The first flashback is to this morning. We woke up realizing we would never sleep in such hard beds again for a very long time. Then the checkout ritual starts, but after a short time everyone was ready to explore the city one last time. Some took the chance to visit an area of Stockholm they missed the past days, others visited some areas one more time to view them in daylight. I went to the Royal Palace, where at 12:15 the royal guarded turned shifts in a very traditional way. This happened in a traditional way where the new guard entered the palace on horses, leaded by the military fanfare. After saying a few pledges, the old guard took the horses and walked them to their stables. Some of the new guards then marched through the city to various guard posts, relieving the old guard standing there.

But eventually we had to leave Stockholm. We flew with KLM, so checking in and changing seats to your preferences went very flexible and we were two hours to early at the gate. At the luggage claim in Schiphol it was so nice that all the participants went to everyone of the committee thanking them for the whole trip. Guys, you made my day.

Since I was then too tired to thank you all back, I will do it now. At first I’ll start with the participants that were the most close to us, namely the board of De Leidsche Flesch. They put much effort in a study trip which is most of the times not recognized. Thank you Vera for always giving up time to make the payments for the train, metro and bus tickets, passage fees, more tickets, more fees etcetera. Thank you the board for always thinking with us, giving advice when we asked for it, giving advice when we didn’t ask for it but at hindsight really needed, giving us suggestions and contacts, helping us with searching for companies to visit, etcetera. Without your help and advice the construction of the program would have started much slower and the program would be much thinner.

Now I will think all our fundings, namely the Universiteit Leiden, LUF, NNV and EPS, for making this whole trip possible for the students. During this trip I realized how much value a study trip has in connecting students with research, education and external contacts. This study trip may have opened the doors for some to study abroad in Sweden and Denmark. This study trip piqued the interest of students about research areas which the student did not know existed. Without your help this trip would for many of us be too expensive to participate and they would have missed some wonderful opportunities.

Parents, brothers, sisters, other relatives of our participants, colleagues and everyone else who I may have missed, thank you for reading the blogs and saying to your relatives here that you like them. Everyone underestimates the amount of work in such a post; an average post took 1.5 hours to construct. As you may have noticed our days are planned full, so most of our sleep has been lost to making these posts. Therefore your liking to the blog stimulated us in keeping it updated. I can say we truly enjoyed every minute of writing, no matter the time, and this blog turned out to be a beautiful description of the study trip and to an everlasting memory of this wonderful week.

A big thank you must go the our teachers in Leiden and our lecturers at the study trip. Without the teachers, the construction of the program would have been much slower, as almost every lecture of my program, apart for one, was only found through a connection with the teachers on Leiden. One must also notice that the speakers spend their free time for giving our students a lecture. They are voluntarily giving these lecture, so thank you for making time for us. We enjoyed listening to you. A special thank you must be made to the lecturers of Thursday and Friday, as on Thursday and Friday there was a holiday so these speakers spend their free day for their speech.

Participants, you were awesome. Your enthusiasm kept the committee standing and motivated to do more for you when we could. Also thank you to the participants that were really helpful to the committee when they noticed that the committee were in a pickle. The positive feedback from all of you on the program made the organization much more rewarding and I can really say that the week was much less fun without it. Please, I advice you, be as enthusiastic and motivated as you were last week on further study trips, weekends or other activities organized fully by volunteers. Keep up the good work. When I was tired and did not have the motivation to work further on the program, your smiles cheered me up and got me working again to make this week more exciting for you. I think I can say the last sentence on behalf of the whole committee.

Speaking of the committee, my last and biggest thank you must go to you. Every Tuesday from 13:00 to 13:45, the meetings at Esmee, our weekend, our trip to the Efteling, I had so much fun time with you. The hours we all put in our study trip are staggering, where Esmee and I made about 4 hours a week on average for 11 months and I think the rest of the committee just as much. Since you are all so wonderful, I will conclude this blog with a special thanks to each of you.

