Surfaces with triple points

In this paper we compute upper bounds for the number of ordinary triple points on a hypersurface in $P^3$ and give a complete classification for degree six (degree four or less is trivial, and five is elementary). But the real purpose is to point out the intricate geometry of examples with many triple points, and how it fits with the general classification of surfaces

Roots of polynomials of degrees 3 and 4

We present the solutions of equations of degrees 3 and 4 using Galois theory and some simple Fourier analysis for finite groups, together with historical comments on these and other solution methods.Comment: 29 page