The most difficult math class available at universities is combinatorics, according to Cornell University. The difficulty and complexity of a math subject is subjective, however, and depends on the individual. Graduate-level mathematics courses at the Institute of Mathematical Sciences include subjects like real analysis, hyperbolic geometry and algebraic topology.
Combinatorics studies the relationships between numbers with regard to patterns, such as those found in computer-generated algorithms. In many cases, combinatorics bleeds into other mathematical subjects, such as algebra and topology.
Algebraic topology is the study of topological spaces using algebraic theory, while real analysis studies the relationship between points, such as connectivity and convergence. Hyperbolic geometry is a related subject that deals with the second and third dimensions.