Mathematics Faculty WorksCopyright (c) 2017 Loyola Marymount University and Loyola Law School All rights reserved.
http://digitalcommons.lmu.edu/math_fac
Recent documents in Mathematics Faculty Worksen-usFri, 17 Mar 2017 01:32:54 PDT3600Doing the Scholarship of Teaching and Learning in Mathematics
http://digitalcommons.lmu.edu/math_fac/113
http://digitalcommons.lmu.edu/math_fac/113Wed, 15 Mar 2017 15:36:29 PDTJacqueline M. Dewar et al.SOTL and Interdisciplinary Encounters in the Study of Students’ Understanding of Mathematical Proof
http://digitalcommons.lmu.edu/math_fac/112
http://digitalcommons.lmu.edu/math_fac/112Wed, 15 Mar 2017 15:36:22 PDTCurtis D. Bennett et al.Fermat's Last Theorem for Rational Exponents
http://digitalcommons.lmu.edu/math_fac/111
http://digitalcommons.lmu.edu/math_fac/111Wed, 15 Mar 2017 13:57:17 PDTCurtis D. Bennett et al.Situating SoTL Within the Disciplines: Mathematics in the United States as a Case Study
http://digitalcommons.lmu.edu/math_fac/110
http://digitalcommons.lmu.edu/math_fac/110Wed, 15 Mar 2017 13:57:10 PDT
After two decades of work, many in the SoTL community are pondering the future of the SoTL movement. Will it sustain its influence? Will it continue to attract new participants? What role should the disciplines play? From the perspective of mathematics, this paper examines efforts by the Carnegie Academy and individuals within the mathematical community to build disciplinary support for the scholarship of teaching and learning. The authors, both mathematicians and Carnegie scholars, restrict their observations to the efforts undertaken in the United States during the last decade and examine the situation in mathematics in greater depth than has heretofore appeared. They shed light on particular complications they have observed for SoTL in their discipline and offer suggestions for improving the situation within mathematics. Practitioners in other disciplines, or those involved with SoTL at a “meta-level” may find their observations applicable in other venues.
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Jacqueline Dewar et al.Linear forms in the logarithms of three positive rational numbers
http://digitalcommons.lmu.edu/math_fac/109
http://digitalcommons.lmu.edu/math_fac/109Wed, 15 Mar 2017 13:57:03 PDTCurtis D. Bennett et al.Recounting the Odds of an Even Derangement
http://digitalcommons.lmu.edu/math_fac/108
http://digitalcommons.lmu.edu/math_fac/108Wed, 15 Mar 2017 13:56:56 PDTArthur T. Benjamin et al.The Probability of Relatively Prime Polynomials
http://digitalcommons.lmu.edu/math_fac/107
http://digitalcommons.lmu.edu/math_fac/107Wed, 15 Mar 2017 13:56:49 PDTArthur T. Benjamin et al.Congruence Classes of 2-adic Valuations of Stirling Numbers of the Second Kind
http://digitalcommons.lmu.edu/math_fac/106
http://digitalcommons.lmu.edu/math_fac/106Wed, 15 Mar 2017 13:56:42 PDT
We analyze congruence classes of S(n,k), the Stirling numbers of the second kind, modulo powers of 2. This analysis provides insight into a conjecture posed by Amdeberhan, Manna and Moll, which those authors established for k at most 5. We provide a framework that can be used to justify the conjecture by computational means, which we then complete for values of k between 5 and 20.
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Curtis Bennett et al.Finding Common Ground: Collaboration Across the Disciplines in the Scholarship of Teaching
http://digitalcommons.lmu.edu/math_fac/105
http://digitalcommons.lmu.edu/math_fac/105Wed, 15 Mar 2017 13:56:36 PDT
Many recent writings on the scholarship of teaching discuss the need to locate this scholarship within the disciplines. The authors argue that while scholarship within the disciplines is important, it should not come at the expense of work across the disciplines. They demonstrate the usefulness of cross-disciplinary collaboration for the scholarship of teaching and learning through the specific example of how collaboration contributed to their understanding of the role of such scholarship in the teaching of mathematics and negotiations courses. The authors also outline some of the pitfalls of cross-disciplinary collaboration, and they offer suggestions for beginning collaborative initiatives.
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Elaine K. Yakura et al.The automorphism groups of the hyperelliptic surfaces
http://digitalcommons.lmu.edu/math_fac/104
http://digitalcommons.lmu.edu/math_fac/104Wed, 15 Mar 2017 13:56:29 PDT
In this paper, the automorphism groups of the seven classes of the so- called hyperelliptic surfaces are calculated. Writing these as (E×F)/G, where E and F are elliptic curves and G is a finite group of translations of E acting on F not only as translations, covering space theory is then used to calculate the automorphisms. Letting M be the centralizer of G in Aut(E)×Aut(F), it is then noted that in all cases M is generated by its E-translations, its F-translations, its E- automorphisms, and its F-automorphisms. Finally, two tables list the automorphism groups and generators for each.
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Curtis Bennett et al.Zero estimates for polynomials in 3 and 4 variables using orbits and stabilisers
http://digitalcommons.lmu.edu/math_fac/103
http://digitalcommons.lmu.edu/math_fac/103Wed, 15 Mar 2017 13:56:22 PDT
To solve many Diophantine equations it often requires good lower bounds for linear forms in the logarithms of a small number of algebraic numbers. This in turn depends on good zero estimates: A non-zero polynomial cannot have a "grid" of zeros of size N unless it has large degree (in terms of N). Building on ideas of Wustholz (but using orbits and stabilisers) we obtain smaller bounds for the zero estimate for polynomials in 3 or 4 variables. We give an application to Catalan's conjecture.
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Curtis Bennett et al.