Travis Kulhanek

I have several published math papers.

Dilated Floor Functions That Commute Sometimes
Abstract:
We explore the dilated floor function f_a(x)= ⌊ax⌋ and its commutativity with functions of the same form. A previous paper found all a and b such that f_a and f_b commute for all real x. In this paper, we determine all x for which the functions commute for a particular choice of a and b. We calculate the proportion of the number line on which the functions commute. We determine bounds for how far away the functions can get from commuting. We solve this fully for integer a, b and partially for real a, b.

Published at the PUMP Journal of Undergraduate Research.
Link to paper:
https://journals.calstate.edu/pump/article/view/1916

The Power Mean Test
Abstract:
We devise a new test for convergence or divergence of an infinite series — the Power Mean Test. We explore the strength of this test relative to that of the Ratio and Root Tests and provide a family of series where the Power Mean Test is the most useful of the three tests.

Published at the PUMP Journal of Undergraduate Research.
Link to paper:
https://journals.calstate.edu/pump/article/view/2314

Surprises in Knockout Tournaments
Abstract:
Sometimes the second-best player in a knockout tournament is more likely to win that to finish second. We characterize this surprising situation, under certain natural conditions.

Published in Mathematics Magazine.
Link to paper:
https://www.tandfonline.com/doi/abs/10.1080/0025570X.2020.1736892

Math at home

COSMOS Summer Program at UCSD

Summer 2016