EXPOSITIO

This paper tries to create an intuition behind the proof of the fundamental theorem–Weierstrass approximation theorem–which will be shown using Bernstein polyno- mials and its generalization beyond polynomials–the Stone-Weierstrass theorem. The paper will look at a few applic…

An essay that presents a first-principles approach to eigenvalue dynamics of the wave equation applied in context of timpani tuning.

This expository paper explains tessellations of the hyperbolic plane from a differential-geometric viewpoint. We review the upper half-plane (H) and Poincaré disk (D) models and the Cayley transform linking them. We prove that orientation-preserving isometries are precisely PSL(…

We validate an inverse-drag estimation pipeline for finned spherical projectiles and, within this experimental regime, detect a robust non-monotonic effective-drag anomaly near L≈1.00. The pipeline pairs a custom fourth-order Runge–Kutta trajectory simulator with a monotonicity-…

In this paper, we begin with the concept of a projection in the familiar vector space R^n, and then extend it to an arbitrary inner product space. This foundational idea enables us to compute a line of best fit, approximate functions using polynomials, and decompose a function i…

In this paper, we explore matroids, which generalize properties of linear independence of vectors and cycles in graphs. We investigate properties and operations on matroids, then we look at how we can represent matroids using matrices.