Synopsis
Basic theory of finite fields: construction, Galois group, Norm and Trace. (Some of the basic results will be assumed without proof.)
Polynomial multiplication: Karatsuba, Discrete Fourier Transform, Fast Fourier Transform.
Polynomial factorisation: Berlekamp's algorithm, Cantor-Zassenhaus's algorithm.
Point counting on curves: Chevalley-Warning theorem, Dwork trace formula, Wan's algorithm.
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