Advanced/Higher Stream Compulsory Mathematics (1 Viewer)

[Amleops]

I am considering doing various degrees in combination with Science or Science (Advanced Maths), majoring in Financial Mathematics. I wanted to, if I can, at least try out the higher compulsory maths stream even though I’m not doing 4U maths currently. Maths is probably my favourite subject at the moment and I am currently topping 2U Maths at my school, and I'm towards the top of 3U as well.

From what I gather the only difference between courses like MATH1001/MATH1901 at USYD and MATH1131/1141 at UNSW is that there are harder exams, and otherwise the classes and content are the same. So is the only reason they recommend 4U for the higher maths courses or the Advanced Mathematics degree in general is because of the exposure they have had to harder questions in the HSC course, not so much as knowing the content itself?

If I’m wrong and it is the latter, what topics in particular should I be looking at learning beforehand? Because I would think that (again I could be wrong, just guessing) a topic like Mechanics wouldn’t come up too much in those junior maths courses, would they? I was going to learn the 4U syllabus with my tutor in the summer holidays, but if that knowledge is expected than I’d definitely have to commit myself to it.

 

[Carrotsticks]

Great to see another student who also enjoys Mathematics!

From what I gather the only difference between courses like MATH1001/MATH1901 at USYD and MATH1131/1141 at UNSW is that there are harder exams, and otherwise the classes and content are the same. So is the only reason they recommend 4U for the higher maths courses or the Advanced Mathematics degree in general is because of the exposure they have had to harder questions in the HSC course, not so much as knowing the content itself?

You are indeed correct. The Normal and Advanced Stream learn the exact same content. However, the Advanced stream tends to go into a bit more detail regarding the theorems and proofs. If you enjoy Mathematics and decent at it (and from what you're saying, I'm sure you're MORE than decent), then I suggest you try the Advanced stream. It is much more rewarding in a sense that you feel like you 'learn more Maths' overall. It is a difficult concept to properly describe, but I hope you understand what I'm saying.

I had a look through the Normal lecture notes and their exams at the University of Sydney where I study. They have a lot more numerical examples as opposed to actual proofs of cool things. The Normal exams are very mechanical-like ie: Find the directional derivative in the direction of this vector, calculate the determinant of this matrix etc etc. However, the Advanced Exams and tutorials cover cool questions like "A Hessian Matrix is defined to be XXXXXX such that there is a saddle point at (x,y,z) if the Matrix is indefinite. Show that f(x,y) has a saddle point." etc etc, can you see the difference?

And indeed, 4U is recommended for the higher courses because they expect a certain level of speed and competence from you in order to do those units.

If I’m wrong and it is the latter, what topics in particular should I be looking at learning beforehand? Because I would think that (again I could be wrong, just guessing) a topic like Mechanics wouldn’t come up too much in those junior maths courses, would they? I was going to learn the 4U syllabus with my tutor in the summer holidays, but if that knowledge is expected than I’d definitely have to commit myself to it.

They teach you everything from scratch actually, so you do not really need to have a tutor. However, you can significantly facilitate the first couple weeks of 1st year by having said tutor.

You actually guessed correctly, the topic "Mechanics" is not used at all during 1st Year Mathematics (at USYD at least). But here is a list of topics that you will want to learn ahead to ensure that your first few weeks go as smoothly as possible:

- Complex Numbers (if possible, ask your tutor to teach you the exponential definitions as well, because these are omitted from the HSC Syllabus)

- Integration & Volumes

- Curve Sketching

 

[Amleops]

Great. Thanks a lot