Hmm, this new 'advanced' linear algebra unit is certainly an interesting idea - but I wonder about its motivation. The general consensus (from fellow students) I got when studying MTH2021 last year, was that most didn't mind the computational and applied aspects of the unit, but there didn't seem to be a lot of love for the purer, abstract, general stuff (as you can probably guess at from the comments above).
A peer summarised this feeling quite well - MTH2021 is classified as an 'applied' unit, but is taught more in the style of a 'pure' unit. What does that mean? Well, firstly, part of the course deals with more general and abstract concepts relating to matrices and vectors. A lot of people said that trying to get through 'general vector spaces' was when the hate first started. The whole concept of matrices and vectors had basically become abstracted to something so vague and general that it was hard to conceptualise what our minds were grappling with now.
What kinds of properties did these 'general vectors' have? Well, it turns out this is where the counterintuitive proofs came in - essentially proving stuff that appears to be intuitive. Why do we do this? So we KNOW that we are justified in manipulating these objects as our intuition suggests. This is a quality that is more associated with pure maths - we want full rigour; we want to build up a general mathematical framework from the most basic of axioms, and we most certainly want proof! However, I think that for most students studying MTH2021, it is not the process (proving intuitive properties) that is of greatest importance, but rather the end result (knowing that you can use those properties). As a result, attempting to place these bits of pure maths in the unit probably resulted in an inhomogeneous blend that just made things worse for pretty much everyone.
When it was time for assessments, it was mostly the computational and procedural aspects of this unit that ended up being tested. The simpler proofs that ended up being questions did not contribute too much to the overall final mark.
With all this in mind, perhaps MTH2025 is meant to be for those who enjoy engaging in purer, more abstract-styled maths. How will it be different to MTH2021? I reckon the lectures will be the same, but the weekly tutes will probably have some additional stuff on there. That, and/or the assessment questions will probably have more proof-based material. I guess time will tell. It looks like MTH2021 is still going to contain those purer aspects in its design, so I guess things aren't really going to change there.
With regard to the 'advanced' maths units as a whole, I personally think that while it can be fun to extend your learning and delve deeper, the time needed to understand the material (keeping in mind how much of it is assessable) really has to be considered. Taking the advanced units also means less tute time to discuss the bits of the 'standard' unit that may prove challenging. My overall opinion of these units is that if you're the kind of student these programs target, you'll probably have *some* fun being exposed to new concepts and learning extensions/background to the stuff you do in the normal classes. But at the same time, if you do the regular unit, I'd say you're definitely not missing out on all that much.
If you're still undecided on advanced units - I say give it a go; most course coordinators are more than happy to 'transfer' you back to the regular unit after a couple of weeks if you decide this isn't for you, no harm done. But I reckon it takes a bit of commitment (or masochism) to persist beyond that, so perhaps if you're still uncertain, erring on the side of caution might be prudent.
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