The Mathematical Association of America Maryland-District of Columbia-Virginia Section

Understanding factors that affect crime is an essential part of crime prevention. The goal of this project is to better understand how travel patterns and crime are related, as well as how the relationship changed before and after the COVID-19 pandemic in Baltimore City. The United States Census Bureau divides the country into census tracts, and then those tracts are further divided into census block groups (CBGs). A linear regression was run on travel patterns and crime at the CBG level, and the slopes of the linear regressions were collected using Python. The slopes represent the crime rate of each CBG. The crime rates were categorized, and a chi-square test was run on the pre- and post-COVID crime rates for each CBG. The results showed that the crime rates before COVID were statistically independent from the crime rates after COVID. Another chi-square test was run on the pre- and post-COVID data to determine whether adjacent CBGs have statistically independent crime rates. The results showed that adjacent CBGs did have statistically independent crime rates before COVID but did not have statistically independent crime rates after COVID. Overall, these results show that the COVID-19 pandemic has significantly changed the relationship between both crime and travel patterns and the relationship between crime rates in adjacent CBGs.

Obsidian is a versatile and robust tool for educators, offering an innovative approach to organizing teaching materials and enhancing the overall teaching and learning experience. In this session, I will explore key features of Obsidian that I used in the creation of my book College Calculus Preparation.

Rockets are powerful vehicles that play a critical role in space exploration, satellite deployment, and scientific research. Their value lies in their ability to overcome the challenges of Earth's gravity and enable human exploration of space. However, a major challenge in rocket launches is the threat of the massive acoustic loads that occur during liftoff. These acoustic loads can be caused by many factors, including engine exhaust, aerodynamic turbulence, and shock waves. Predicting acoustic loads on rockets is crucial because the excessive noise and vibration can cause damage to the vehicle's structure, equipment, and payload. By accurately predicting these loads, engineers can design rocket structures to withstand such vibrations, and minimize damage. With the recent surge of interest in reusable rockets, predicting loading is especially important for rockets subject to a high number of cycles. A semi-empirical model, NASA SP-8072, was developed in 1971 using existing rocket data to predict the acoustic power generated by a supersonic rocket exhaust. Despite being over 50 years old, it is still the best model available today for acoustic load prediction on rockets. This paper will discuss and compare possible improvements upon the NASA SP-8072 model.

The games RED-BLUE CHERRIES and CUTTHROAT are played on an undirected, unweighted graph with each vertex colored either red or blue. Previous work covers game values for each of these games independently. Here, we will apply the rules of both games to create CUTTHROAT CHERRIES, a new game with unique game values. We will compare CUTTHROAT CHERRIES to both of the original games to see what features carry over and what new patterns emerge.

Throughout this talk we will showcase various mathematical modeling and optimization applications using numerous concepts that college mathematics majors will encounter during their undergraduate education. Our goal for the talk is to bring awareness to the importance of applications of mathematics, as college classes are often focused on methods of computation or theory. In the talk we will touch on applications utilizing linear, non-linear, and theoretical mathematical methods. The examples covered will range from theoretical mathematics topics such as graph and set theory to more applied concepts relating to physics, chemistry, biology, and economics.

At some point, math students have to make the transition from learning about mathematics to creating their own. But you can't teach creativity, so how can we learn it?The history of mathematics offers a number of "case studies" of how mathematicians came up with new ideas. We'll discuss Hamilton's creation of the quaternions and suggest ways it could be used to promote creative thinking.

This project aims to estimate and predict crime intensities for small geographical regions in Baltimore City. Previous research utilized a parametric approach and determined that crime intensity could not be estimated by a constant rate for regions of any size across Baltimore. Expanding on this, we take a non-parametric approach and assume that crime intensities in Baltimore City are determined by a probability function dependent on the city’s road network. Utilizing Baltimore City Police Department and OpenStreetMaps data, we explored two methods for modeling crime intensity: (1) Kernel Density Estimation and (2) Diffusion Model on Road Network. Examining the similarities and differences between the well-studied kernel density estimation and our diffusion algorithm, we explore the significance of both findings.

In this talk, we will share our journey in creating web-based mathematical games for our math classes at MC. These games can be integrated into Blackboard or any LMS platform. The main goal of developing these games is to increase student engagement with the material by creating fun, engaging, and rewarding experiences. Through elements of enjoyment such as rewards, challenges, and exploration modes, students gain insights into math topics and deepen their understanding

Current research has sparked interest in understanding the contribution of natural killer (NK) cells and their role in the resolution of viral infections, including influenza infections, commonly referred to as the flu. Despite their significance, NK cells' precise mechanisms, immune functions, and the correlation with cytokines like interferon gamma (IFNg) remain unclear. We aim to model immune dynamics using delayed differential equations, linear chain trick with ordinary differential equations, and traditional ordinary differential equations. Our study integrates immunology and mathematics to investigate the roles of NK cells, T cells, and IFNg in influenza infections by utilizing data from the University of Tennessee's Department of Pediatrics. These models will allow the exploration of possible mechanisms related to IFNg production during an infection.

