U.S Maths syllabus

1. 0-0 Arithmetic index
2. 0-1 Basic geometry index

3. 1-0 Pre-algebra index
4. 1-1 Algebra I index
5. Geometry
6. Algebra II
7. Precalculus

Example Syllabus - MIT BSc Pure Mathematics

8. Single-variable calculus
9. Multivariable calculus
10. Linear algebra
11. Complex variables
12. Ordinary differential equations
13. Partial differential equations

• Abstract algebra
• Number theory
• Real analysis
• Advanced calculus
• Complex analysis
• Probability theory
• Statistics

By now I'll know enough to choose what specialisms interest me. Some likely useful starters are:

• Set theory
• Mathematical logic