Here at PSU, Sergei Tabachnikov just finished giving a two-week mini-course on the “geometry of polynomials.” The collection of topics was diverse: various proofs of the fundamental theorem of algebra, resultant and discriminants, Chebyshev polynomials, harmonic functions in three-space, and a sketch of the proof of the four-vertex theorem. The lectures presupposed familiarity with no more than elementary analysis and linear algebra, though more advanced topics were referenced (without proofs).

Two weeks really means about seven days; class was cancelled because apparently people thought that most of us were interested in an art show.

For the benefit of the huddled masses yearning to be educated, here are the notes that I took from these lectures.  The file is rather large (40 MB) because of the insertion of jpg images that someone else in the REU drew. The djvu file is a lot smaller, but WordPress won’t let me post it, so email me if you want it.

The notes are mostly a faithful representation of what I took in class, but I have edited them lightly to moderate my tendency to embarrass myself.

Next week, Yakov Pesin is lecturing on fractal geometry and dynamics; I’ll post those notes when I’m done with them.