Colloquia, Seminars, and Conferences
Friday, March 29th, 2013 at 3:00 PM, NS 212C
"Some Elementary Number Theory Results and Algorithms Are Revisited"
Western Kentucky University
Abstract: Starting from a well-known graph theory conjecture, (Caccetta-Häggvist conjecture), I became interested in the behavior of the products of matrices with 0 or 1 entries, their eigenvalues and eigenvectors, and thus the roots of polynomials with integer coefficients. The deeper I went into these problems, I realized that I personally and the rest of the mathematics community do not know much about real numbers. While discussing these facts with a colleague, David Neal, he asked me a loosely related question about the normal distribution in statistics that I found intriguing. I also recognized that to answer either the graph theory conjecture or the question in statistics we need to know a lot more about elementary number theory. I also realized that even the facts that we should know are not conveyed to our students in algebra, calculus, discrete mathematics, and number theory classes. I believe we sacrifice the simplicity for efficiency; we miss out on elementary proofs in order to show more sophisticated approaches. In this talk I will address these issues. Unfortunately, as I dug into these problems further I recognized that I am much farther from solving my original problem than I believed before. Since I am old enough to collect Social Security benefits, I still remember the beginning of the famous Midwest Graph Theory (MIGHTY) meetings when researchers were not embarrassed to talk about mathematics in which they were interested but did not yet have significant results. This experience gives me the courage to present this talk to you. I believe my discussion is suitable for students, teachers, and researchers in mathematics and statistics.
Some of the results are joint work with György Petruska, Department of Computer Science, Indiana University Purdue University Fort Wayne, Fort Wayne, Indiana
The following research seminars meet weekly in the Natural Sciences Building. Everyone is welcome to attend. For more information, please contact corresponding coordinators.
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