Creating my own theorem
In my MYP Personal Project, I delved into exponential functions, driven by a fascination with patterns and their relationship to factorials. I was intrigued by how exponential functions behaved in sequences and noticed specific patterns in the differences between consecutive numbers within various exponential series. My goal was to capture these patterns in a general formula and create a theorem that could express these differences mathematically, including subsequent differences within the sequence.
The project involved rigorous research and problem-solving, particularly in translating my observations into a formal mathematical representation. I relied on summation techniques and identified smaller patterns within complex expressions, which led me to a broader generalization. Using mathematical induction, I was ultimately able to prove my theorem, validating the pattern I had observed.
Exponential Series
One of the major challenges I faced was breaking down my pattern into manageable components and finding a consistent way to represent it through a theorem. This required building numerous expressions and finding underlying patterns within them, which gave me insights into how mathematical problems are constructed and solved in advanced contexts.
Through this project, I gained a deeper understanding of mathematical reasoning and the value of persistence in tackling complex problems. This experience also provided me with a glimpse into the process of formalizing abstract patterns, expanding my ability to think critically and work systematically in mathematics. It reinforced my passion for mathematical inquiry and inspired me to pursue further projects that explore the beauty and structure of mathematics on a larger scale.
