- Points: 30
- Code: M337
- Level: 3

- On this page

A great module,.......I did it a year ago, and there was so much new material on offer there. It felt like a 60 credit module which moved quickly. Tutor support was great and the forums were well used.

Christopher O'Regan

Course starting: **October 2017**

Review posted: **April 2019**

This is a fantastic course with a lot of new information just waiting to be absorbed. Tutor support was great.

I found much of the content stimulating, but quite difficult to understand, with just an occasional glimpse of some quite remarkable material. A revision of past exam papers singles out many of the highlights of the course and gives one a broader perspective which alluded me during the course.

Enjoyed B2-> C1, Cauchy's theorem to Residues, the middle part of the course more than both extremes.

I did not do well in the final exam, but, enjoyed the content nevertheless.

Christopher O'Regan

Course starting: **October 2017**

Review posted: **August 2018**

I really liked this course - it's certainly pretty hard in places, but the course books guide you through the important material pretty well. The recorded e-tutorials (on my presentation) were superb and I hope the course team select some of the best for future students.

I've read that complex analysis is a beautiful subject - well, I admit, at first it was hard to see the beauty, especially when you're struggling with the basics but, by the end, when studying the Mandelbrot set, you realise what an intellectual achievement this all was. I kept asking myself throughout the course: how did someone think of all this?

Some advice: this is a 'proper' maths course, with full supporting proofs, but you don't need to follow the proofs in detail to understand the concepts; just ensure you can answer the TMAs and relevant past exam questions. And some advice doing the exam: print out some past exam papers (which you can buy from OUSA) and ensure, as you go through the course, you can answer them - the style of the questions don't change too much from year to year.

As a graduate of the course I now feel more mathematically confident, able to take on other Level 3 modules without trepidation and, perhaps, the OU maths MSc at some point.

Stuart Reynolds

Course starting: **October 2014**

Review posted: **November 2015**

Everybody commenting on this course seems to love it so I'm about to go against the grain here.

This was my second level 3 course and I really didn't enjoy it at all. I had done well on M208 and was looking forward to some more pure stuff.

The books for this course however are very functional, lots of empty space and only a few problems in each topic. I felt they never really explained why I would need or want to do anything, but just goes crazy on the proofs.

It felt like the course was a series of never ending theorems and proofs, with the latter being pretty pointless as I couldn't remember any of them about 2 days after doing them. After a while I just gave up on the proofs but it didn't seem to matter anyway. For me the course stayed as independent blocks of material and never joined up at any point.

At first I thought I was missing some materials as usually the course notes are detailed with extra exercise booklets, but not here. The TMAs were pretty hard due to not enough practice with the topics. I needed an extra course book (Priestly) to make any headway.

Passing the course wasn't a problem, I could do the math but simply got bored to death about 3 months in so my eventual good grade was a miracle. However I feel I don't know any more about Complex Analysis now than I did before I started.

The tutorial day presented by my tutor was very good. What I got from it mainly was that I was able to perform the calculations as required but that the subject is hard to conceptualize. A lot of people at that tutorial felt the same although some TMA questions had literally two paragraph explanations to go on.

An essential pure math course with practical leads into physics and other important areas but you wouldn't know it from this course. Nothing wrong with the OU, the breadth of the material was the same as a brick uni (I checked) and all the other courses have been really good but this one just didn't agree with me.

Course starting: **October 2012**

Review posted: **January 2014**

This is an excellent rigorous course. The material is well presented often with a geometric flavour. Basic concepts are presented in full. The text is certainly better than standard textbooks e.g. Stewart and Tall or Priestley. There are plenty of examples to do. Conceptually I suspect it is the hardest of the Level 3 maths modules.

The exam is formulaic and not too hard but it is time intensive. You cannot afford to get in a serious muddle. It is important in the exam to explain everything quoting conditions and theorems and this takes time in the exam. Some questions have algebra that is fiddly (not hard) and it is easy to make minor errors..

Most students I know disliked Fluid Flows sections 3 and 4 but post exam reading may cure this! It is interesting to note that a third of students get a distinction in the exam. Food for thought. Tutors gave excellent support during the course.

John Moffat Scott

Course starting: **October 2012**

Review posted: **July 2013**

M337 is a great course - it builds nicely on the real analysis covered in M208, but although it does include full proofs of virtually all of the theorems in a proper, pure maths rigorous way, it is really a course all about developing techniques in calculus, such as residue calculus, improper integrals, sums of infinite series...

