About Max Misterka
Max studied q-calculus, a version of traditional calculus, and generalized it to what he calls s-calculus. With his generalization, Max was able to prove many things about s-calculus which are analogous to known results in q-calculus and traditional calculus. He hopes his new tool will be useful in studying quantum physics.
A Generalization of q-Calculus Using Formal Group Laws
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Max Misterka, 16, of Harrisonburg, studied q-calculus for his Regeneron Science Talent Search mathematics project. In calculus, students learn about the derivative and some of its rules. In q-calculus, students work with a quantized derivative, called the q-derivative, which has analogous rules. Initially, Max set out to prove properties about a related topic concerning F-de Rham complexes, but had a key insight, and introduced a new tool called the s-derivative. Using this tool, itself a generalization of the q-derivative, Max proved far more than he anticipated by showing that his s-derivative satisfied many of the analogous rules of their q counterparts. Max hopes that his s-derivatives will prove useful in quantum physics and spur mathematicians to think of other ways to use and generalize the q-derivative.
The son of Shannon Fitzgerald and Jason Misterka, Max is homeschooled. He enjoys playing basketball and has sung in a local choir for six years. He loves pure research and says, “Real math is about being creative, noticing and exploring patterns and giving logical arguments to show why the patterns happen.”
Beyond the Project
Max is an accomplished pianist and composer. He entered original compositions in the Young Composers’ Contest held at James Madison University and won four times.
FUN FACTS: Max wrote his own programming language, which he named for his sister. He is also writing two video games using the Unity game engine; he plans to release them next year.
