It might seem early in the year to start thinking about the Simon Marais Maths Competition but it’s really not.
If you’re an undergraduate maths-or-maths-loving student looking to prove your mettle, then the SMMC is likely the arena for you (outside of your courses, that is). It is the maths competition for uni students in Australia (though it is quickly becoming more global) and is modelled closely on the well-known Putnam competition in the US.
In some sense, the SMMC follows on from the high school maths olympiads, but don’t let that put you off if you haven’t been involved in olympiad-style maths. Plenty of people are finding the SMMC as a suitable entry point to competition maths. You might just want to work through a few years of practice problems over the year (or go through some problems in Arthur Engel’s fabulous book Problem Solving Strategies).
Note: I favoured the law over equity by having the above link point to the expensive print version rather than the free PDF one can find when they do a quick google search.
Dynamical Mathematical Gazette 