Thread: How does HS maths compare to University maths?

I am in my final year of high school at the moment, thinking about doing BSc (Adv.) at the university of Sydney next year. At the moment I do English (compulsory), chemistry, physics and 4 units of maths, which is the highest level possible here in Sydney. The topics I'm studying are curve sketching, complex numbers, polynomials, integration, mechanics, conics, series and induction, inequalities, circle geo, combinations and permutations, binomial theorem, probability, and more...
I just want to know what topics we do in first year uni, how much harder than high school is it? I am thinking about maths + physics majors since I am allowed to pick two majors for science advanced degree.

Hey mate. I am doing Engineering & Science up in Queensland. I have done 2 math courses this year and currently doing 1 in summer. Math1051 (the first course if you had done the hardest high school math... which we call MATHS C in QLD) was a lot of revision of high school stuff , especially to do with integration and matrices. We also began series and sequences . Although much of this course was revision , I found it the hardest.... I think mainly due to the fact that uni was very new and my study habits weren't up to scratch. Math1052 was next, and we did all very new stuff .. a lot of work with planes and gradients.... but although it was quite new it was pretty easy. Now I am doing Math2000 which builds on the other two.

If you wanted to find the exact topics you can go to this link Multivariate Calculus & Ordinary Differential Equations - Courses and Programs - The University of Queensland, Australia and press COURSE PROFILE. *note you can change the MATH1051 on the end to math1052 or 2000 to view the other two maths subject. I am sure your uni in Sydney will have something similar.

I'm studying math on the university of Århus in Denmark, and on the first year we had the following:

Calculus (half a year):
-Integrals (Double integrals and triple integrals).
-Differentiation (Partial differentiation and a bit of differential equations),
-Infinite sequenses and Series (Power series, Taylor/Maclaurin series)


Modular Arithmetic (quarter of a year):
- Greatest common divisor
- Prime numbers
- Congruenses (Fermat's little theorem, Eulers theorem)
- Cryptography (Introduction/intuition)


Discrete Math (3 quarters of a year):
1st quarter
- Random variables and vectors (Absolute continuous and descrete)
- Mean, variance and covariance
- Transformation of random variables and vectors
- Distributions (Normal, binomial, possion...)

2nd quarter
- A lot of statistics stuff I don't really remember (I didn't like statistics much and as a result was inattentive)

3rd quarter
- Probabillity/density functions
- Markov chains
- Recurrent and transient states
- The stationary distribution


Linear Algebra (half a year):
- Linear equation systems
- Matricies
- Linear combinations
- Basis and dimension
- Vectorspaces and subspaces
- Linear transformations
- Least squares method
- Orthogonal and orthonormal sets
- Determinants
- Eigenvalues and eigenvectors
- Matrixexponential


Mathematic Analysis - In this subject we prove rigorously some of the things we just take for granted in Calculus (3 quarters of a year):
1st quarter
- Sequenses (Convergence, Cauchy-sequenses, Supremum/Infimum and Limes supremim/infimum)
- Infinite series (Geometric series, alternating series, convergence tests, power series)

2nd quarter
- Metric Spaces
- Continuous functions and uniform continuity
- Integrals of functions (Riemann sums, approximation of integral, middle value theorem for integrals)

3rd quarter
- Differentiation (Proving all the rules of differntiation known from Calculus)
- Taylor series
- Convergence of sequenses of functions
- More power series
- Fourier series


Here on the second year I've finished measure theory and differential equations, and at the moments I'm studying algebra and real analysis.
I'm sorry for all the spelling errors and I hope it wasn't overkill, but you asked for topics XD
As for the level compared to high school I can't really tell, I had an awful high school so the level was high to me, but others not so much... You'll know if you can recognize some of the topics.