Iqon's New Zealand Blog

My studies

by on 28 September 2009, under New Zealand, UoA

I will try to see if I can’t make my blog posts a bit more manageable in the future, i.e. shorter, not necessarily less filled with boring nonsense, as this post is probably a good example of. Except that this post is also way too long, which means its actually the opposite of what I want to achieve. Well, next time, maybe…

So far my blog might have given the (wrong) impression that the only things I do down here is climb through caves, go on hiking trips, go to the beach, make horrible attempts at climbing, go to quiz nights and go to the movies. While I certainly have done that stuff a lot, I actually also study down here which is lucky since it is one of the primary reasons for my trip to New Zealand.

As I have mentioned earlier, I have been so lucky/good/studious (the last word my dictionary just taught me) that I have received scholarships from Otte Mønsteds Fond, Knud Højgaards Fond and Oticon Fonden which I am certainly very grateful for. Most of that money has already been spend on accommodation, the trip down here and the usual costs of living. Therefore I was certainly not sad when I a couple of times the past weeks was told that I had received yet another couple of scholarships:

Frk. Marie Månssons Legat (10,000 DKK = 2,750 NZD)
Civilingeniør Frants Allings Legat (10,000 DKK = 2,750 NZD)

Of course I also want to thank these foundations (although nobody associated with those read my blog – especially not in English) since they make my stay and my studies so much easier down here. As I said, I do study also, and therefore I thought it would be a good idea to give a small description of my classes down here. This way, people might get a better idea of what I am actually studying.

Applied Modelling in Simulation and Optimization
This class (or “paper” as they for some reason call them here) is actually an undergraduate course but we (Skott and I – we are taking all the same classes down here) chose to take it anyway since it among other subjects contained an introduction to simulation which we thought sounded pretty interesting. The focus is put on application and we therefore only have one hour of lecture week, while we spend three hours in labs doing exercises and assignments.

The course started out with some basic mathematical modelling on computers which Skott and I both have a good deal of experience with. It is basically concerned about taking some kind of problem which needs optimization after some performance measure and constrained by some parameters, put it into a computer and get the optimal solution. In the project we are going to hand in at the end of the semester, we are supposed to formulate a model which can set up a network using hubs and switches so that each component can send the correct amount of data to another component in the network. The task is to create this network at the lowest cost, i.e. using the cheapest possible cables, and fewest number of hubs and switches which can still support the required data flow. It has actually proven to be a bit harder problem than we first thought but in the end we did create a model which seems to take everything into account and also seems to work.

As mentioned, the course also contains an introduction to simulation which was our main reason for taking it. Simulation can be used to, yeah, simulate situations which do not necessarily have a specific, deterministic outcome but is instead dependent on stochasticity (randomness). In our project, for example, we are going to test our created network by simulating computers which send random amounts of data to each other in random time intervals in order to see if our network can actually support this.

Advanced Simulation and Stochastic Modelling
This class is actually the successor to the class mentioned above since it contains advanced simulation. In the beginning it didn’t seem like the smartest idea to have chosen to jump directly to the “advanced” class but now that it is over and we have had the short introduction to simulation in the other course, most of it actually makes a lot of sense. A lot of the first part of the course have been about how to generate random numbers on a computer which can be done in a lot of different ways depending on the “type” of randomness is connected to the number. It is actually not as easy to create a random number as one could be fooled to think.

We have handed in a single assignment in the class where we were supposed to calculate the probability of being dealt a full hand in computer. This was done by simulating the dealing of cards a lot of times and then seeing how many times the first person was dealt a full house. We were also asked to explain how to create a random number with a certain probability distribution. The last part of the assignment was to explain how one could estimate how much water there would be in an entire region if it was known that tests in small areas showed that there on average could be found two water tables with depth and size connected. While the first two questions seemed straightforward, the last part was a bit tricky since it was very vaguely formulated. We were also told that it did not have a specific “right” answer. I did give a suggestion for a solution so now I’ll just have to wait and see how it is received.

The second part of the course is about stochastic modelling. It is mathematical modelling where you work with probability distributions instead of fixed numbers. The classical example is the Newsvendor problem where a newsvendor can buy newspapers early in the morning for a certain price, sell them with a profit during the day and sell the leftovers (if any) at a loss in the end of the day. The problem is to find out how many newspapers the newsvendor should invest in in the beginning of the day in order to maximize the expected profit. It is not easy, though, since the profit depends on how many newspapers can be sold (i.e. the demand) which is not known for certain – it is instead a “random” number with a certain probability distribution. This should be taken into consideration during the solution process.

