Ph.D. Candidate in Computer Science @ Stony Brook University &
Adjunct Assistant Professor in CS/Math @ St. John's University
I am a Ph.D. candidate at Stony Brook University working at the intersection of computer algebra, and symbolic mathematics. My research reimagines foundational mathematical operations to simplify complex problems, particularly in geometric computation.
I am also an Adjunct Assistant Professor at St. John's University in the Division of Computer Science, Mathematics and Science.
Submitted to RACMAS 2026
Abstract: This paper builds upon Karl Menger’s function-focused perspective on calculus as the foundation for a more streamlined and rigorous framework. In the first part, we revisit Menger’s introduction of the identity function symbol and the resulting clarifications it brings to differentiation and limit operations. This historical context sets the stage for the second part, where we extend Menger’s construction. We argue that by restricting ourselves to an appropriately chosen function space—one that is inherently compatible with continuity and differentiation—we can dispense with the need for explicit limit processes. The result is a calculus that is both conceptually simpler and more robust, bridging the gap between Menger’s insights and a modern limit-free paradigm for differentiation and algebraic manipulation.
Contribution: Under these refined conditions, seemingly heuristic operations (such as those involving “indeterminates”) are naturally integrated into a rigorous, well-defined framework.