I am excited to present my comprehensive learning portfolio for MATH 441, along with this reflective cover letter that encapsulates my journey of exploration and growth throughout the course. On my website, you will discover a diverse array of artifacts, each representing a milestone in my understanding of mathematical optimization concepts and techniques. As I reflect on my work, I aim to convey not only the breadth of knowledge gained but also the depth of insight and skill development that has occurred.
Reflecting on my experience in MATH 441, what stood out to me the most was how optimization is intertwined with various aspects of our lives. Whether it involves planning logistics, managing finances, or allocating resources, optimization principles play a crucial role in enhancing efficiency and effectiveness. This realization has instilled in me a newfound appreciation for the practical applications of mathematics, highlighting the connection between theory and real-world scenarios. It is evident to me now that optimization is not merely a theoretical concept but a fundamental tool driving progress and innovation in contemporary society.
Throughout MATH 441, I embarked on a journey into the world of optimization, guided by knowledgeable instructors and fueled by curiosity. We explored a wide range of optimization techniques, from fundamental principles like the Fundamental Theorem of Linear Programming and the simplex method, to more advanced topics such as Optimal Transport, Shortest Path Algorithms, and Personal Portfolio Optimization using Quadratic Optimization. Additionally, we delved into practical applications like the Traveling Salesman Problem, OpenStreetMap integration, Assignment Problem optimization, and Scheduling optimization. Each concept presented its own challenges and opportunities for learning, enriching my understanding of optimization theory and its real-world applications.
My approach to creating artifacts was systematic, focusing on understanding, skills, and innovation. I began by thoroughly understanding the theoretical aspects, engaging with lectures, and discussing with peers to grasp complex ideas. Then, I utilized Python and LaTeX to translate these concepts into algorithms, visualizations, and clear solutions. Throughout this process, I continuously refined my work based on feedback, aiming for polished presentations and clarity.
In my portfolio, I dedicated significant effort to addressing the Assignment Optimization Problem, devising strategies for efficiently assigning Teaching Assistants to courses while ensuring compliance with qualification matrices.
One of my primary focuses was on exploring Shortest Path Algorithms, where I analyzed intricate network structures to identify patterns and behaviors, particularly examining whether the optimal graph consistently adheres to planar properties when determined using brute force. Through this endeavor, I not only demonstrated technical prowess but also showcased my capacity for creative problem-solving and algorithmic design.
Furthermore, my exploration of Personal Portfolio Optimization using Quadratic Optimization demonstrated my ability to synthesize theoretical principles with real-world applications. In this context, I concentrated on optimizing four distinct digital payment methods to minimize associated risks effectively. By integrating mathematical concepts seamlessly, I provided a comprehensive framework for decision-making processes, showcasing a nuanced understanding of optimization theory and its practical implications.
Additionally, my exploration of the Interior Point Method provided insights into the iterative process of updating values to approach boundary points as the parameter mu tends towards zero. This experience deepened my understanding of optimization algorithms and honed my analytical skills, fostering a greater appreciation for the nuances of numerical optimization techniques.
In addition to these pursuits, I also delved into approximating the value of pi and tackling Sudoku problems. These seemingly disparate endeavors offered valuable opportunities to apply mathematical concepts in novel contexts, further enriching my learning experience and expanding my problem-solving skills.