Author: "Storm, Christopher K." - Searchworks@Jio Institute Digital Library Search Results

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Author: Storm, Christopher K.
Subjects: Mathematics - Combinatorics, Mathematics - Number Theory, 05C38 (Primary), 11M41 (Secondary)
Abstract: Stark and Terras introduced the edge zeta function of a finite graph in 1996. The edge zeta function is the reciprocal of a polynomial in twice as many variables as edges in the graph and can be computed in polynomial time. We look at graph properties which we can determine using the edge zeta function. In particular, the edge zeta function is enough to deduce the clique number, the number of Hamiltonian cycles, and whether a graph is perfect or chordal. Actually computing these properties takes exponential time. Finally, we present a new example illustrating that the Ihara zeta function cannot necessarily do the same., Comment: 15 pages, 3 figures, 26 references
Published: 2007

Author: Storm, Christopher K.
Subjects: Mathematics - Number Theory, Mathematics - Combinatorics, 05C38 (Primary) 11M41 (Secondary)
Abstract: We generalize the Ihara-Selberg zeta function to hypergraphs in a natural way. Hashimoto's factorization results for biregular bipartite graphs apply, leading to exact factorizations. For $(d,r)$-regular hypergraphs, we show that a modified Riemann hypothesis is true if and only if the hypergraph is Ramanujan in the sense of Winnie Li and Patrick Sol\'e. Finally, we give an example to show how the generalized zeta function can be applied to graphs to distinguish non-isomorphic graphs with the same Ihara-Selberg zeta function., Comment: 24 pages, 6 figures
Published: 2006

Author: Storm, Christopher K. and Zullo, Holly
Subjects: *MATHEMATICS education, *MATHEMATICS teachers, *MATHEMATICS students, *UNDERGRADUATES, *MATHEMATICAL errors
Abstract: When we teach mathematics, we strive to teach students to think like mathematicians. In this paper we discuss one particular mathematical habit of mind that students do not naturally display. More specifically our study of voting patterns in data collected from classroom voting questions indicates that the undergraduate students who were in the classes using these questions did not understand the significance of counterexamples to statements, or lacked the ability to construct them, or both. Searching for counterexamples to disprove statements is a natural habit of mind for professional mathematicians. In this paper we give examples, and make some recommendations. We believe that if our students get used to routinely seeking out counterexamples, as they play with various mathematical ideas, they may also end up enjoying their mathematical experiences more. [ABSTRACT FROM AUTHOR]
Published: 2015
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Author: Storm, Christopher K., Petrilli Jr., Salvatore J., and Petry, Susan
Subjects: *EDUCATION research, *MATHEMATICS education (Higher), *HIGHER education, *CALCULUS education in universities & colleges, *MIDTERM examinations
Abstract: We explore using a "Study Challenge" to help students become active studiers in mathematics courses. We describe how a Study Challenge works and how we implemented it in calculus and differential equations courses. We discuss qualitative reactions from students who accepted the Study Challenge, which suggest that this might be a useful tool for students to add to their exam preparation toolbox. Finally, we offer some suggestions for implementing a Study Challenge within the mathematics classroom. [ABSTRACT FROM AUTHOR]
Published: 2014
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