Paul, you tried many times to discipline me. Thank you for trying, but also thank you for keeping the whole committee together, for hosting every meeting, for knowing every detail of the trip and for knowing what everyone of us was doing. Your directness and typical sense of humor always lighted me up. You always took your time when one of us was in trouble and when someone asked for advice. Thank you for keeping overview, as I lost it on my work already after a very short time.

Alex, thank you for keeping my small breaks entertaining. You documented everything of our meetings in a creative fashion, making your documentations attractive to read. We were only kicked out of the communication channels twice as some chairmen do not understand our humor. I did not know you before the trip, but I am so glad you decided to apply for this committee. I am looking forward to what the rest of our student time has to bring us.

Brenda, thank you for always opening your honest mouth. You were an amazing treasurer who always could find a way to financially support our wild ideas. You worked really hard to control the money flows on the study trip and I can say from experience that this is a very hard task. Therefore you can be proud that all the spendings went between margins. You did a good job.

Esmee, I can say I collaborated with you the most. All those decisions that we had to make during the program construction, namely with part goes where, how long the breaks must be, joined or split program, which day do we travel from Copenhagen to Stockholm, first Copenhagen or first Stockholm, which group of students to write to, we did them together and you were always open for discussion. Also the small competitions like who is the first to fill their program and who is the first to find a company kept me motivating to always try even harder. Many do not know how much influence you had on the computer science and mathematics program and without your help the program would not have gone as smooth as it did now.

Kevin, without you we all would have been lost. You were responsible for the hotels, the public transport, the maps, all the routes from A to B, the flight and more. Without you we would have walked to our destination and slept on the streets. The evenings before the study trip you walked all the routes by yourself on Google Street View, which shows how dedicated you were to your task.

Last but not least, Sarah. You knew and cared about every participant as if he or she was your own child. During this trip every detail about every participant was always in an arms reach from you, so if something would have happened you could directly tell all the details to provide the appropriate help. Furthermore, in discussions you always thought about cases we did not consider or rendered insignificant, but in retrospective turned out to be quite relevant. You also were not shy to directly tell someone if you disagree with him, which sometimes strangles strangled a terrible idea at birth.

The quote of the day is the next lines I heard from the participants at Schiphol:

{{Insert commissioner}}, you can be very proud of yourself after organizing such a fun and smooth week. We enjoyed every minute of it. Thank you for this study trip.

Mathijs Kolkhuis Tanke signing off.

We started our day with a visit to the Vasa museum. The Vasa is a huge ship built between 1626 and 1628. However, due to construction and mathematical errors the ship was not wide enough and there was not enough ballast. Therefore, when it first hit the water, it sailed for 600 meters and then sank. Fifty people drowned and the ship remained at the bottom of the sea for years. Over time, people wanted to restore the ship, but the technology was not developed enough to retrieve the ship. In the 1950’s and later, technology was finally developed enough and after a few decades the whole ship could be extracted from the sea bottom. The whole ship is now viewable with various exhibitions about life on the ship, ship battles, ship building simulations, and more around the ship. It was quite impressive to see the rich detail in the woodwork of the ship, only to know that it sank in a few minutes. You could crouch in a replica of the hull, which is very low (indicating the rate of growth of Europeans over the years), and view the ship from the keel to the crows nest. It is really worth it to visit the ship while you are in Stockholm, since it is one of the most preserved artifacts from Swedish history.

In the afternoon we went to the mathematical faculty of Stockholm University. The lectures were situated in a beautiful lecture hall. Our first lecturer was Mia Deijfen, a university lecturer at Stockholm University. Her lecture was about mathematics on large networks. Examples of large networks are the world wide web, social networks and chains of sexual intercourse. The last network was the leading example of the next lecture. She first started with defining the properties of a large network. A typical property of a large network is the so-called ‘short distances’. It is most famous in a social network where it is claimed that two random persons are just six degrees away from each other. While that is not exactly true, it demonstrates that a network of over a billion people have very short distances. Another property is clustering. For example if X and Y are friends with Z, it is highly likely that X and Y are friends. Following this, Mia Deijfen demonstrated three models, starting with the simple Erdös-Renyi graph. She then continued with the configuration model, which also did not really show a large network. The last network was about preferential attachments, which was the best simple approximation to a large network.

