MAST20026 Real Analysis Lecture Note + Problem Sets

Melbourne university

For sale by Georgina for $8

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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Hi, I'm Wilson, currently a Masters student at unimelb studying Applied Mathematics and Engineering....


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Last year I finished a Masters of Science in mathematics and statistics with a WAM of 89.25 and an a...


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I am a tutor in the maths department at the University of Melbourne for Calc 2, and am a masters stu...


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I am currently studying a Master of Science (Pure Mathematics) at The University of Melbourne. In 20...


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I am a PhD research scholar in Mathematics. I have a very good experience in tutoring university mat...


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

A very interesting and enjoyable subject if maths is your thing. It's easy to become overwhelmed and fall behind in the course content, but the tutes help to keep you on track. The content is hard and you are made to think about maths in a totally new way, so don't be afraid to feel stupid in the tutorials and ask questions - thoroughly understanding what is going on is the only way to pass this subject!

Anonymous, Semester 1, 2016

Quite an interesting subject. After doing this subject you'll never look at a proof the same way again! Having two tutes a week was quite useful. Unfortunately it is very easy to fall behind, and the level of rigour required for your proofs can be quite inconsistent between lectures, tutes and assignments, so that became a bit confusing also, but otherwise a good subject if you're interested in maths.

Anonymous, Semester 1, 2016

Nice introduction to pure maths, you learn how to prove a lot of fundamental calculus theorems which is pretty cool. Lectures are recorded and fairly good. While tutorials are super useful, they don't always line up with the pace of the lectures. Overall fairly easy subject, but exams seem to be getting harder every year.

Anonymous, Semester 2, 2015