MATH3611: Higher Analysis

- 3 x assignments (10% for the first two, 20% for the main assignment)
- Final exam (60%)

Pre-requisites are 12 UOC of Level 2 Mathematics with an average mark of at least 70, including MATH2111 or MATH2011 (CR) or MATH2510 (CR), or permission from the Head of Department.

Definitely the most challenging course out of the four courses I did this term, and it's not surprising why. This is one of three core courses for anyone planning to go into Pure Mathematics and it serves to be the more "calculus" heavy course out of the three. Essentially, this is a rigorous calculus class and you need to have a certain mathematical maturity to do well in the course. The lecturer doesn't cover many proofs but rather develops the intuition for what the proof should look like and it's your job to fill in the details, and it's a pretty nice system to have.

The course begins with a conceptual understanding of what it means for you to say "cardinality" of sets (in particular, infinite sets), covering topics such as countability and uncountability before diving into the first real topic of analysis -- metric spaces. You'll develop an understanding for abstracting away from the concrete (instead of talking about distance functions, we can talk about metrics of a space). The course ends with a fairly dense topic on compactness of topological spaces, a topological property that generalises the notion of boundedness and closed-ness.
In all, I found this to be a really interesting course and the lecturer does an excellent job at explaining these topics in a way that seems fluid and cohesive. If you're interested in pure mathematics and want to dive into some more calculus, then this is definitely a course for you.

- 2 x 2 hour live lecture.
- 1 x 1 hour tutorial.

3.5/5

Yes.

- Lecturer: A/Prof. Pinhas Grossman

Lecture slides are sufficient.

4/5

The recommended textbook is Introductory Real Analysis by Kolmogorov.

2021, Term 2

78 DN.

Prerequisites:

My favourite maths course so far. I really love analysis, so that's sort of to be expected, but the proof were really fun, and the content was right up my alley. Dr. Grossman was a great lecturer, although we went an a few long tangents which dropped us a little bit behind schedule (they were interesting tangents though, to be fair). I would highly recommend this course to anyone interested in pure mathematics. Our class collectively wrote up some solutions to a few of the problem sets, though as the term progressed that kind of died; definitely helped when studying for the final though. A lot of the interesting exercises are in the lecture notes, rather than the problem sets. Not really much to say, just a good course all-round.

2x 2hr, 1x 1hr Lecture (2nd hour of the last lecture of the week was basically a tutorial)

4/5

No.

Dr. Pinhas Grossman

Lecture notes uploaded, as well as solutions to the minor assignments. Problem sets with no solutions.

5/5

Note: I don't use textbooks and can't comment on their usefulness.

2019 T1

97 HD

- 3 x Short assignments, each 10%
- Main assignment, 20%
- Final exam, 50%

Formal prerequisite involves 12 UoC of Level 2 mathematics courses, one of which must be (MATH2111 or MATH2011(CR)). Essentially, first year calculus and MATH2111 concepts are assumed knowledge. MATH2701 gives you useful skills to make this course easier, but is not required.

This course is one of the core courses for a major in Pure Mathematics.

Analysis generalises the concepts of limits, continuity and all of the basic stuff taken for granted in calculus. It goes into the theory of all such concepts, and expands their applications into not just involving what you see IRL, such as numbers and vectors. Analytic tools can appear less rigid; the whole notion of limits is not something that's really observed and requires us to believe in some kind of 'extension' on what we can actually see.

Personally, I find it works better with my brain. Especially after losing it with algebra, I needed some kind of pure maths left in my soul. I found that I was alright with constructing counter-examples a lot and didn't have too much figuring out the proof, but probably lacked the ability to write it out properly at times. More or less accepting this grade whilst biting my teeth because hey, an HD is an HD, but I would've much preferred a 90+.

Some analysis proofs are pretty long, whereas others are no-brainers. A part of the skill in this course is spot what you can do easily and then come back to the hard stuff later. Finding examples and counterexamples is pretty common stuff. Perhaps the other thing I'd say is that you really want to know all of your definitions and theorems. Because I've found that with analysis proofs, bashing definitions and theorems is quite a fair bit of what you do.

There's a mix of hard and soft analysis in this course, but I think there's slightly more soft analysis; epsilons were everywhere but still a fair bit of the course involved topological spaces and compactness.

(The course outline isn't really accurate in my year; the course content was somewhat cut down. Quite grateful to Pinhas for it; I had a better understanding of what was examinable as a result of it.)

3 x 1 hr lectures, 1 hr tutorial

3.5/5

No

Dr. Pinhas Grossman

The lecture notes and the past papers provided are generally all you need. Some other past papers may be floating around if you look hard enough.

4/5

A.N. Kolmogorov and S.V. Fomin: Introductory Real Analysis (Dover, 1970; Call number: P517.5/125). All content is taken out of this textbook, but it's really unnecessary; the notes are enough

18 s1

85 HD