Undergraduate Mathematics Day: Proceedings and Other MaterialsCopyright (c) 2020 University of Dayton All rights reserved.
https://ecommons.udayton.edu/mth_epumd
Recent documents in Undergraduate Mathematics Day: Proceedings and Other Materialsen-usSat, 16 May 2020 02:58:35 PDT3600Poster: 2019 Undergraduate Mathematics Day
https://ecommons.udayton.edu/mth_epumd/41
https://ecommons.udayton.edu/mth_epumd/41Thu, 14 May 2020 07:06:07 PDT
Poster promoting the conference; highlights the event's plenary speakers, Tommy Ratliff of Wheaton College and Rachael Kenney of Purdue University.
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University of Dayton. Department of MathematicsProgram: 2019 Undergraduate Mathematics Day
https://ecommons.udayton.edu/mth_epumd/40
https://ecommons.udayton.edu/mth_epumd/40Thu, 14 May 2020 07:06:04 PDT
Conference program
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University of Dayton. Department of MathematicsClimbing the Branches of the Graceful Tree Conjecture
https://ecommons.udayton.edu/mth_epumd/39
https://ecommons.udayton.edu/mth_epumd/39Thu, 14 May 2020 07:06:01 PDT
This paper presents new ways to look at proving the Graceful Tree Conjecture, which was first posed by Kotzig, Ringel, and Rosa in 1967. In this paper, we will define an adjacency diagram for a graph, and we will use this diagram to show that several classes of trees are graceful.
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Rachelle Bouchat et al.Derivation of the (Closed-Form) Particular Solution of the Poisson’s Equation in 3D Using Oscillatory Radial Basis Function
https://ecommons.udayton.edu/mth_epumd/38
https://ecommons.udayton.edu/mth_epumd/38Thu, 14 May 2020 07:05:57 PDT
Partial differential equations (PDEs) are useful for describing a wide variety of natural phenomena, but analytical solutions of these PDEs can often be difficult to obtain. As a result, many numerical approaches have been developed. Some of these numerical approaches are based on the particular solutions. Derivation of these particular solutions are challenging. This work is about how the Laplace operator can be written in a more convenient form when it is applied to radial basis functions and then use this form to derive the (closed-form) particular solution of the Poisson’s equation in 3D with the oscillatory radial function in the forcing term.
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Anup R. Lamichhane et al.Analysis of Weights in Central Difference Formulas for Approximation of the First Derivative
https://ecommons.udayton.edu/mth_epumd/37
https://ecommons.udayton.edu/mth_epumd/37Thu, 14 May 2020 07:05:53 PDT
Manipulations of Taylor series expansions of increasing numbers of terms yield finite difference approximations of derivatives with increasing rates of convergence. In this paper, we consider central difference approximations of arbitrary order of accuracy. We derive explicit formulas for the weights of terms and explore their limits for increasing orders of accuracy.
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Preston R. BoorsmaBaseball: Defense or No?
https://ecommons.udayton.edu/mth_epumd/36
https://ecommons.udayton.edu/mth_epumd/36Thu, 14 May 2020 07:05:50 PDT
Defense wins championships, or so they say. How do baseball organizations find the right defenders to win games? FanGraphs has published a series of metrics that teams throughout Major Leage Baseball use to quantify players’ fielding prowess. Baseball analysts use Wins Above Replacement, WAR, to predict who should be the league most valuable player, MVP. This uses defensive metrics to quantify how many runs the player produces when the team wins. The paper will discuss the metrics that already exist, and the technology that has been developed to analyze these metrics and other measurements of a player’s defensive skills.
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Jacob D. StemmerichMathematics with Only Rods
https://ecommons.udayton.edu/mth_epumd/35
https://ecommons.udayton.edu/mth_epumd/35Thu, 14 May 2020 07:05:47 PDT
We discuss in this expository paper the rod system used in ancient China based on the mathematical classic work of Sun Zi, with a focus on application to solving systems of linear equations. The mathematics involved is authentic and beautiful, and we believe it is also of interest from historical, cultural, and pedagogical perspectives.
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Jianqiao Mao et al.How One’s Risk Preferences Affect Their Investment Decisions
https://ecommons.udayton.edu/mth_epumd/34
https://ecommons.udayton.edu/mth_epumd/34Thu, 14 May 2020 07:05:44 PDT
The purpose of our project was to display how our personal risk preferences affect our investment decisions, if we invested on two assets: one risky asset (stock) and one risk-free asset (bank account). We considered the problem in both discrete and continuous case. In particular, the stock price follows a multinomial tree in the discrete case; and follows a Geometric Brownian motion in the continuous case. We then found the expected value of the stocks at varying times. By setting what we expect our bank account to be at those times equal to these expected values, we solved for the interest rates, at which investing on either asset are equivalent. We then incorporated risk aversion in the power utility function. Using different levels of risk aversion, we again solve for the interest rate, at which investing on either asset are equivalent. By comparing the first interest rate with the interest rate that incorporated the risk aversion, we saw how this risk aversion affects our investment decisions.
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Kari Hayes et al.Generalized Catalan Numbers And Objects: X; Y Equivalence Classes And Polyominoes
https://ecommons.udayton.edu/mth_epumd/33
https://ecommons.udayton.edu/mth_epumd/33Thu, 14 May 2020 07:05:40 PDTEmily S. Dautenhahn et al.Magic Polygons and Their Properties
https://ecommons.udayton.edu/mth_epumd/32
https://ecommons.udayton.edu/mth_epumd/32Thu, 14 May 2020 07:05:37 PDT
Magic squares are arrangements of natural numbers into square arrays, where the sum of each row, each column, and both diagonals is the same. In this paper, the concept of a magic square with 3 rows and 3 columns is generalized to define magic polygons. Furthermore, this paper will examine the existence of magic polygons, along with several other properties inherent to magic polygons.
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Victoria Jakicic et al.Finite Sum Representations of Elements in R and R2
https://ecommons.udayton.edu/mth_epumd/31
https://ecommons.udayton.edu/mth_epumd/31Thu, 14 May 2020 07:05:33 PDT
In February 2017, a number theoretic problem was posed in Mathematics Magazine by Souvik Dey, a master’s student in India. The problem asked whether it was possible to represent a real number by a finite sum of elements in an open subset of the real numbers that contained one positive and one negative number. This paper not only provides a solutionto the original problem, but proves an analogous statement for elements of R2.
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Lewis T. Dominguez et al.Alcoholism: A Mathematical Model with Media Awareness Campaigns
https://ecommons.udayton.edu/mth_epumd/30
https://ecommons.udayton.edu/mth_epumd/30Thu, 14 May 2020 07:05:29 PDT
In this paper, we study how media awareness campaigns influence the spread and persistence of drinking behavior in a community. Here, we present a compartmental population model with an additional differential equation to describe the dynamics of media awareness campaigns in combating problem drinking ([10], [12], [21]). Our model indicates a basic reproductive number, R0, where there exists an asymptotically stable drinking-free equilibrium if R0 < 1, and a unique endemic state, which appears to be stable when R0 > 1. We found that the following two components affect the basic reproductive number: the strength of peer influence of problem drinkers on susceptibles and the average overall time spent in the problem drinking environment. Furthermore, we conclude that the existence of media awareness programs and effective treatment options does not eliminate a drinking culture in the community, it only temporarily alleviate the issue. To support our findings, we present analytical and numerical approaches.
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Erik H. Ander et al.