It all depends on how you feel after revising those topics. I'm sure the curricula between the two states don't match up exactly, but for the most part, you seem to have a decent foundation (particularly with matrices, which NSW student don't encounter during secondary education).
I think both universities' advanced mathematics degrees are excellent. But there are differences:
- At UNSW, the Advanced Mathematics degree requires you to complete an honours year, whereas for USYD, you only have to major with units under the advanced stream. (Personally, I found the latter more attractive, since I initially planned to do an honours in economics. So it really depends on your goals.)
- The two degrees have slightly different requirements. For example, UNSW has general education units, whereas USYD requires you to complete 4 junior science units from at least two areas of study outside of mathematics.
- The two universities offer different units of study.
I personally found USYD to be more flexible (an advanced mathematics major at UNSW requires at least 84 credit points [including the honours year, I think], whereas at USYD, I only need a minimum of 48 credit points). This allows me to pursue an additional statistics major in my degree (on top of my economics major as a part of B. Arts). I also really enjoyed the Special Studies Program for mathematics at USYD (I chose not to do the Talented Students Program, but a lot of students enjoyed it).
Someone else at UNSW could elaborate on their degree better than I. Both universities are great, and people pick them based for their own reasons.
