One of my new students is from the UK.

Showed me what she covered in Math in "Further Maths"

Includes:

Elementary Number theory and modular arithmetic

Abstract algebra incl group theory

AP BC level of calculus (+ more integration techniques (+ are second order diff. equations + Taylor series + Hyperbolics)

Series and sequences; Linear recurrence relations (of all orders)

Linear reg y x ing, correlation (incl Spearmans), discrete random variables and distributions, continuous random variables, nonparametric tests, and some other stats stuff

Kinematics, projectiles, other mechanics/physics stuff

Vectors, matrices

Polar co-ordinates, complex numbers

Some stuff that vaguely resembles the beginning of Real Analysis

Lots of proof and modelling

Highly impressed. Anyone else familiar with the syllabus?