Exploring Quantitative Reasoning through the Internship at California State University
As a Research Intern at the Center for the Advancement of Instruction in Quantitative Reasoning, California State University, under the guidance of Dr. Frederick L. Uy, I had the incredible opportunity to explore advanced mathematical techniques and apply them to real-world decision-making processes. My research focused on polynomial computation methods and probability models, ultimately leading to a deeper understanding of how mathematical reasoning influences human behavior, personal choices, and societal trends.
Optimizing Polynomial Computation: Horner’s Method vs. Synthetic Division
One of the core aspects of my research involved comparing Horner’s Method with regular synthetic division in polynomial calculations. While synthetic division is commonly used in algebraic simplifications, Horner’s Method offers a more computationally efficient approach by reducing the number of multiplications and additions required for evaluating polynomials.
🔎 Research Process:
✅ Theoretical Analysis – I studied the mathematical foundations of both methods, analyzing their computational complexity and efficiency in different polynomial structures.
✅ Algorithmic Implementation – I wrote scripts in Python and MATLAB to compare the execution speed of Horner’s Method vs. synthetic division, testing them across large polynomial sets.
✅ Applications in Probability Analysis – I extended this research by applying these methods to probability functions, investigating whether Horner’s Method could optimize probability calculations in complex statistical models.
Through this, I discovered that Horner’s Method significantly improves computational efficiency when applied to probabilistic models, offering faster, more accurate results for statistical forecasting.
Quantifying Life Decisions: The Role of Probability in Human Choices
Beyond polynomial efficiency, my research took a broader perspective, examining how probability influences human decision-making. People often make choices without realizing that probabilistic reasoning plays a crucial role in determining outcomes. My study explored how quantitative models could predict patterns in life decisions, such as:
💍 Marriage & Relationship Decisions – Using Bayesian probability models, I analyzed trends in marital stability, studying how factors like age, education level, and financial stability statistically affect long-term relationship success.
🔄 Personal & Career Choices – I explored how expected value calculations influence decisions like career shifts, financial investments, and risk-taking behaviors, quantifying how people unconsciously use probability to weigh potential gains and losses.
📊 Behavioral Economics & Decision-Making – Inspired by Daniel Kahneman’s and Amos Tversky’s work on prospect theory, I investigated how human biases (such as risk aversion and overconfidence) impact probabilistic reasoning.
By integrating quantitative models with psychological decision-making frameworks, I found that many real-life choices follow predictable probability patterns, reinforcing the importance of mathematical literacy in everyday life.
Reflections on Research & Impact
Working under Dr. Frederick L. Uy at California State University was an eye-opening experience that deepened my appreciation for quantitative reasoning as a tool for both mathematical advancement and real-world problem-solving.
Through this research, I:
✅ Optimized polynomial calculations for probability applications
✅ Used mathematical models to analyze major life decisions
✅ Bridged the gap between theoretical mathematics and human behavior
This experience reinforced my passion for mathematical research, data science, and decision theory, showing me that math is not just about numbers—it’s about understanding the world in a more structured and logical way.