Echoing what the previous review said, the subject was not taught as well as it could've been. The lecturer (Paul Zinn-Justin) seemed quite uninterested in the content some of the time. Additionally, he didn't give any examples or ways to apply the theorems and ideas he was proposing (basically saying that all these methods exist, and we have proved they exist, but we aren't gonna tell you how to do these methods) This happened the most when we studied the Jordan Normal Form of matrices (which I imagine only 10% of the cohort understood) and permutations (where we were not taught how to use cycles at all in-lecture, as if it were assumed knowledge). The assignments were incredibly challenging and punishing, with little to no sources for help if you were getting stuck at any point (so if you had a gap in your knowledge, you would have a very hard time figuring out any way to start your assignment questions). I don't know of anyone who did half decent on the exam, as it was so incredibly challenging. It felt like you were expected to memorise every single little corollary mentioned to do well. As it is a pure maths subject, you expect that you will have to think about the proofs in-depth, how to approach them and what theory to apply to prove the given statement. However, the exam was more similar to an applied mathematics exam, where you were expected to have the process come to you automatically, churning through the questions and applying techniques. Personally, that is not what a pure mathematics exam should be like, as you should be tested on your proficiency in proof writing and depth of knowledge, not being able to quickly recall something written on page 17 of the topic 5 notes. That being said, the content was quite interesting. I found the group theory stuff incredibly intriguing.

I have a few things to say about MAST20022, most of it pretty bad. To begin with, this is a very hard subject, I'd say much harder than real analysis. The assignments were pretty hard as well, there was three of them and the marking was dumb because it'd be out of 100 marks so like one small question could be 10 marks or something. The exam was extremely difficult and much harder than previous years exams despite being the first year with no cheat sheet. There's pretty much no worked examples in class, and the lecturer wasn't great either, he just read from the notes verbatim.

Absolutely recommend it to everyone who loves pure math! The content is half linear algebra and half group theory. The linear algebra side helps you to dig deeper from the first-year subject with the direct sum, Jordan normal form, minimal polynomials, etc It is really useful, especially since the Jordan normal form is widely used and helps you to comprehend the nature of matrix. The group theory side is really much introduction and pure, but it can generalize and produce strong math results. You can see many impressive combinatorics results using group theory. Some proof on this side is tricky but if you love the nature of math, take the subject!

Hard, but interesting.

If you get the lecturer Arun Ram for this subject, withdraw IMMEDIATELY. He ran the subject entirely through his own website, and it was nearly impossible to follow his directions (these include copying out simple but long solutions FIVE times). He diverted from course material, explained concepts poorly, and frequently made mistakes in his examples. He was haughty and condescending to students, and spent much more time talking about himself than about the content. At one stage, he forced us to navigate through some manifesto-like ramblings that included everything from inappropriate political commentary to strange and awkward poetry. Not to mention, he accidentally compromised the exam at the end of semester. He is undoubtedly the worst lecturer I've ever had, and I write this review not to insult him, but to warn other students. He's completely unprofessional and incompetent. I hope this saves others from struggling like I had to.

I loved this subject! It was the first subject I really honestly and completely understood the nature of what proof is. I studied the class under Arun Ram, who is a bit of a contreversial lecturer, in that his teaching style is a bit unorthodox, but I believe it was a very rewarding experience. I would recommend this subject to anyone who wishes to really understand what pure maths is like. Don't think that you have to recall everything from linear algebra in first year, everything is built from the ground up. Highly recommend :)

I found this to be an excellent subject. For me it was very hard as it was the first real 'pure maths' subject I have done. If nothing else, you learn how to write proofs properly.

Not for the faint of heart, this is well and truly a Pure maths subject. If you thought Real Analysis was pretty abstract then you might be in for a surprise! It is a lot less pedantic than Real Analysis though, so that's a plus. As a previous review says, Alex Ghitza is a great lecturer if he's taking it again, with a nice technique of writing everything up as we go on the whiteboards. For us though he had to use doc cam 2 lectures a week, but it does mean it's important to go to lectures when he's using the boards as these were not recorded. As far as content is concerned, it's a great subject, mostly focusing on proofs of theorems extending from Linear Algebra, and introducing Group Theory (obviously!). It's very important to go to tutorials and do problems Alex leaves as an exercise in lectures as there is a lot of stuff to learn. I won't comment too much on the exam as it wasn't Alex's fault about the evacuation, but it does leave a slightly sour taste in the mouth... In summary, I really enjoyed this subject, and if you enjoy Maths for the beauty of it, and enjoy proofs, then you too will enjoy it, so long as you can keep up!

Alex Ghitza has the cleanest, and most perfect lecture technique i have seen in my life. No mistakes. He never gets confused. He is genuinely very good. The content is amazing also, but is very difficult, be prepared to study hard for it!

Although the exact notes in lectures will be post online, it is better to study them step-by-step and never lag behind. Otherwise, you might get lost in a few weeks