MAST30021: Complex Analysis

- 4 assignments (5% each)
- Exam (80%)

Dr Mario Kieburg

5 years worth from library, NO solutions.

3.5 out of 5

None, slides are sufficient.

- 3 one-hour lectures
- 1 one-hour tutorial

2021 Semester 1

H1

---

Three written assignments totalling 20%; One 3 hour examination (70%)

I really enjoyed this subject! I did Accelerated Mathematics 2 rather than Real Analysis, so I did have 6 months to a year longer than most students to get to grips with the notion of mathematical rigour, but quite frankly rigour wasn't really required in Complex Analysis (unless Penny Wightwick was your tutor). Especially with Peter Forrester, who is a mathematical physicist, being the lecturer, the course had a strong applied mathematics-y flavour to it in comparison to previous years, which would certainly be refreshing for those still licking their wounds from the highly formal manner in which Real Analysis was taught.

After reviewing complex number arithmetic, we dove headlong into complex function theory, defining the usual concepts of limits, continuity and differentiability (with very little focus on Messrs Epsilon and Delta), thereby introducing the key concept of analyticity. After some topology (which was explained in a pretty hand-wave-y way!) we explored the various exponential functions and how singularities occur in complex functions. Then onto sequences and series, which was pretty standard stuff if you remembered how real series worked, with some interesting asides along the way. However, the truly interesting theory didn't materialise until the following topic - integration. The theory of contour integration - through Cauchy's theorem, Cauchy's integral formula (in Complex Analysis, we differentiate stuff by integrating them!) and residues - represented some of the most eye-opening concepts that I have learned in mathematics so far. Along with the associated theory of Laurent series and meromorphic functions, these provided vital links to other fields of mathematics such as vector calculus, partial differential equations and algebra (we found an 'easy' proof of the fundamental theorem of algebra). Finally, there was a brief jaunt into the world of conformal mapping, while the final week's topic of special functions (Gamma, Beta and Riemann Zeta) was omitted to allow for revision.

The main drawback of this subject, though, was the delivery of the lectures. In the very first lecture, Peter told us that he hadn't taught this subject for around 20 years, and it really did show. With all respect to Peter, it often seemed like he was clueless about how to finish off a proof and even as if he was winging it through a lecture. In addition, quite a few topics were skipped over, and the teaching of later topics was a dog's breakfast. A frequent complaint (though not mine) of the assignments was that while they weren't overly difficult, the connection to the subject's theory was rather tenuous. The exam wasn't too bad either, but some complained that it was too long, and because the course was being taught by a lecturer who hadn't coordinated this course since before most of us were born, it was also significantly different from those from previous years. To be fair, though, he did give adequate warning about this, and even omitted the Week 12 material in order to give us problem sheets roughly indicative of the exam. He was also extremely helpful in fielding our enquiries, somewhat more so than most of my previous maths lecturers, hence my docking of only half a mark

In short, the subject was highly interesting, but the experience perhaps left much to be desired.

Yes, with screen capture.

Prof. Peter Forrester

Yes, from at least 2010 - this course has probably been running in a similar form since Moses led the Israelites out of Egypt, but the lecturer decided to set a very different exam to those of the immediate past exams, so do them at your peril

4.5 Out of 5

None - the course notes were available as a single downloadable PDF on the LMS.

3 x 1 hour lectures per week; 1 x 1 hour tutorial per week

Semester 1, 2014

81 [H1]

4x assignments 20%; final exam 80%

This subject is quite interesting, and has a fair balance of pure and applied maths. It is not as ‘annoying’ as real analysis and much more fun. In terms of difficulty, the subject is fairly easy as long as you keep up to date and make notes. Since you do not receive premade notes, going to lectures and writing notes yourself is not only important, but also very handy in not falling behind. In doing so, I only had to memorise some of the theorems and do some practice problems (there is a whole practice booklet to do) and it was fine. The first few assignments were tricky but the exam was very doable (and quite similar to past exams).

No

Alex Ghitza and Paul Norbury

Yes

4/5

Didn’t use one.

3 x 1 hour lectures; 1 x 1 hour practice class

2011, Semester 1

88

Four assignments totaling 20%; Final exam worth 80%

I personally found the subject quite easy to grasp in terms of the lectures (up until the last few) and the assignments were approachable. The real curveball with this subject is the exam. The exam was very different to past exams with questions on topics that are so subtle that you (well I especially did) can skip over when studying. Alex Ghitza was a great lecturer and just reading over his notes was enough to grasp the material, whereas Paul Norbury was lazier and understanding certain concepts required outside reading (the recommended textbook). The practice classes were pretty stupid, but completing the questions is essential for only them and the assignments and practice exams is the practice material for the exam.

Yes

Alex Ghitza and Paul Norbury

Yes

4/5

Jerrold Marsden and Michael J. Hoffman, Basic Complex Analysis, 3rd Ed. Freeman, 1998.This textbook covers all the content, but not in the same order as the lectures are given. I would definitely get this book since it helps a lot.

3 x 1 hour lectures; 1 x 1 hour practice class

2011, Semester 1

59

4 Assignments worth 20%, 3 hour end of year exam worth 80%

First of all, this is a difficult subject. Although you could probably do semi-decently without fully understanding the concepts, some of the concepts took me quite a while to grasp. It is a subject where almost everything is interlinked, and in an exam or assignment, you may have to use those links to quickly and correctly answer a question. I feel that this is what made the subject difficult for so many. The tutorials were next to useless. In fact, as 50 people were in each tutorial, they were required to call them practicals. They involved being given a set of problems and solving them at your desk. Admittedly, the format may have improved, but I stopped going after the first week. The lectures were decent, with Alex being one of the clearest lecturers I’ve had. Paul would sometimes make mistakes and his handwriting is sometimes hard to read, however he was better at visualising the material than Alex. The saving grace for this subject was the content. If you put some time into it, you will begin to appreciate why you learnt all those seemingly unrelated things. It wasn’t until a couple of days before the exam, when I actually knew what the hell was going on, that I fully appreciated this subject.
As far as offering advice on going well in this subject (I’m not sure if I’m qualified to give it); Make sure you have the mechanics down pat, as they are underemphasised in the lectures. Know your trig functions well, know the basics of complex numbers. The lectures mainly involve proving things that you will use to solve problems in tutorials, assignments and the exam. It is not important to remember the proofs 100%, although doing so will definitely give you more insight into the material. In the assignments and exams make sure to offer explanation of all steps, especially if you are using a theorem derived in class. I lost quite a few points due to this.

No

Paul Norbury & Alex Ghitza

We were given 2 past exams from 2004 and 2005, they were not entirely relevant. Also had access to exams from Semester 1 2010 and Semester 2 2010, again, not entirely relevant due to change in lecturer / style.

4 Out of 5

Jerrold Marsden and Michael J. Hoffman, Basic Complex Analysis, 3rd Ed. Freeman, 1998. Stopped using it after week 4. Didn’t flow in the same way that the topics did, which is very annoying. If you wanted to follow what was happening in the lectures in the book, you would have to switch sections every 5-10 pages. Also, some sections were presented differently in lectures. Some questions from the assignments were pulled from the book, but answers were not present. Would not recommend purchasing the book.

3x1 hour lecture, 1x1 hour tutorial

Semester 1 2011

80