"Welcome to the inaugural issue of College Mathematics. This collection represents the bridge we aim to build between inquiry and rigor. In this issue, we explore topics ranging from analytic number theory to novel pedagogical approaches in calculus."
We present a new elementary proof concerning the density of prime numbers in intervals of the form [x, x + x^theta]. This result has significant implications for the efficiency of prime-generating algorithms.
This paper surveys distinct methods for visualizing functions of a complex variable, comparing domain coloring techniques with Riemann surface projections.