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The MATHUSLA detector to be installed on the surface above and somewhatdisplaced from the CMS interaction point (IP) will cover an area of $100\times100$ m$^2$ containing many layers of scintillators planes to establish thespace and time coordinates of charged particle tracks. This is an unprecedenteddetector in terms of size and continuous sensitivity over an area of $10^4$m$^2$. This document describes the present MATHUSLA detector concept that issensitive to both long-lived particles produced in the LHC collisions in CMSand cosmic ray extended air showers (EAS). The ability to improve significantlycosmic ray studies by adding a $10^4$ m$^2$ layer of RPCs that have bothdigital and analogue readout similar to the ARGO-YBJ experiment will bediscussed with focus on large zenith angle EAS.

Exploring the lifetime and cosmic frontier with the MATHUSLA detector