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2017 Summer Undergraduate Applied Mathematics Institute
May 30  July 25, 2017
► Students
► Faculty
Projects:
 The Impact of three point differential on winning in the
national basketball association, Yu Pan
Advisor: Aris Winger
Abstract: The impact of the three point shot has increased over the last decade in the National Basketball Association (NBA). Teams, most notably the Houston Rockets, have centered their entire offenses around the shot as a means of victory. In this paper we examine the last 10 years of NBA games to investigate the impact of three point differential on victory. In addition to the analysis of the data, we use the date to create constraints as we formulate an integer programming model to assess the feasibility regions for winning with and without an advantage in three point differential. The model is then compared to what the data suggests and conclusions are made.
 Comparison of Nperiod Binomial and Trinomial Asset
Pricing Models, Thomas Devine, Myles Ellis, Branndon Marsical
Advisor: David Handron
Abstract: The trinomial model is used to model stock prices and compute the present value of options. The factors that measure up, middle and down movements are u, m, and d, respectively. To ensure that our model is arbitragefree, we choose u = 1+r+a and d = 1+r+a for some a between 0 and 1+r. The program we implement webscraped historical stock prices and current strike prices from Yahoo Finance, a maturity date, an interest rate, and the current stock price. Utilizing gradient descent, we compare the realworld data to our model and develop an expression for the SSE to measure our model's error.
 Modeling Optimal Race Strategies: A look at conquering World
Records through fitting protocols, Timothy Woods
Advisor: Aris Winger
 AntiRamsey Multiplicities, Xiang Si, Yunus Tuncbilek, Ruifan Yang
Advisor: Michael Young
Abstract: For a graph $G$ with $m$ vertices, $\frac{M(G,n)}{\left(\frac{\binom{n}{m}m!}{Aut(G)}\right)}$ is called the $\textbf{density}$ or $\textit{Ramsey multiplicity constant}$ and is denoted by $C(G,n)$. Burr and Rosta proved that $C(G,n)$ is nondecreasing in $n$, stated that $G$ is $\textit{common}$ if $\displaystyle{\lim_{n \to \infty} C(G,n) = 2^{1e}}$, and Jagger showed that any graph containing $K_4$ is noncommon. This paper discusses the maximum of rainbow subgraphs in $K_n$ of certain graphs (i.e. disjoint stars, complete graphs, bipartite graphs).