Research Topics in Operations Research 1
This class is divided into three parts. The first part was about non-linear optimization, mostly without any constraints. This means that the most of this part of the course was about how to find out where a complex mathematical function has its maximum or minimum value. I have had a couple of courses like that at DTU but the approach here was a bit more theoretic than what I have been used to. I must have understood some of it anyway, though – at least if you are going to take the assignment in that part of the course as any kind of indication. I received 25 out of 20 marks for the assignment! The lecturer sent out an e-mail where he told us that some students had made an outstanding report and he wanted to reward that with some bonus points. I was apparently one of those students.

The second part of the course, which we have just finished this week, was about advanced linear optimization. A lot of the optimization problems you encounter in the real world can be formulated linearly and therefore there have been done a lot of research on how to solve this problems to optimality as fast as possible. This part of the course introduced a lot of different methods which can be used to solve those problems. Some of them I knew already, others were completely new to me. I feel I have really learned a lot in this part of the course.

The last part of the course will be about game theory (among other things). It does not have anything to do with video games, however but is instead concerned with finding solutions to problems with several interest groups. A classical game theoretical problem (Prisoner’s Dilemma) goes like this: Two suspects are taken in for questions by the police. The two suspects are put in separate interrogation rooms and offered a deal by the police: If one cooperates while the other remains silent, the former will be released while the other has to serve the full sentence, 10 years. If both of them talks they will each get 5 years. Do they both remain silent they will receive a sentence of six months.

Clearly the two suspects will get the least amount of time behind bars (collectively) if both remain silent – this will result in a total of one year in prison compared to the 10 years in total for any other solution. The dilemma is that if each prisoner is only concerned about himself, he will co-operate with the police: No matter what the other guy chooses to do, this tactic will result in less jail time for the first person – either from 10 years to 5 (if the other talks), or from six months to no time at all (if the other remains silent). Both prisoners will however think like this, and thereby end up in the so called Nash equilibrium (it is John Forbes Nash who is portrayed in the movie, A Beautiful Mind – he had a big influence on the development of game theory) where they will each be put behind bars for five years.

This is one kind of the problems game theory deals with. As far as I know it is mainly used in economics but can also be used in other fields.

Research Topics in Operations Research 2
This class was originally supposed to be cancelled but “unfortunately” they didn’t get to take it down before people had already signed up for it (including Skott and me). Since so students had signed up (six in total) the course was changed to function more like a seminar type course. The first part of the semester we didn’t have any lectures and we were just given a paper each. They are all about multi objective linear programming – optimization of problems where you try to look at several (conflicting) goals at once, e.g. a factory which wants to minimize cost and maximize CO2 emissions. We were told that we would get an introduction to the subject after the mid-semester break so we didn’t really think much about it before last week where we had our first lecture. Here we got a bit of a shock when we told to begin the presentation of our paper the next week. It so happened that I was the first to get the honor to hold a 40-minute presentation about 16 pages of hardcore math which I had had for several weeks and not understood much of. Luckily it was postponed for a week the day after so this weekend has been spend on trying to understand the article so I can make a presentation for the rest of the class and be prepared for questions which the lecturer has promised there will be lots of.

That is basically all my courses but I would also like to make some general notes about studying here. There are a few points where it is completely different from DTU. For instance are all my classes pretty small, from 6 to approximately 25 students but of course I have also encountered a few classes like that at DTU, especially the last couple of years when I have taken more specialized courses. I am, however, not used to having all my courses in the same two small class rooms instead of lecture halls.

Things seem a bit less structured here than what I am used to from DTU. We were pretty surprised the first day when one of our lectures was suddenly moved to another time slot without warning and that almost all our lectures tried to reschedule the classes in the first days. We had spend lots of time trying to figure out which courses we could take which would not have any time clashes. We had even had to ignore some really interesting courses since they clashed with others. Therefore it was pretty frustrating that it was suggested that the times were changed already from day one. It all worked out in the end, though.

I am not used to the idea about changing lecturers during a course but almost all my courses are split into smaller sections with different lecturers. I don’t really know what I prefer; on one hand it seems like you can get through more stuff in this way but on the other hand we don’t really get to go into as much depth with a single subject as we do at DTU.

I also know the days of my exams now: 9th, 11th and 14th of November. It is going to be interesting since none of them allows any books or other types of aid. I don’t think I have ever had an examination like that at DTU but I have gotten the impression that this just makes the exams a bit easier since they cannot ask us questions about stuff we are not supposed to be able to memorize. But of course that is impossible to say until the exams are over. The lectures end the October 23 which gives us about two weeks of study period before the exams. There is a possibility that one of those weeks will be spend on Fiji for instance – but I don’t know that for sure yet :)

And that’s it for now. As usual it ended up being way too long but I’ll try make it shorter next time.

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