A university mathematics degree is a three-year climb from the tools of school into the structures of modern mathematics — where every idea is stated precisely and proved. Year 1 rebuilds calculus, algebra and logic on rigorous foundations; Year 2 opens the core theories — analysis, groups and rings, complex functions; Year 3 fans out into the advanced landscape: measure theory, functional analysis, Galois theory, geometry and more. This is the shape of a typical honours degree, mapped onto the tree.

The three years

• Year 1 — Foundations — proof, calculus, linear algebra, discrete maths and a first look at groups.
• Year 2 — Core — real & complex analysis, rings & groups, numerical methods and optimization.
• Year 3 — Advanced — measure theory, functional analysis, Galois theory, geometry and specialised topics.

By subject

Prefer to dive into one field top-to-bottom? Each of these hubs is a whole subject on its own.

• 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