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ED16 Abstracts 73 ED16 Abstracts 73 IP1 industrial problems. She will give examples of some indus- Mathematical Modeling with Elementary School- trial research problems that student teams have tackled, Aged Students discuss some of the skills that are needed to be successful working with and in industry, discuss the challenges that Modeling, a cyclic process by which mathematicians de- one may face when working with corporate partners, and velop and use mathematical tools to represent, understand, present a summary of some of the lessons that have been and solve real-world problems, provides important learning learned over the years in these collaborations. opportunities for school students. Modeling opportunities in secondary schools are apparent, but what about in the Suzanne L. Weekes younger grades? Two questions are critical in mathemati- Worcester Polytechnic Institute (WPI) cal modeling in K-5 settings. (1) How should opportunities [email protected] for modeling in K-5 settings be constructed and carried out? (2) What are the tasks of teaching when engaging el- ementary students in mathematical modeling? In this talk IP5 I will present a framework for teaching mathematical mod- Title Not Available at Time of Publication eling in elementary classrooms and provide illustrations of its use by elementary grades teachers. Abstract not available at time of publication. Elizabeth A. Burroughs Philip Uri Treisman Montana State University The University of Texas at Austin [email protected] [email protected] IP2 CP1 Graduate Student Education in Computational Regime Switching Models and the Mental Account- Mathematics and Scientific Computing ing Framework Abstract not available at time of publication. We extend Markowitz’s mean-variance portfolio theory (1952) and the Mental Accounting framework developed Margot Gerritsen by Das et al. (2010) from their stationary setting to a Dept of Energy Resources Engineering dynamic one. To generate time-varying scenarios for as- Stanford University set returns, we employ dynamic programming with Regime [email protected] Switching Models (more specifically Hidden Markov Mod- els and Gaussian Mixture Models). We combine these con- cepts into a unified framework, evaluate its feasibility and IP3 performance, and perform an analysis of the most common Mathematical Modeling: Changing the Landscape pitfalls and practical considerations. of the Mathematics Classroom Felix Andresen As math modeling gains more attention in the K-12 cur- d-fine GmbH riculum, we consider the questions: How do we introduce [email protected] students and teachers to modeling? What can students gain from engaging in modeling experiences? How do we teach modeling? In this session, I will share some of my CP1 mathematical modeling experiences working with students Modelling Uncertainty Without An Assumed Dis- and teachers and solicit ideas on how we can work together tribution: Turbulent Cloud Microphysics to support the teaching and learning of mathematical mod- eling. We model uncertainty, without any assumed probability distribution function, by using physical features of the phe- Maria Hernandez nomena to reshape state-space fluctuations into fluctua- North Carolina School of Science and Mathematics tions in a stochastic process. Statistics on these stochastic Deerfield Academy processes become system parameters which have physical [email protected] meanings that can be acquired from data. In the applica- tion to bulk models of cloud droplet collision and coales- cence, the systematic decomposition of density functions IP4 (mixing ratio and number), into a mean and a set of point- Lean Out: Connecting Outside the Ivory Tower wise fluctuations, provides a novel way to represent higher moments of the kinetic collection equation and thus close It is important that mathematics and statistics educators this system of bulk equations. Additionally, conservation are well attuned to the research and employment opportu- of mass and consistency of number result intrinsically from nities that exist outside academia for people trained prop- the derivations rather than being applied externally. The erly in the mathematical sciences. In particular, to increase independent derivation of the four autoconversion terms the number of well-prepared students going into mathemat- provides for (to the best of the author’s knowledge) an un- ical sciences careers, there is a need to better connect the precedented constraining of the autoconversion parameter work that is done in business, industry, and government and subsequent fine control of the evolution of the droplet with what is taught at universities, and to give students size spectrum. We compare results from this (stochastic and faculty active exposure to the sort