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MAST20026 - Real Analysis Notes

Written by Chris

This is a comprehensive compilation of information from MAST20026 lectures, the textbook, tutorials,...

24 pages, 5923 words


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Back when I took Real Analysis, it was kind of boring, because it was almost entirely on pure maths theory without much application. Sure, it would have been great if I wanted to pursue a maths career, and I've used some of the material here and there over the years, but not much. Most of the useful things I've learned could have been gained from reading a textbook, such as various methods for mathematical proofs. It's entirely possible that the course has changed though. (I took this subject in semester 1, 2013, but that doesn't appear in the drop-down menu, so I'll select semester 1, 2017, which is the oldest option available.)

Anonymous, Semester 1, 2017

Really hard. Tutorial sheets were ridiculously hard which made it difficult to understand what you actually needed to sit down and work on. Tutors would be like 'yeah thats a tricky one but don't worry, it won't be that bad on the exam', not really acknowledging the fact that to get comfortable with easier questions, you need to practise with easier questions and use them to figure out what you know and don't know. It was a lot of frustration and wondering if you'd fail or not / how you were sitting in the cohort. Also, who's idea was it to have 5 x 4% assignments that each took hours and hours of work?? The assignments were useful in guiding my revision but they should have been worth more. E-d proofs were super cool, the content of the subject is actually really interesting and nice. It's just the expectations in tutes/assessment is crazy- if I could do this subject without assessment, it would have been the best thing in maths so far. Alas, I found it borderline traumatic. Advice: go to the lectures. Ask the dumb questions in tutes because chances are someone wants help too. Use past exam questions and assignments to guide your revision.

Anonymous, Semester 1, 2019

Don’t trust the past exams!

Anonymous, Semester 1, 2019

Lecturer wasn't clear with what he wanted from us, skipped over examples. Very difficult

Anonymous, Semester 2, 2018


Anonymous, Semester 1, 2018

I found most of the content in this subject interesting and definitely liked the concept of this subject. However, as many previous comments have suggested, the tutorials were more challenging or at a different pace to the lectures. While challenging yourself is a good thing, I felt that the tutorials didn't really help in preparing for the exam, which was frustrating. The problem booklet was similar, with simply not enough *exam related* questions for me to truly feel comfortable with the subject. Of course, I know that learning is far more than exams, but I feel like enough exam-related practice material should be made available first and foremost, and then the additional, deeper content for those who want it. One additional gripe I had was the fact that lectures were slow for the first few weeks, and just took off after the mid semester break. That's a general problem with many subjects, they take too long with the introductory (and generally easier) content, and explode after the mid-sem break, making it a stressful rush to cover everything in adequate detail. The lecturer is decent, but he teaches some chapters a lot better than others (IMO), and at this level more consistency would be appreciated. If you like maths, this subject is worth taking, but as mentioned by others, is a big step up from the level 1 maths subjects, in my opinion.

Anonymous, Semester 1, 2018

I think everyone should try analysis, it is very important, but personally I did not enjoy it (mostly because I found it exceedingly more difficult that other courses). But this is purely a personal taste, and there are some very interesting things within real analysis. You cannot know without trying your hardest at it, you never know!

Anonymous, Semester 2, 2016

I liked the subject and the way it was taught, however I think that the way they teach proof-writing is incredibly poor and it could use work. It wasn't until 'Metric and Hilbert Spaces' in third year that I learned "Proof Machine" and honestly I think it should be taught during Real Analysis.

Anonymous, Semester 1, 2016

I'll be honest. I disliked this subject - and I know many others who do too because the return I received was not enough for the amount of hours I put in the subject. The lecturer's fine but there were times where I had to seek out youtube videos and even lecture videos from the previous semester to understand what he was explaining. I would say all of the content you learnt were relatively easy/reasonable (you can understand it as it was pretty basic), but when you enter the tutorials, you will begin questioning yourself as to whether you really DID understand it. I struggled with the tutorial questions because they were out of my comfort zone. The tutorial questions pushes you to think further about the concepts more than what the lecturer had showcased in the lectures. I didn't get much out of the tutorial because I found it too difficult. Because the subject is under the pure mathematics department, don't expect it to be a breeze if you came out doing well in the first 3 maths subjects (calculus 1, calculus 2 and linear algebra). Rather than expecting a certain answer (like what the calculus subjects taught you to find), the subject focuses on proofs. One of the things that annoyed me about the proofs was that sometimes you had to work backwards to be able to write up the whole proof. My tutor was harsh on taking off marks but the assignments were ok. They weren't hard but I would say dedicate a day to complete them. The problem book did not provide answers to all the questions. overall the subject was definitely.. different. The main reason I disliked the subject was because the amount of hours I spent on the subject only got me an okay mark. otherwise, despite it being a painful journey across the semester, I am thankful that I got the subject over and done with.

Anonymous, Semester 1, 2017

I want to clear something up. People wil call this class "needlessly particular" or "too pedantic" etc. But they are WRONG!!! The correct thing to say is that it is "particular" and "pedantic". Absolutely. A high attention to detail is required for this class, but what is amazing abiut this subject is that it also shows you why this level of specificity is avtually needed. The high detail is not unnecessary, in fact it's critically needed. Try to think about why as you take this subject, and you will be rewarded with more tha just a high mark.

Anonymous, Semester 1, 2014