# 2021 Senior Projects Conference

## Mathematics and Statistics

### Room 302 Session: Join us on Zoom.

1:00 p.m. |
## Spatial Visualization in the Engineering Fast-Forward Program
This research project discusses the Spatial Visualization Curriculum: Developing Spatial Thinking, endorsed by ENGAGE, and the Purdue test results from students in the Engineering Fast-Forward Program. The summer after acceptance, students in the Engineering Fast-Forward Program take Engineering 220: Statics and Mechanics of Materials, Math 243: Calculus III, and Engineering 198B: Professional Planning with Spatial Visualization. Engineering 198B is a section in which students are taught from the Developing Spatial Thinking Curriculum. The students take the Purdue Rotations test as a pre- and post-exam in the course. A statistical analysis is completed using the results from these tests. |

1:30 p.m. |
## Mathematical Modeling of Neurons: Analyzing the Hodgkin-Huxley Model
The Hodgkin-Huxley Model, named after its creators Alan Hodgkin and Andrew Huxley in 1952, showed the initiation and propagation of a neuron’s action potential. This model was created using a squid’s giant axon to help explain the behavior of nerve cells. The main focus of this project is to explore MATLAB coding and modeling of the Hodgkin-Huxley Model and incorporate ordinary differential equation solvers to approximate the solutions of the Hodgkin-Huxley model. Euler’s Method is used to approximate the Hodgkin-Huxley ordinary differential equation. All constant, channel, current, and voltage functions are created in MATLAB and use Euler’s First Order Approximation. Plots of Voltage vs. Time and Potassium and Sodium-Ion Conductance vs. Time are also generated using the functions in MATLAB to display graphs in a simulated Neuron. The most significant result of this research project is being able to generate the MATLAB code to solve the Hodgkin-Huxley ordinary differential equation and to use the solutions to plot Voltage vs Time and Potassium and Sodium-Ion Conductance vs Time graphs. |

2:00 p.m. |
## Convergence of the Fibonacci Sequence in Polynomials
The purpose of this research is to show progress toward the proof that the Fibonacci Sequence when applied to polynomials with positive coefficients, converges to the Golden Ratio. A proof of this convergence does not currently exist in the literature. The Golden Ratio is derived from the Fibonacci Sequence. Therefore, in order to reach our goal, we first provide an original proof of convergence of the ratio of consecutive Fibonacci numbers. By using Binet’s formula within a ratio test and limit test, it is shown that the Fibonacci sequence does converge to the golden ratio. Key Terms: convergence, Golden Ratio, Fibonacci sequence, polynomial |

2:30 p.m. |
## The Einstein Field Equations
A tensor is an object used in mathematics to describe physical properties. In this presentation, we will specifically be looking at three important tensors. These are the Ricci curvature tensor, the scalar-tensor, and the stress-energy tensor. These tensors come together and are the foundation of what we refer to as the Einstein Field Equations. These equations are a collection of ten different equations that come together to relate the geometry of spacetime and the matter inside of it. Using the Einstein Field Equations and the results from it, we will look at what gravity is and how it affects the space-time around it. In this presentation, we will examine how they came to be what they are today, as well as how the Einstein Field Equations may be used to describe and predict changes in space-time due to gravity using the Schwarzschild metric. |

3:00 p.m. |
## Categorical Stock Prices Forecasted by the ARIMA Model
This project is primarily on using the ARIMA (autoregressive integrated moving average) model to predict three quarters of stock prices. Using categories of stock prices: Fast Food, Grocery, Clothing, and Mobile Providers, we can analyze the average stock price quarterly over four years (2014-2017) and forecast the next year (2018) using the ARIMA Model. Once the ARIMA Model has forecasted the quarters, we then check the actual stock price averages of the quarters to see which category or categories work best. We use actual data that has already occurred to check our forecasting. The ARIMA Model shows a confidence interval, and we use this to compare the categories. This research gives a better understanding of what types of stocks are suited best for ARIMA Model forecasting. For this research project, we think it is best to use data that is pre-COVID because it has a much more steady data range. |