Emily Madden and Pav Pavlovic, Predicting Stock Movements with Markov Chains: A Probabilistic Approach to Financial Time Series Forecasting, Fall 2025.
Rita Lin, Understanding Limit Theorems: From Randomness to Predictability, Fall 2025.
Caiden Woolery, Monte Carlo Simulation of Random Generation in $S_n$, Fall 2025.
Jason Richard, Quantifying "Time Underwater'' via First-Passage Analysis: Monte Carlo Evidence on Drawdown Duration, Fall 2025.
Lucas Collier and Amol Srivastava, Probability Theory and Epistemology, Fall 2025.
Amelia De Herrera-Schnering, Lucy Walton, and Aqua Chung, Random Walk of a Photon Out of a Star, Fall 2025.
Felina Marie Tanner, The Backslide of Democracy Under Authoritarian Rule: A Stochastic Model, Fall 2025.
Dharma Johnson, How the Kinetics of a Reaction Determine the Overall Rate, Fall 2025
Jasmine Wright, Nonlinear Dynamics and Chaos Theory: From Order to Unpredictability, Fall 2025.
Real roots of random polynomials [Link]
Description: Random polynomials arise when the coefficients of a polynomial are treated as random variables. This seemingly simple change transforms a fundamental mathematical object into a powerful tool connecting mathematics, physics, and other fields. Since the coefficients are random, the number of real roots of these random polynomials itself becomes a random variable. A central challenge in this area concerns the behavior of this random variable: How many real roots are there typically? How are these roots distributed along the real number line? And how do their positions relate to each other? This project investigates these questions for a specific type of random polynomial: generalized Kac polynomials. We will explore the correlations between the real roots of these polynomials by combining theoretical insights from analysis and probability with hands-on computer simulations. The work is designed to be accessible, even for participants with no prior programming experience.
Dates: May 12 - June 27, 2025
Undergraduates: Farid Ahmadov, Ayush Khadka, Melanie Fouque, and Connor Shanley.
Ella Todd, Giselle Wipper, Dan Sweeney, and Anika Dragan, Winning the Majority: Integrating Markov Chains into Election Strategies, Spring 2025. This poster was presented at the Math For All poster session. [Poster]
Sam Schiller, Cosmic Coin Flips: Simulating Microlensing with Monte Carlo Methods, Spring 2025. This poster was presented at the Math For All poster session. [Poster]
Max Bradybury, Harrison Getches, Thomas Ghirmatsion, Tate Middleton, and Blake Zimmerman, Measuring Market Uncertainty Using Shannon Entropy and Monte Carlo Simulations, Spring 2025. [Poster]
Calvin Pielke, Probabilistic Modeling of Stock Price Movements Using Markov Chains: Analyzing Market Dynamics and Trading Strategies Through State Transition Probabilities, Spring 2025. [Poster]
Andrew Fox and William Cockayne, Comparison of Numerical Analysis Methods For Differential Equations, Fall 2024. [Poster]
Alexander Pavlovic and Rowan Calvert, The Fourier Heat Equation and the Black-Scholes Model, Fall 2024. [Poster]
Ngoc T. Y. Vo, Lyapunov's inequality and applications, 2015.
Hue T. K. Do, Generalized trigonometric and hyperbolic functions, 2024.
Cuc T. T. Pham, Opial-type inequalities and applications, 2013.
Bao Q. Le, Convolution inequalities and applications, 2013.
Them T. Nguyen, On some convergence theorems, 2013.
Xuan T. Nguyen, On the theory of reproducing kernels, 2013.
Chuan T. M. Tran, On n-normed spaces, 2012.
Quyen B. Tran, Laplace transform and applications, 2012.
Phung D. Tran , Some norm inequalities in Sobolev spaces, 2011.
Hao V. Nguyen, Convolution inequalities in $\ell_p$ spaces and applications, 2011.
Bao Q. Le, Convolutions and applications, 2013.
Xuan T. Nguyen, A generalization of Opial's inequality, 2013.
Analysis Training sessions for Quy Nhon University Students, 2007 - 2015.
Algebra Training sessions for Quy Nhon University Students, 2007 - 2015.