Highly recommended - do it before it disappears from the options, although as far as I'm aware there are no plans for it to do so just yet.

Ian Wright

Course starting: **February 2011**

Review posted: **December 2011**

This is a good course that should be highly recommended (if not compulsory) for any math degree. It covers all the points of a standard complex analysis undergraduate courses and the reading materials are, as usual for the OU, crystal clear.

I would have liked to see a few more connections with multivariable analysis in the real domain (e.g., what is at the root of the difference between a complex analytic function and a differentiable or even smooth function of two real variables? How exactly are we slipping a potential rabbit in the complex differentiable hat?), but that's just me being greedy.

I also found that (as in M208) the exercises and TMAs were a bit too closely related to the solved examples in the text. A few plug-and-play exercises are definitely necessary, but I think that some more "stretching" exercises would greatly help students realize whether they really "got" the material.

The exam questions were very similar in spirit to the TMA ones, which is exactly how it should be (this did not prevent me from running out of time, making a mess of it and dropping a grade, but that was my fault; I strongly advise trying a mock exam under timed conditions before going for the real deal).

Course starting: **February 2009**

Review posted: **February 2010**

Very well prepared course. If you have previous experience with OU Maths there should be no surprises. I found the workload manageable although towards the end I was struggling a bit. I found last block most challenging and with the exam approaching I was forced to rush things. In retrospect I wish I had an oportunity to take it in a 60 point year instead of 90. But nevertheless, thorougly enjoyable course and I'd guess a must if you're eyeing with MSc Maths as it's cited quite often under the Entry section.

Course starting: **February 2009**

Review posted: **January 2010**

Many students like this course on complex analysis, but I think that it is too light. I am now an MSc student with the OU and I've found that M337 hasn't prepared me well enough for the postgraduate course on complex variables. In M337 all the exercises are straightforward. They do not require any thinking. You just have to work through the standard steps of the strategies given in the course notes. On the postgraduate level it is assumed that you can go through much more difficult exercises. I think that Level 3 undergraduate mathematics courses should use real textbooks instead of special written course notes. Course notes are TOO student friendly and do not contain lots of material. I think that a good mathematician should be able to understand mathematical ideas from textbooks, being able to understand which topics are the most important. Perhaps there should be some courses like the old Level 4 courses, somewhere between Level 3 undergraduates courses and postgraduate courses for those who plan to continue their mathematical studies at a more advanced level.

Course starting: **February 2007**

Review posted: **May 2008**

A very enjoyable course. The material is laid out in a rigorous fashion, yet the course texts manage to sew all the definitions, theorems, and examples together into something that is more 'alive' than standard mathematics texts making the ideas presented all the more comprehensibe.

The course starts off with the very basics of the complex number system and develops the theory behind differentiability and integration of complex functions in the first block of the course. We are then taken on a journey through the field of complex analysis, on the way picking up knowledge of such things as Cauchy's Theorems, Residues, the Argument Principle, Singularities, Stone-Weierstrass, and much more. The sheer breadth of the material I found very satisfying.

There are plenty of proofs, some of which I found highly lucid and ingenious.

The final block looks at some applications of complex analysis. This is where I found the material to be too much so late into the course. The unit on fluid flows - while very interesting - took just a little too much effort for me to fully comprehend with the stress of the exam looming on the horizon.

The exercises are very much of a practical nature - the emphasis lies on calculation and less on doing proof-based problems. The TMA questions are very doable. Personally I would have liked to see more proof-based problems.

In conclusion, this is a course I am proud of having done and I cannot help but to be impressed with the course team for putting together a course so enjoyable while at the same time managing to present so many interesting concepts within complex analysis.

Willem Hessel De Boer

Course starting: **February 2007**

Review posted: **March 2008**

I really enjoyed this course.

I found it largely built on the pure and geometry aspects of my Level 2 study (which were my favourite parts).

The text books set the pace of learning spot on (unlike some other Level 3 courses which can get a bit hectic toward the end), and were filled with useful diagrams and exercises.

Overall one of my most preferred Level 3 courses, even though it does only touch on fractals, I would highly recommend.

