The main topic is what the title indicates: to collect, survey and categorize the results and theories achieved in the last 30 years with “polynomial methods”, mostly (but not exclusively) in finite geometries. It contains techniques based on the careful examination of coefficients of polynomials, resultants, algebraic curves, subspaces generated by certain polynomials, random-like behaviour, etc. Our polynomials are usually defined over a finite field, and they express some combinatorial or geometric property of a combinatorial or geometric structure. We go through several types of applications of the methods. There will be more than a hundred exercises with short solutions.
Peter Sziklai is an Associate Professor of Computer Science at Eotvos L. University, Budapest, Hungary. There he heads the ELTECRYPT research group. He is a doctor of the Hungarian Academy of Sciences and has won the R’enyi Kat’o prize and the Grunwald prize of J. Bolyai Mathematical Society. Peter has also won awards for teaching. He serves as the Managing Editor of the international journal Combinatorica.
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