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I'm new to these forums but I've actually used these forums a lot in the past for research, etc. I decided to make an account because I'm just about to go through year 12 exams in an Australian high school doing Specialist Maths (Highest level maths), maths studies(High level), physics(the only level) and english. I've always been interested in IT, I have most of my Adv Diploma of IT in computer networking, but I tend to look at that as a hobby/personal knowledge. I love programming and that's driven a lot of my maths skills throughout high school, for instance writing a program that uses the theorems from cyclic quadrilaterals to solve for theta, etc.

Recently I've taken to just doing maths and physics by itself, without IT and I love it. I've started pushing the boundaries in physics and I'm getting there in maths.

Problem:

I don't really know where I want to go, I'm thinking a double degree of some form of engineering with a degree of science/maths. I'm really struggling with specifics though. I'm not going to ask you "What type of engineer should I be?" because only I can really make that choice for myself, so I was thinking I could get some books for the summer holidays and just read some of them and see what makes me tick. BUT I'm also reading because I want to expand my knowledge in some areas, like physics mainly. So, I was hoping that I could give you guys a run down on the topics I've covered in maths and physics at school, and you guys could give me some good reads I could look at getting? I would like to get my hands dirty in some examples too if there are any other more 'involved' reads available.

In Maths we've done the following this year

Single variable calculus (Integration and deferential equations)

cyclic quadrilaterals

complex numbers

real polynomials

trig preliminaries

3d vectors

trig calculus

exponential/log functions

stats (binomial dists,etc )

matrices

I'd like to get a head start in uni maths so I cruise a bit smoother through first year

And in physics

electromagnetism

classical mechanics

wave mechanics

a lot of physics history (like the different models (plum pudding atom, etc))

fields

the particle model of light

orbital mechanics

I'd ultimately like to be able to look at the maths that is string theory and other GUT's and actually understand whats going on.

Looooooonnnnnnnnggggg thread sorry guys but this is a big thing going through my head at the moment, I wanted to be thorougher haha.

Thanks