Course starting: **February 2007**

Review posted: **January 2008**

An extremely well written and thorough course in complex analysis. I found it refreshing to see a coverage of material that other similar courses(offered elsewhere) barely touch on such as mobius transformations, fractals and fluid flow. However the most important results from 'standard' complex analysis are presented clearly and form the backbone of the course.

The TMAs and exam are well gauged providing sufficient challange to keep you on your toes but still manageable for a motivated student. I found the tutorials invaluable as this area of mathematics is very rich in concepts and it pays to get involved in tutorial and discussions.

The subject is fundamental. It appears everywhere in maths and physics and if, like me you wish to pursue higher pure maths it is essential. A first rate course!

Course starting: **February 2007**

Review posted: **January 2008**

I enjoyed this course, and found pretty much all of it very interesting, it was one of those courses that gets better and better as you get into it and it is very much an extension to M208 Pure Mathemetics. Complex Analysis is a core to any advanced study of Mathematics and, like Abstract Algebra, some of the results are surprising and quite 'beautiful'. This course does a pretty good job of getting that feeling over.

In some places the course was a little rushed and I'm not a fan of the audio format pages, but overall material presents the course very well.

I found that like most Level 3 Maths courses the TMAs required work but were very doable from the course material, and the exam is a fair representation of the course.

Course starting: **February 2007**

Review posted: **December 2007**

Loved this course, my only regret is I didn't do it earlier in my degree, and thus not suffer the inevitable ennui that pervades everything you do after having studied for so long.

This is a really challenging course, probably shares first place with M435 in difficulty for me. You will need lots of time to think about what you have just read. I recommend doing all the exercises. And definitely go to the tutorials - I only managed to make one and that was a big regret.

TV programs are a bit pointless, but other than that a wonderfully self-contained introduction to complex analysis (it must have worked because I am now going on to do even more math after my bachelors has finished).

Douglas Allen Salt

Course starting: **February 2005**

Review posted: **January 2006**

Complex analysis has some amazing results that really blew my socks off, even though I am not usually enthused by pure maths - a nice juicy differential equation is normally more my thing! But this was fascinating stuff and the course does a very efficient job of guiding the student through the material. In my view you should previously have done M203 or M208 to have the basic ideas of mathematical analysis at your fingertips. The exam was very do-able and even an unrepentant applied mathematician like me managed a distinction. I strongly recommend this course.

Course starting: **February 2005**

Review posted: **January 2006**

Each of the views expressed above is an individual's very particular response, largely unedited, and should be viewed with that in mind. Since modules are subject to regular updating, some of the issues identified may have already been addressed. In some instances the faculty may have provided a response to a comment. If you have a query about a particular module, please contact your Regional Centre.

The figures below are taken from a survey of students who sat the exam/completed the end-of-module assessment for the October 2016 presentation of M337. The survey was carried out in 2017.

89 students (a response rate of 35.5%) responded to the survey covering what they thought of 10 aspects of the module.

*Please note that if the percentage of students who responded to this module survey is below 30% and/or the number of responses is below 23 it means that only a small proportion of students provided feedback and their views as shown here may not be fully representative of all students who studied the module.*

See this page for the full text of questions and more information about the survey.

% | Count | |
---|---|---|

Overall, I am satisfied with the quality of this module | 85.4 | 76 |

Overall, I am satisfied with my study experience | 80.7 | 71 |

The module provided good value for money | 75.3 | 64 |

I was satisfied with the support provided by my tutor/study adviser on this module | 84.3 | 75 |

Overall, I was satisfied with the teaching materials provided on this module | 85.9 | 73 |

The learning outcomes of the module were clearly stated | 85.1 | 74 |

I would recommend this module to other students | 75.9 | 66 |

The module met my expectations | 80.7 | 71 |

I enjoyed studying this module | 81.8 | 72 |

Overall, I was able to keep up with the workload on this module | 81.6 | 71 |

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Faculty comment:"Thank you to students and tutors for making the module such a success. We're grateful for the positive response to the survey. Some students expressed concern about the difficulty of the October 2017 examination. The module team are looking very carefully at this matter. We'll ensure that exams are balanced, varied, and of an appropriate standard. Other students have suggested that some of the module materials, particularly the audio sections, ought to be modernised. We're in the process of refreshing the appearance of the module. Some aspects of this process should appear for the October 2017 start, and others will appear for the October 2018."