of interesting math- differential equation) ’SDE-based’ stochastic model to a ematical problems that are encountered. In this talk, the deterministic bulk model and use detailed results as bench- speaker will discuss some of the research and educational marks. Simulations are driven by hydrodynamic and tur- partnerships that she has been involved in that actively bulent kernels. connect faculty, students, and teachers directly with in- dustry and that has allowed them to engage in research on David Collins 74 ED16 Abstracts University of Victoria [email protected] [email protected] CP1 CP1 Extreme Risk, Value-at-Risk Modeling Educational Magic Tricks Based on Error- Detecting Codes We apply an approach for estimating Value-at-Risk (VaR) describing the tail of the conditional distribution of a het- Magic tricks based on discrete mathematics and comput- eroscedastic financial return series. The method combines ing concepts help grab student attention and can moti- quasi-maximum-likelihood fitting of AR(1)-TGARCH(1,1) vate them to delve more deeply. Error detection ideas long model to estimate the current mean as well as volatility, used by computer scientists provide a rich basis for work- and Extreme Value Theory to estimate the tail of the ad- ing magic; probably the most well known trick of this type justed standardized return series. We employ the approach is one included in the CS Unplugged activities. This pa- to investigate the existence and significance of the calen- per shows that much more powerful variations of the trick dar anomalies: seasonal effect and day-of-the-week effect can be performed, some in an unplugged environment and in Americas Indexes VaR. We also examine the statisti- some with computer assistance. Some of the tricks also cal properties and made a comprehensive set of diagnostic show off additional applied mathematics concepts in the checks on the one decade of considered Americas Indexes areas of information theory and cryptography. returns. Our results suggest that the lowest VaR of con- sidered Americas Indexes negative log returns occurs on Ronald I. Greenberg the fourth season among all seasons. Moreover, compara- Loyola University of Chicago tively low Wednesday VaR is captured among all weekdays [email protected] during the test period. Zijing Zhang CP1 University of Massachusetts Amherst Cumulative Prospect Theory with Skewed Return YOYO Distribution [email protected] We investigate a one-period portfolio optimization prob- lem of a cumulative prospect theory (CPT) investor with CP2 multiple risky assets and one risk-free asset. The returns of Graduate Student Mentorship for Diverse Teams multiple risky assets follow multivariate generalized hyper- of Undergraduate Researchers in an REU Site bolic (GH) skewed t distribu-tion. We obtain a three-fund separation result of two risky portfolios and risk-free asset. Some summer research programs for undergraduates in- Furthermore, we reduce the high dimensional optimization volve graduate students as well as faculty in research men- problem to two 1-dimensional optimization problems and torship. As a graduate student, the opportunity for growth derive the optimal portfolio. We show that the optimal and development before transitioning to a faculty career is port-folio composition changes as some of investor-specific especially valuable. Graduate students can relate to the parameters change. It is observed that the consideration of undergraduates and to provide guidance for the near fu- skewness of stock return distribution has considerable im- ture, as they guide the undergraduates with the research pact on the distribution of CPT investors wealth deviation, project. I will discuss my experiences and what I have and leads to less total risky in-vestment. learned as a graduate student working with diverse teams of undergraduates over the past three years in the UMBC Traian A. Pirvu REU site: Interdisciplinary Program in High Performance McMaster University Computing. More information on this REU site can be [email protected] found here: http://hpcreu.umbc.edu/. Minsuk Kwak Jonathan Graf Hankuk University of Foreign Studies, Korea Department of Mathematics and Statistics [email protected] University of Maryland, Baltimore County [email protected] CP1 Online Games in the Calculus Classroom CP2 Education for Simulation and HPC at JSC Online games can be a useful tool that, when coupled with traditional lecture, allows the student to become immersed Fostering a sound education for students and young re- in the subject, creating a kinetic and energetic environ- searchers at bachelor, master and PhD level in simulation ment that will not only help learning, but spark interest and high-performance computing (HPC) is an essential in the
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