| Abstract:
The only non-trivial fact about the group operation on an elliptic
curve is the associative law. We kept postponing its proof because of
the inherent difficulties in giving a direct proof using the actual
algebraic formulas defining the group law. Given the background and
the richness of this topic, there are bound to be several proofs for
the associativity (ranging anywhere from linear algebra techniques to
model theory to complex functions to topological methods). In this
talk, I plan to give the outlines of some of these proofs and give
one complete proof in detail.
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