Date of Graduation
Master of Natural and Applied Science in Mathematics
elliptic curves, plane curves, associativity, groups, Mordell, Weil, Fermat, Andrew Wiles, Maple
Algebra | Algebraic Geometry | Number Theory
An elliptic curve over the rational numbers is given by the equation y2 = x3+Ax+B. In our thesis, we study elliptic curves. It is known that the set of rational points on the elliptic curve form a finitely generated abelian group induced by the secant-tangent addition law. We present an elementary proof of associativity using Maple. We also present a relatively concise proof of the Mordell-Weil Theorem.
© Montana S. Miller
Miller, Montana S., "On Elliptic Curves" (2021). MSU Graduate Theses. 3604.