Mathematics
Abstract Algebra
Groups, rings, fields, modules.
Algebraic Number Theory
Algebraic numbers, quadratic fields, zeta functions, cyclotomic fields.
Algebraic Topology
Fundamental group, homology, cohomology.
Analytic Number Theory
Prime number theorem, Dirichlet series, Sieve methods, Riemann zeta function, arithmetic functions.
Category Theory
Categories, morphisms, functors, natural transformations.