I asked about this on the academic and career guidance forum but didn't get any useful replies.

Which of these maths subjects (all at fourth year level) would you recommend for someone interested in the subjects listed in the title? What would you say is missing from this list?

Functional analysis

Partial differential equations

Algebraic topology

Algebraic geometry

Commutative algebra

Representations of the symmetric group

http://www.maths.usyd.edu.au/u/UG/HM/pure2007.pdf

By the time I reach fourth year I will have taken courses in metric spaces (topology), rings fields and Galois theory, differential geometry and Lagrangian and Hamiltonian dynamics (applied maths).

Thanks

James