The math degree at ANU is pretty flexible and autonomous. You could study math purely or integrate it with philosophy, humanities, sciences, etc. There are options for you to switch focus after a semester and choose between various areas of math for specialization. In a way, you have an opportunity to construct your course degree.
Consistently, the career options also lie on a diverse spectrum. On one end, you could get into mathematical research and academia. But you can also change directions and get involved with areas to apply your learning, such as computational genetics, financial modeling, etc.
Your degree could last for three or four years, depending on your preferences. The optional fourth-year leads you to an honours degree and requires you to present a thesis. The specialization you have acquired for the first three years will help you identify the area you want to research. There are also some exchange programs available generally for six months, where you could explore a foreign country and gain a different dimension in terms of learning a subject.
To prepare yourself for university maths, which is often poles apart from the mathematics you learn in high school, having some touch with logic and sets could reduce this gap. Get acquainted with proofs, especially if you are into pure mathematics. In all, you need to be able to adopt a new pattern of coherence and thought and communicate mathematics.
You can learn more about mathematics at ANU here.