The remarkable fact that \(2^n \sqrt{2-\sqrt{2+\sqrt{2+ \cdots + \sqrt{2}}}} \rightarrow \pi\) as \(n \rightarrow \infty\) where \(n\) is the number of nested radicals, inspires an obvious question. What other similar sorts of results hold? This leads first to an entire family of related sequences, such as \(\sqrt{6}^n \sqrt{3-\sqrt{6+\sqrt{6+ \cdots + \sqrt{6}}}} \) and \(4^n \sqrt{8-\sqrt{56+\sqrt{56+ \cdots + \sqrt{56}}}},\) and then to a curious function \(C(x)\) that encompasses them all. Numerical and graphical investigation suggest many conjectures about \(C(x)\). Some of these we have managed to prove, but most have stubbornly resisted our efforts.

Inverse problems in time-dependent heat conductivity models pose significant challenges due to their ill-posed nature, where small perturbations in data can lead to large deviations in solutions. This work presents a novel numerical framework leveraging the Radial Basis Function - Finite Difference (RBF-FD) method to approximate heat conductivity coefficients and solutions of parabolic partial differential equations. The RBF-FD approach offers a computationally efficient, higher-order alternative that enhances stability and accuracy while mitigating the limitations of conventional numerical methods, such as instability and excessive computational costs. Through numerical experiments, we demonstrate the effectiveness of the proposed method in addressing inverse parameter identification problems, highlighting its robustness and potential for broader applications in heat conduction modeling.

In this talk we will discuss how we can use algebraic combinatorics to model the flooding properties of graphs. The flood polynomial, which encapsulates how a graph floods, can be used to reveal properties about the graph. A few families of graphs even have ties to popular sequences, such as the Fibonacci and Lucas sequences.

Does population density correlate to crime rates and travel patterns in Baltimore City? Understanding how these three variables are related can help cities allocate resources effectively to reduce crime rates. These three variables are strongly correlated, so changes in one of the three variables: crime, mobility, and population are likely to affect the other two variables. Conducting a Kernel Density Estimation on the crime data produces the crime intensity. This crime intensity data is then split into each Census Block Group in Baltimore City. Mapping the crime intensity, mobility, and travel pattern data to each Census Block Group allows for a Principal Component Analysis to be conducted. 90 percent of the variance is captured by the first two components of our Principal Component Analysis. Therefore, the three data sets representing crime intensity, travel patterns, and population are interdependent, demonstrating that there is a strong correlation between the three variables.

During the Fall 2024 semester four Precalculus instructors from different schools participated in a “Teaching Square”: sitting in on each other’s courses and discussing what they observed and learned from the observations. We will discuss the results of the Teaching Square, lessons learned from the observations, and plans for future collaborations between instructors across schools.

Rocket liftoff and Coanda Flares used to burn excess gas have one thing in common: harmful Shock Associated Noise (SAN) from Coanda flows. Coanda flows are flows that follow a curved surface, and the shock cell structure determines the SAN characteristics present in such a flow. This paper aims to expand efforts to model the poorly understood shock cell structure of turbulent supersonic Coanda jets, enabling accurate SAN predictions. While the Coanda Flare is used here, methods developed can then be applied to other Coanda Flows, such as the noise emission from rocket flame trenches. Previous work has developed an equation for the Jet Boundary of the Coanda flare from hand-digitized flow visualization (Schlieren) images. Understanding the jet boundary enables the modeling of the shock cell structure. The Jet Boundary model currently has a 2-8% error and must be improved to understand SAN from Coanda flows better. This error resulted from poor Schlieren image quality combined with human error in manually digitizing images. The current work aims to capture more precise images of the Coanda Flare Jet boundary at various operating conditions and automate the digitization process to develop a new Jet Boundary equation. This paper discusses methods of improvement, including the upgrade of a Z-type Schlieren system, the development of a 2D Coanda Flare, and the implementation of Canny Edge detection to digitize the jet boundary.

Given a number field K, the set of units forms a lattice. We say that two lattices have the same shape if they are the same up to isometry and scaling. We discuss the space of rank 3 lattices along with an algorithm to determine which part of the space a given unit lattice lies. The goal is to study which parts of the space are filled by rank 3 unit lattices, and which restrictions on the Galois group lead to different shapes of lattices.

We use Maya diagrams to refine the criterion by Fulton and Woodward for the smallest powers of the quantum parameter q that occur in a product of Schubert classes in the (small) quantum cohomology of partial flags. Our approach using Maya diagrams yields a combinatorial proof that the minimal quantum degrees are unique for partial flags. Furthermore, visual combinatorial rules are given to perform precise calculations.

We will consider a particular family of odd symplectic partial flag varieties denoted by \(\IF\). In the quantum cohomology ring \(\QH^*(\IF)\), we will show that \(q_1q_2\cdots q_m\) appears \(m\) times in the quantum product \(\tau_{Div_i} \star \tau_{id}\) when expressed as a sum in terms of the Schubert basis.