Academic Programs
Mathematics
Studying mathematics at Denison
MATHEMATICS IS THE STUDY OF ABSTRACTION, recognizing similar patterns in seemingly different settings and communicating those patterns precisely.
Professor Michael Westmoreland instructs a student in Denison's state-of-the-art F.W. Olin Science Hall
The mathematics faculty at Denison perform research and teach courses in knot theory, topology, functional analysis, operations research, algebra, quantum information theory, quantum computing, complex analysis, and differential equations.
Mathematics is taught at Denison within the joint department of Mathematics and Computer Science, which offers both B.A. and B.S. degrees with majors in both mathematics and computer science. For more information about the computer science major, please click here.
We offer many opportunities for mathematics students to become actively involved in research and other activities. The department hosts a chapter of Pi Mu Epsilon, the national mathematics honorary and an active math club. In addition, student fellows in the department are selected each year, based on their understanding of mathematics and their ability to communicate their ideas to other students.
We are located on the second floor of F.W. Olin Science Hall, a 46,000-square-foot facility with innovative laboratory and classroom space. We maintain three computer labs for student use, one containing Macintosh computers, one containing Linux workstations, and another "majors' lab" containing a mix of machines with non-standard software installed for student research projects.
The mathematics major and minor
We offer both a B.S. and a B.A. degree in Mathematics. Both degrees share a core of five common courses covering calculus, linear algebra, differential equations, and proof techniques.
In addition to the core, the B.S. degree requires a year each of advanced analysis and abstract algebra, a course in discrete mathematics, a course in continuous mathematics, introductory computer science, and two electives.
The B.A. degree requires, in addition to the core, one course in either advanced analysis or abstract algebra, a course in discrete mathematics, a course in continuous mathematics, introductory computer science, and two electives.
A minor in mathematics requires the five core courses and two additional electives.
For more detailed information, please visit the department's math curriculum page or the Denison course catalog.
What do mathematics majors do after Denison?
Michael Khoury '03 (right) co-authored a book with Professor Don Bonar titled 'Real Infinite Series' which has been published by the Mathematical Association of America.
Mathematics majors pursue careers in business, banking, teaching and government service, or continue their studies in graduate school. In recent years, our graduates have attended Clemson, North Carolina State, University of Texas, Indiana University, University of Illinois at Urbana-Champaign, Ohio State, West Virginia University, University of Wisconsin, and Purdue to pursue graduate studies.
Here is what some of our recent graduates are doing:
Colleen Hughes (2006)
Graduate Student, Clemson University
Jason Salazer-Adams (2006)
Graduate Student (Operations Research), North Carolina State University
Kati O'Neill (2006)
Graduate student, West Virginia University
Christopher Long (2005)
Graduate student, University of Texas
Patricia Garmirian (2005)
Graduate Student, Indiana University
Ethan Branum (2005)
Graduate Student (International Business), Brandeis University
Elizabeth Ehret (2004)
Graduate Student, The Ohio State University
Vanessa Miller (2004)
Business Analyst, Deloitte Consulting
Michael Khoury (2003)
Ph.D. Candidate, The Ohio State University
Ryan Mills (2003)
Manager of the Granville Office, Park National Bank
Opportunities for student research
Honors student Colleen Hughes '06 presented her summer research, 'Linked Triangle Pairs in K6,' at the Joint AMS/MAA Mathematical Meetings in Atlanta. Her work was chosen as one of the top undergraduate projects at the event.
Mathematics majors have numerous opportunities to engage in independent research projects with a faculty mentor. Independent research allows students to pursue topics that interest them in depth and is excellent preparation for graduate school. Anderson summer research fellowships pay students a stipend to work with a faculty mentor for 10 weeks in the summer. A student can also pursue a Senior Research Project or an Honors Thesis during his or her senior year.
Here are a few of the research projects recently completed by our mathematics students. For more, visit the department's research page.
Selected honors and senior research projects
Linked Triangle Pairs in K6
Colleen Hughes '06 Honors Project
Encoding Algebra as Affine Geometry
Patricia Garmirian '05 Honors Project
Selected summer research projects
Classifying n-Uniform Parseval Frames
Amanda Moore (2006)
Determining Links in Complete Graphs on Seven Vertices
Pamela Arbisi (2006)
Alliances in Graphs
Kati O'Neill (2005)
The Bus Driver's Sanity Problem
Jennifer Swank (2005)
Geometric Characterizations of Algebraic Systems
Patricia Garmirian (2004)
Straight Edge Embeddings of the Complete Graph on Six Vertices
Colleen Hughes (2004)
An extension of Colleen's work was recently published as Linked triangles in straight edge embeddings of K6 in the Spring 2006 issue of The Pi Mu Epsilon Journal.
