Rather than march year by year, you can follow a single subject all the way up — from its first rigorous appearance to the specialist final-year material. Eighteen strands run through an undergraduate mathematics degree; pick one and climb it. Each is a whole subject hub on its own.

The eighteen subjects

• Calculus & analysis
• Linear algebra
• Abstract algebra
• Complex analysis
• Number theory
• Topology
• Measure theory
• Functional analysis
• Differential geometry
• Statistics
• Combinatorics
• Graph theory
• Numerical analysis
• Dynamical systems
• Optimization
• Set theory
• Proof & logic
• Mathematical logic