Then the Dutch Pieter Trapman continued with a lecture about epidemics on large networks. He introduced a widely used model to describe epidemics called the SIR-model. In that model everyone in the population is susceptible to disease. When a sick person interacts with a susceptible person, that susceptible person gets sick immediately. The sick people get cured over time, after which they are called recovered. With cured we mean either dead or really cured; in mathematics those are the same. A disease like the flu could be modeled, but interacting with a person that has the flu does not always lead to the flu. However, HIV and chlamydia are excellent diseases to model, since an interaction between a susceptible and infected person is easily defined and contact almost always leads to sickness. Pieter Trapman showed the following picture of a graph detailing all the intercourses in an American High School in a year.

In this network the spread of HIV and chlamydia can be analyzed. One thing is rather interesting: HIV is in Africa a real problem, and in Europe less so, but the opposite is true for chlamydia. The diseases spread in exactly the same way, so it is a mystery to mathematicians why those diseases prefer those specific regions.

The last lecture of the whole study trip was held by Mathias Lindholm about the mathematics of insurances. There are two types of insurances, namely life insurance and non-life insurance. A special case of non-life insurance is insurance for chronic diseases and permanent handicaps. Many questions arise, such as: what is the likelihood that certain events happen, and the most important question: how would you set the price to transfer risk for certain time? There is no single answer to the last question. Other needs for insurances are calculating resources and making re-insurances. Then Mathias elaborated about the types of insurances, how they model such insurances and how the costs of insurances can be calculated.

In the evening we went to our final dinner at Il Forno Italiano. Kevin and I found this restaurant in Gamla Stan, the old city of Stockholm. Our dinner took place in our own room in the restaurant. The menu was outright delicious. We had a three course dinner and we were so lucky that this restaurant was so forthcoming in organizing this dinner. Without them, such a dinner could not be organized as restaurants in Sweden are so expensive for foreign guests. We could choose dishes from carpaccio and gamberi to a huge chunk of calf beef and pasta with ox-filet. Our chairman Paul first gave a speech honoring everyone of the committee. After the main course the president of the association, Tineke, gave a nice thank-you speech to the committee. After her speech we all sang the song of De Leidsche Flesch, which is a tradition at study trips. Last but not least, Larissa thanked everyone of the committee with a personal mug. After this wonderful night we went to explore Stockholm, since as the organizing committee there wasn’t much time to explore the city.

Thus at 2:40 we think we conclude this blog with our quotes of the day:

Esmee, we Stoopen ermee.

Wanneer Tineke klaar was met haar speech: “Tineke, we willen Nog a rede!”

Signed by Mathijs Kolkhuis Tanke & Kevin Oost

In the morning we went to the city of Kista, just a little metro drive from our hostel away, to visit the Computer Science department of the KTH Royal Institute of Technology, from now on referred to as KTH. Our day started with Thomas Sjöland, the department head for Software and Computer Systems. He talked about the KTH institute in general and how their school of ICT is organized. Afterwards Anders Västberg, the head of Undergraduate Education, talked about how the education in the Computer Science department is organized and what kind of bachelor and masters programs KTH has to offer. He invited everyone of us to apply at one of their programs as full-time, exchange or another type of student.

