MTH2025: Linear Algebra (Advanced)

This is the first time the unit run, so we could be seeing some massive changes in future years. The unit itself runs very similarly to 2021 content, and so feel free to look through those reviews as well. Importantly, this unit doesn't run like the advanced equivalents 2015 and 1035 where you learn a bunch of new content to support what you're currently doing - instead, 2021 teases some proofs and information, and then 2025 properly goes through them. So, if you're interested in pure maths, 2025 is the unit for you. Unfortunately, the content done in 2025 doesn't extend to applications, but they're of course still assessable since you're also doing 2021.

As for 2021 material, it's fairly standard, really. I'm not going to go into it, just look at other reviews/the handbook - I don't really have anything to add. However, a lot of people *do* say that the unit is "quite pure". I disagree - the unit is certainly rigorous, and is most likely the first rigorous maths unit you will take, but a lot of the stuff covered is quite general, and anything that's very "pure maths" (such as inner products or eigenspaces) is offset by an application of some sort, and this unit is very good in that it dabbles in everything. You see some applications in discrete maths, solving DEs, and even some statistics stuff.

The 2025 material essentially just goes through all the proofs you missed in 2021, with only two new additions in content. You learn about some group theory (just for fun, I guess? Essentially to show that matrix multiplication forms a group), and more importantly permutation matrices, Leibniz formula for calculating determinants and dual spaces. The last three bits are used to make their own little additions (show some nice things about them, how they work, etc.), but are required for some of the proofs missed in 2021. You are of course expected to use these by themselves, but otherwise they're just tag-along to make everything more rigorous.
Tl;dr, this is just like MTH2021, but with more rigour.

Tim Garoni

Yes, 2 for 2021 and 1 for 2025.

4 out of 5

Yes, with screen capture

Some book by Anton and Torres. You definitely don't need it.

2015 Semester 1

81 HD