Aparna Higgins

Professor
Full-Time Faculty
College of Arts and Sciences: Mathematics

Profile

Dr. Higgins was born and raised in Bombay (now Mumbai), India. She completed a B.Sc. degree with mathematics as her principal subject, and physics as her subsidiary subject, in Bombay, and then earned her M.S. and Ph.D. degrees in mathematics at the University of Notre Dame, USA. Her current area of research is in graph theory, with special interests in pebbling on graphs and iterated line graphs. She joined the faculty of the University of Dayton's Department of Mathematics in 1984. She has spent her sabbaticals and other leaves of absence teaching at the Naval Postgraduate School and at the United States Military Academy.

Aparna Higgins has been honored with teaching awards from the College of Arts and Science and the Alumni Award at UD, and the Award for Distinguished University or College Teaching from the Ohio Section of the Mathematical Association of America. Dr. Higgins is known within the mathematics community for her work on undergraduate research in mathematics. She has directed Honors theses at UD, and has co-directed Research Experiences for Undergraduates sponsored by the National Science Foundation. She is invited to conduct workshops and minicourses around the country for mathematics faculty on getting students involved in undergraduate research.

Aparna Higgins is very involved with the work of the Mathematical Association of America (MAA), which is the largest professional society devoted to the teaching of undergraduate mathematics. She currently serves as a co-director of Project NExT (New Experiences in Teaching), which is a professional development program for new and recent Ph.D.s in the mathematical sciences, and which addresses all aspects of an academic career: improving the teaching and learning of mathematics, engaging in research and scholarship, and participating in professional activities. Dr. Higgins also served as member and chair of the MAA Committee on Student Chapters, helping to establish and maintain student chapters of the MAA at colleges and universities, and to provide programming directed towards undergraduates at the national and regional meetings.

Faculty Perspective

I love mathematics, and I love teaching. I enjoy reading mathematics and reading about it, I enjoy discussing mathematical things - even jokes, and I enjoy spending time with mathematicians and with students who are interested in mathematics. My current interests are in pebbling on graphs, a concept that can find applications to any kind of movement of supplies or information during which some loss of supplies or information can be expected. I am also interested in networks - if you have six cities and the means of connecting any nine pairs of those with cables, which pairs should you choose to create a "strong" network? Another research is purely mathematical and has no application that I know of - except to engage the mind - an area known as iterated line graphs. I am happy to work in a wonderful department with colleagues who are passionate about teaching and learning and mathematics, and who want to pass on this zeal to students who are interested.

I teach all kinds of mathematics and enjoy the material anew every time, be it calculus or abstract algebra, contemporary mathematics or analysis, linear algebra or graph theory. I like to try various types of course delivery and various types of assessment, to see whether some students benefit more by one or another. So, I often lecture, but I also have students work in groups, and assign projects, and web assignments. In my upper-level courses, students spend some time reading a paper in the mathematical literature, filling in gaps, and presenting the results as an expository talk.

The most fulfilling part of my career has been the privilege of working with undergraduates on mathematical research. UD provides interested undergraduates with the opportunity of writing a senior thesis in their major. See more on this program at http://honors.udayton.edu/. For those students who don't really want to commit a year researching a topic in mathematics, there are plenty of opportunities for a taste of such activity - working with some math faculty and then presenting results of your research at a mathematics meeting. I enjoy working with students on these shorter projects too. I was honored to be a co-director of an NSF-sponsored REU (Research Experiences for Undergraduates) program here at the University of Dayton in the early nineties.

I am a co-director of Project NExT (New Experiences in Teaching), which is a program of the MAA for new and recent Ph.D.s in mathematics. I love every aspect of this program (http://archives.math.utk.edu/projnext/), from selecting and meeting sixty new teaching colleagues each year, to organizing a workshop for them at the beginning of their year-long sojourn as a Project NExT Fellow, to helping them organize future workshops for themselves, to matching them with more experienced faculty who serve as consultants to the Fellows. This was a perfect fit for my interests and strengths after a long stint as one of the charter members of the MAA Committee on Student Chapters. I enjoy serving the MAA in various capacities - some of the more enjoyable assignments have been helping to select invited speakers at national meetings. I am also involved with the Ohio Section of the MAA, and served as its President a few years ago.

Degrees

  • Ph.D., University of Notre Dame, 1983

Research Interests

  • Pebbling in graphs
  • Iterated line graphs
  • Measures of the strength of networks

Selected Publications

1. "Research by undergraduates is hot!" (with Joseph A. Gallian), FOCUS, newsletter of the MAA, March 2002.

2. "Multi-faceted undergraduate research in mathematics at the University of Dayton," Proceedings of the Conference on Summer Undergraduate Mathematics Research Programs, AMS Publications, June 2000.

3. "Helping students present their research," (with Joseph A. Gallian), Proceedings of the Conference on Summer Undergraduate Mathematics Research Programs, AMS Publications, June 2000.

4. "Project NExT," (with Joseph A. Gallian, Matt Hudelson, Jon Jacobsen, Tammy Lefcourt, T. Christine Stevens), Notices of the AMS, February 2000.

5. "Maximum Degree Growth of the Iterated Line Graph," Stephen G. Hartke and Aparna W. Higgins, Electronic Journal of Combinatorics, 6 (1999), #R28.

6. "The Pebbling Number of C5xC5," (with David Herscovici), Discrete Mathematics, 187 (1998) 123-135.

7. "What is the lowest position of the center of mass of a soda can?" PRIMUS, Volume VII, Number 1, March 1997.

8. "An interesting example using induction", Mathematics and Computer Education, volume 24, number 2, Spring 1990, 130-134.

9. "A little algebraic equivalence." The Mathematical Gazette, volume 73, number 463, March 1989.

10. "A representation theorem for weak automorphisms of a universal algebra." Algebra Universalis 20 (1985) 179-193.