Then Christian Schulte, a professor at KTH, gave a lecture about constraint programming. One example of constraint programming is solving a sudoku. Everyone field in a sudoku is a variable and the numbers from 0 to 9 are the constraints. Then one has to fill in the fields according to the sudoku rules. Then for every field a set of possible numbers can be described. After describing these sets, you can eliminate numbers from sets in a smart way. For example, with the sets x={1,2,3}, y={1,2} and z={1,2}, one can deduce that x=3 must hold. Then he moved on to more difficult puzzles. You can try one at home. Look at the equation SEND + SOME = MONEY. Every letter is a number from 0 until and including 9 and every letter holds a distinct number. Assign to each letter a number such that the equation holds. The more amazing example was a kakuro. He tried to solve a simple kakuro from the newspapers with constraint programming, which originally took almost 3 minutes for a computer. Then he wanted to solve a Japanese huge kakuro, but after 6 months of computation he stopped the program from calculating the solution. Then he made a smart algorithm that solved the newspaper kakuro in 45 milliseconds and the Japanese in 245 milliseconds.

The next part of the program was a lecture about the Electrum laboratory and a guided tour through the lab. The laboratory is focused on making faster computer chips for various purposes, including heat detection, phone chips and medical solutions. Nils Nordell, head of the Electrum lab, first showed us the wet room, where non-clean experiments were run. Then we continued to the clean room, where there is at most 1000 particles per square foot. We walked not in but around the clean room and Nils Nordell showed us all the process steps from researching a nanoparticles to manufacturing the end product. These facilities can, after payment, also be used by companies who not have the resources to build their own clean rooms. The lecture was held by Per-Erik Hellström, a docent at KTH, who described which machines where used in the clean room for research, for building mobile phone chips and for other purposes.

After the lunch break we moved on to the main KTH campus in Stockholm where the mathematical program would take place. First I was a little bit disoriented by the floor numbers; when I walked through the front door I was on floor 5. However we found the lecture fairly quickly and Kristian Bjerklöv received us for his lecture. His lecture was titled: “Dynamics of quasi-periodic driven systems”. At first he defined a dynamical system. His lecture was focused on the circle. First define a function that sends points from the circle to other points on the circle. If you track what happens to every point on the circle after many times applying the function, then you have a dynamical system. The systems Kristian Bjerklöv focused on were systems that were influenced by external force. If you track the multiplication of rabbits, the strength of the sun is an external force since the rabbits are happier with more sun but the sun does not shine brighter due to a rabbits climax. Then he elaborately explained what kind of dynamical systems were purely chaotic and which systems behaved in a more fashioned way.

Secondly Maria Saprykina gave a energetic lecture about the behavior of pendulums. Suppose you have two or more pendulums. What will happen to the motion of those pendulums if they are disconnected and what will happen to the motion of those pendulums if they were connected? It happened to be that disconnected pendulums move independent of each other, as you would expect. If you have two pendulums connected by a rubber, then they also move independent of each other. If you have three or more connected pendulums, then everything from nothing to outright chaos can happen. If you set the initial conditions perfectly right, you can let the pendulums swing in the exact order as you want. This is all due to irrational shifts

The last lecture was from Danijela Damjanovic, who gave a really interacting mathematics lecture which is rare. She started with the first question: a biologist is measuring bacteria. There are 2^n*x bacteria with n the number of days and x the starting amount of bacteria. Then a mathematician walked in and asked: is there a positive n such that 12345 are the starting digits of the amount of bacteria? After a few minutes of deductions using irrational shifts we concluded that for any set of starting digits and for any starting amount of bacteria, there is always an n. The next question was about the placing of 12345 at the decimals. The answer is no. The third question is the same as the second, but then with 2^n*3^mx bacteria. This answer is yes. To conclude the lecture, she stated a famous open question from Furstenberg and Erdös.

To conclude this blog, we will give our quote of the day, which is in Dutch to preserve humor:

Vera tegen Alex: “Jij bent zo A(re)laxed!”

Signed by Kevin Oost & Mathijs Kolkhuis Tanke

On this website you can see information about the committee, the program or the travel information and hostels.

The studytrip is organized for students of year 2 and higher. During the trip we’ll post some updates to keep everyone at home updated.