As a bit of context, this was the first proper mathematics subject I completed during my first Semester at the Uni, after taking the extension program subjects of Linear Algebra & Calculus 2. In a nutshell, the 2024 installment of Vector Calculus: 'Advanced' was an unorganised and chaotic detour, akin to a ghost train ride at a derelict carnival fair - the signs were right in front of us within the first lecture, but we stepped into the cramped carriages and continued nevertheless. The content was designed as an intellectually stimulating mix of the mainstream vector calculus content - think computational but occasionally neat calculus in multiple dimensions - with multidimesional analogues of results from Real Analysis; in order to get the best out of this secondary part of the course, I would recommend studying that subject or its advanced component beforehand or concurrently as things will make more sense. As someone who wasn't familiar with this content (mainly epsilon-delta style proofs), I was confused in the first lecture and never properly assuaged this discomfort throughout the semester. Our lecture was the whimsical Gufang Zhao who was an amusing entertainer with several eccentricities, but whose classes lacked rhythm and structure, without a cohesive set of notes, and featured many interesting but not always relevant caveats into other areas of mathematics. To give him credit, those of us who stuck with the subject were rewarded with a very straightforward exam, and assignments were doable if a little tantalising at times. With all this in mind, I would strongly recommend the standard stream of this subject, even for students looking to extend themselves, which confident students will likely find a breeze, as opposed to this carnival ride, a true mockery of the term 'advanced'.

This subject was amazing, one of the hardest but one of the most enjoyable subjects I have ever done. Highly recommend you take either real analysis or accelerated maths 2 before you take this because it is going to be a significant jump from other first year mathematics.

This is a very difficult subject, but for all the right reasons. You are asked to digest abstract concepts at light speed, but coordination was great and you have plenty of support to do so. You will come out the other side more "enlightened" having peered into mechanisms of mathematics that are hidden away in normal courses. I took it as my first math subject after doing a watered down calc 2 and linear algebra for high-schoolers, and I was fine after putting in a serious time commitment (I kept track, averaged 2 hours a day, every day). You may lessen the pain somewhat by taking real analysis or real analysis advanced concurrently since you'll be able to re-use the same kind of mathematical thinking. By doing this subject over Vector Calculus, you are signing up for also learning the rigorous, low-level machinery needed to define multi-variable calculus concepts, so before derivatives and integrals you learn about open sets, connected sets, sequences, Bolzano-Weirstrass theorem, epsilon-delta definitions of limits and continuity, so on. You will also see rigorous and surprisingly detailed constructions of concepts like arc length, and area integrals. In the end, this subject had both an applied and a pure math flavour.---- While the subject matter is daunting, it was an extremely rewarding experience. For those who love mathematics, this is the perfect subject. Even if you're unsure, I still recommend this subject. If things get too hairy for you, switching to the normal stream is an option. But if you stick with the subject, you'll be handsomely rewarded.