MA4491/4492 is an optional module for students in their final year that offers some research experience in the shape of a half-year or a full-year project. Feel free to contact me (or any other staff member of School of Maths, to that matter) about topics for final year projects; I think that solving some problem as a project is more fun, but I can suggest reading–oriented projects as well. Your name can easily end up on the list below!
Jack Kelly, Boson—Fermion Correspondence and its generalisations
Ronan Darcy, Topological proof(s) of Abel's theorem
Ruadhai Dervan, Hilbert schemes of points
Josh Tobin, A case study of Gröbner bases and Anick's resolution
Sean Damery, Complex numbers, quaternions, and sums of squares (summer internship)