Who are our professors?
There are ten full-time faculty in the combined Mathematics and Computer Science department, six of whom primarily teach mathematics. Altogether, we teach roughly 25 distinct courses annually, with an average class size of 25 to 30 in the introductory classes and 5 to 15 in the advanced classes.
Department Chair and Associate Professor Jessen Havill joined the Denison faculty in 1998. He earned a B.A. at Bucknell University and an M.S. and a Ph.D. at The College of William and Mary. He studies efficient approximation and online algorithms for resource allocation problems such as process scheduling and network routing.
The following faculty primarily teach mathematics. See the computer science page for information on the computer science program and faculty.
Professor Daniel Bonar holds the George R. Stibitz Distinguished Professorship in Mathematics and Computer Science. Bonar joined the faculty at Denison in 1965. He earned a B.S. and an M.S. at West Virginia University and a Ph.D. at Ohio State University. His research interests include complex analysis and differential equations and mathematical problem solving.
Assistant Professor Sarah Crown joined the faculty in 2007. She earned an A.B. at Bryn Mawr College and a Ph.D. at the University of Michigan.
Professor Todd Feil joined the faculty at Denison in 1982. He earned a B.A. at Millikin University, two master's degrees and a Ph.D. at Bowling Green State University. His research interests include ordered algebras and neural networks.
Assistant Professor Lewis Ludwig joined the faculty at Denison in 2002. He earned a B.S., a B.A. and an M.E. at the College of Mount St. Joseph, an M.S. at Miami University and a Ph.D. at Ohio University. His research interests include point-set topology, knot theory and domain theory.
Associate Professor Matthew Neal joined the faculty at Denison in 2001. He earned a B.A. and a Ph.D. at the University of Virginia. His research interests include functional analysis and algebra.
Professor Michael Westmoreland joined the faculty at Denison in 1990. He earned a B.A. at Rice University and a Ph.D. at the University of Texas, Austin. His research interests include foundations of quantum mechanics, quantum information theory, quantum computing and logic.
Visiting Instructor/Assistant Professor Laura D. Bosley joined the faculty in 2007. She earned her B.S. at Cedarville College, a M.A. at Miami University and is a Ph.D. candidate at Ohio University.
Visiting Instructor Timothy DeGenero joined the faculty in 2006. He earned B.S. and M.S. degrees at the University of Utah.
Research Publications
The Denison faculty believe that continued scholarship is instrumental to excellent teaching. Therefore, the methematics faculty are active members of the research community. Here are a few recent research publications:
Real Infinite Series
by Daniel D. Bonar and Michael J. Khoury '03, MAA, 2006.
A First Course in Abstract Algebra: Rings, Groups, and Fields, 2nd edition
by Todd Feil and Marlow Anderson, Chapman & Hall/CRC Press, 2005.
Lattice-Order Groups
by Todd Feil and Marlow Anderson, D. Reidel, 1988.
On Annular Functions
by Daniel D. Bonar, 1971.
Tree traversals and Permutations
T. Feil, K. Hutson, and R. M. Kretchmar. Congressus Numerantium, 2005.
Improved Automatic Discovery of Subgoals for Options in Hierarcical Reinforcement Learning
T. Feil, R. M. Kretchmar, and Rohit Bansal '03. Journal of Computer Science and Technology, 2003.
Characterization of Boolean topological Logics
A. Fressola '04, J. Krone, S. Paunov '04, and M. Westmoreland. Journal of Multiple Valued Logics, 2006.
×-Fréchect Urysohn Spaces
C. Liu and L. D. Ludwig. Houston Journal of Mathematics, 2005.
Nagata-Smirnov revisited: Spaces with s-wHCP bases
C. Liu and L. D. Ludwig. Topology Proceedings, 2005.
Hereditary subalgebras of operator algebras
M. Neal, D. Blecher and D. May. Journal of Operator Theory, 2006.
Classification of contractively complemented Hilbertian operator spaces
M. Neal, B. Russo and E. Ricard. Journal of Functional Analysis, 2006.
Reversibility of local transformations of multiparty entanglement
M. Westmoreland, N. Linden, S. Popescu and B. Schumacher. Journal of Quantum Information Processing, 2005.
For more information about the department and curriculum, go to:
or contact:
Jessen Havill, Chair
Department of Mathematics and Computer Science
F. W. Olin Science Hall, Room 208
Denison University
Granville, Ohio 43023
Phone: (740) 587-6582
Fax: (740) 587-5749
E-mail: havill@denison.edu