects

• Carter, N. and Monks, K.; Lurch!: Recipe-based Theorem Proving Software, FSRP project 1996-99

• Johnston, J.,Monks, K.; QuizMaker: Algorithmic Generation of Mathematical Assessments, SFTMP project, 2000-2001

• Pricci, V. and Solfanelli, G.; Algorithmic Generation of Mathematical Assessments in Exam Builder, SFTMP project, 1998-1999

Where do these projects fit in the curriculum?

• Faculty Student Research Program (FSRP)

  • Students get transcript recognition for a successfully semester of work

  • No tuition fee, no credit

  • Can participate for more than one semester

  • No monetary compensation for faculty

  • No reduction of teaching load for faculty

• Student Faculty Teaching Mentorship Program (SFTMP)

  • Analogous to FSRP but for teaching

• Honors program

• Faculty Directed Undergraduate Summer Research Grant

• Math 493-494: Mathematical Research

How do we define successful?

Tips, Tricks, and Logistics

Advice

1. Only mentor one student at a time!

2. Give yourself lots of time: 1.5-2.5 years per project!

3. You and the student must get along personally!

4. Much work is done in the summer and winter intersession.

5. Much work is done outside of school, at home, restaurants, by email, etc.

6. Lots of hand-holding, encouragement, and butt-kicking required!

Rewards of the trade

Benefits to students

• Experience the nature of mathematical research

• Graduate school preparation

• Looks great on graduate school applications

• Learn how to write a mathematical paper

Benefits to Faculty

• Counts toward promotion and tenure

• Justifies released time, grants, etc.

• The joy of talking about open problems at an undergraduate school

• It's just plain rewarding!