Algebraic geometry becomes an ever more important subject, with its involvement in theoretical physics, via string theory, and its use in the solution of Fermat's Last Theorem and in cryptography. For a 3MB project the aim would be to study algebraic curves in the projective plane, working towards Bezout's Theorem and the group law on an elliptic curve. For a 4MM project this could be augmented with further study of elliptic curves, for example Mordell's Theorem that the rational points on an elliptic curve form a finitely generated abelian group.
Prerequisites:
Level 2 Rings, polynomials and fields, and level 1 group
theory and linear algebra.