Re: Complete Guide to 1st Year Uni
I found 1st Year Linear Algebra to be quite difficult. I call it Maths v2.0 jokingly as srsly it's so absurd that I blanked during the exam and ended up getting a low D. Plus you don't even know why your doing it. Even in 2nd Year, we still don't apply Linear Algebra to solving the Schrodinger Equation. Best is to study part of it before you come to uni by searching the UOS handbook and choosing ur uni subjects 2 weeks before coming to Uni.
Retrospectively, I would have felt coaching for Uni would be better than for HSC which admittingly is a rote-learning contest.
When it comes to very basic tertiary-level Mathematics, you don't quite see the applications of it. Why do you need Gaussian Elimination? Who cares if I'm finding the inverse? It's all just number crunching! etc etc.
However it does have huge applications later on ESPECIALLY with eigenvalues and eigenvectors.
What you're saying is the equivalent of holding a nail and saying "lolwut, this nail can't do anything, it's useless!". However when combined with say a hammer and a couple pieces of wood (Analysis for example), you can acquire huge results such as proving the Fundamental Theorem of Algebra.
That's interesting, I always found linear algebra pretty intuitive and it was fun when we did proofs and things with it in 2nd year
I blame the NSW maths syllabus, in better states (hello Victoria) they teach the basics like matrices in year 12
The thing is, the point of the NSW syllabus is to be able to apply your knowledge. Suppose we learn basic matrices stuff like Gauss-Jordan elimination, finding eigenvalues, the determinant etc, it doesn't have too many applications in the otherwise elementary mathematics that constitutes the NSW Mathematics syllabus.
Sure, you can use Gauss-Jordan to solve simultaneous equations, you can use the determinant in Conics problems (the ones like "Prove that the triangle formed by the tangent and blah blah is independent of P"), but it is quite limited and not really worth adding it in to the syllabus without having a decent number of applications (and not adding any new topics to supplement it).
For example, Circle Geometry can be used in various proofs for Circular Motion and numerical problems (2009 HSC Q4(a))
First year Linear Algebra (i.e. the introduction to matrices and vectors) is pretty crap I think. It's just boring. As you said, second year LA with the proofs is much more fun.
This, but I do admit I still haven't fully appreciated the beauty of Linear Algebra. Even Second Year LA just covers fairly basic stuff like kernel, null space, basis etc. I think Third year is where things start getting intense.
Weird. All my friends found it to be easy (because it's just applying formulae blindly...)
I found it to be really boring.
But I really did enjoy Complex Analysis and Several Variables Calculus which my friends hated...
I don't quite enjoy Multi-Variable Calculus, but Complex Analysis is very cool.
