Alex Sangers's blog

Blog of an Applied Mathematics student

Holidays!

Hello everybody,

It has been quite some time since my last blog. Due to the exams of the last weeks, I have been terribly busy preparing those exams. Furthermore, I had to really some work to do on deadlines before the holidays, so no time left to update you. Now, however, my holidays just started, and I am really enjoying my free time. This weekend I visited my parents again (long time no see), and every day I had a BBQ because of the nice weather. Since my holidays the weather is great actually, which is of course perfect!

Nevertheless, before I will only elaborate on my holidays, let me update you with a nice project I did for the course Environmental Simulation and Data Assimilation. This course became particularly interested with the project, which involved the data assimilitation part, namely Kalman filtering. For those of you who never heard of this, let me give you a short description. For our problem, we had a 1D channel (with water) described by a set of PDE’s including the water level and the water velocity. The left boundary is an open boundary, where water can flow in and out, while the right boundary is closed. See also this figure below.

Graphical representation of the channel.

The main issue in this problem is that the inflow at the left boundary is stochastic; the exact amount is unknown. This is called model noise. Furthermore, we can add measurements (to measure the water level, for example), but also these measurements have an uncertainty; the measurement noise. Now, we want to predict as good as possible what the water level and velocity is through the entire channel, using measurements in a smart way.

We found out, that if you put one measurement at the beginning of the channel, then the whole model prediction in the channel is actually quite good. In this figure below you can see how the model prediction is compared to the true state using one measurement at the open boundary (left).

Comparing the model estimate with the truth in the middle of the channel.

 

If all my exams went okay, it means that I am done following courses for my master. Next year I will do my thesis at the numerical analysis group. But for now, I am going to celibrate my holidays. I hope to see some of you next year at EEMCS!

Finite elements

 

Last month passed quickly! To be honest, I spent quite some time on parties and free time, such as the lustrum of our student society’s building and the last Queensday for the next several decades. Furthermore, last weekend I went with my house mates sailing in Friesland (northern part of the Netherlands). It was my first time sailing and I enjoyed it very much; the first day was really windy but a bit cold and the second day there was a lot of sun, but it lacked wind. Basically, we drank some beers and we had a great time!

Now, let us get to business, because I did some real work as well. The new term started, including new lectures of “The political use of models in sustainable development” and “Introduction to C++”. The first course mentioned is mandatory and not all mathematicians are really happy, enthousiastic or talented for the course, since the contents of the course are mainly political. The second course, C++, is an elective course which I like and think is helpful.

Nevertheless, I want to tell you something about Applied Finite Elements. Together with Yvonne, I work on a mathematical model of an AC dynamo and we try to calculate the potential created by the magnetic field. Here, the focus is of course on the numerical computations; we divide the domain of computations into small triangles, which are combined all together (with corresponding relations between them). To do so, we use the software SEPRAN, based on the language FORTRAN.The dynamo contains an iron core in the middle of a vacuum, which creates a (positive/negative) current. First, we had to solve a simplified linear model and soon we hope to get some results for the nonlinear case.

A first result for the potential in the linear model

Intensive!

 

Hi all,

I just returned from two successive intensive weeks in Twente, just like the one of Systems & Control in October. It was quite a journey for me, since I left home with Eastern to visit my parents, then directly go to Twente for the “Applied Finite Elements week”, thereafter I headed straight to Oss for a weekend with family (cousins, etc) and then I went to the second intensive week for “Advanced Modelling”. To be short: I traveled a lot with my suitcase, not coming home for two weeks.

After some good night of sleep (since I was surprisingly tired), I look back now at all events. Both weeks were fun and busy, and I like to tell you more about the second week, since the first week was not a lot different than following lectures and doing homework.

In the second intensive week we formed a group with four students in total (one from Groningen and three from Delft) to dive into a project about atherosclerosis. To create some context; this is the formation of plaque in blood vessels due to bad cholesterol. Our main goal was to construct a (realizable) realistic and liable model for this biological phenomenon and secondly, we tried to find the relation between someone’s lifestyle and atherosclerosis. We started off with a simplified model to get some feeling for the project and after that, we made an extension (based on an existing model) including different chemicals in the blood. One of the results of the basic model is shown below, emphasizing that this is hardly realistic! This figure assumes a small initial plaque, which expands over the years.

Remaining life expectancy vs. lifestyle. No rights can be derived.

Sudoku

Hello everybody!

The last time I wrote on my blog I was still experiencing the stress and pressure of the previous semester, because it had been a busy time. Althought several deadlines are coming closer and closer, I find myself enjoying the upcoming spring and above all, enjoying a lot of free time. Compared to the first half of this college year, this is a piece of cake. I follow (all elective) courses ‘Advance Modelling’ and ‘Applied Finite Elements’ (mastermath) and furthermore, ‘Advanced Numerical Methods’ and ‘Environment Simulation and Data Assimilation’. One thing to notice is that all courses are directed towards Modelling and/or Numerical Analysis and therefore, they have similar content and evidently coherence. I am enjoying the courses, especially for the emphasis on applying, however, I miss the (mathematical) challenge a bit.

To be short, I made my own challenge and last month I created a sudoku solver in MatLab (which is, to be honest, not the best language to solve sudokus). When doing this little project and actually enjoying it, I had to conclude that I am a geek. With a little difficulty accepting this inevitable conclusion, I managed to successfully solve all not-ridiculously-hard sudokus with my MatLab code. For the interested reader, how does this roughly work? It contains two phases:

(i) It fills all elements which can be determined directly when using all (combined) information in rows, columns and blocks. This procedure is good enough to solve puzzles approximately up to three stars difficulty.

(ii) If phase (i) fails after a while, look for a 50-50 guess (often, there are a lot) and try one of these guesses. Then it tries to fill as much elements, similar as in phase (i), with three possible results: 1. contradiction, 2. did not fill at least 5 extra elements, 3. filled at least 5 extra elements without contradiction. When it gets result 1 or 3, it assumes to know the correct fill-in and returns to phase (i). When result 2 is obtained, it tries another 50-50 guess.

Adding phase (ii) to the algorithm will solve almost all sudokus, althought it could not solve the sudoku that claimed to be the most difficult one in the world. However, I am not planning to improve the algorithm any further, because I am getting bored with this little project. Still, here is one of the results:

See you next post!

New semester

 

Hi! It has been quite some time since my last blog post. Due to the exams in January I have been terribly busy, so it is about time to update you. As I just mentioned, we have had the exams of the first semester. It is interesting to see that a lot of exams are oral instead of written; it seems to be usual in the master. To be short on the dull contents of the exams: it was hard work, but after all I passed every course (except maybe Stochastic Processes, which was difficult and not corrected yet).

Last week we were actually free from lectures. A holiday break between the semesters, which was a new concept. Previous years we got a break in March, but that got exchanged for last week, which is an amazing idea. This way we really got a holiday where we do not have to meet deadlines just after the holidays, and moreover, it was an ideal time for skying. In short, I went skying in Switzerland with some friends who also do/did mathematics. We had terrible weather, but a lot of fun!

This semester we have to choose our specialization within Applied Mathematics. Before  (and a bit during) the holidays I decided to dive into numerical analysis combined with modelling and a bit physics. Yesterday I had my first course in Utrecht for Advanced Modelling, one of the two courses with an intensive week in Twente which I both will join. I am excited about how the courses will be and what we will learn!

Furthermore, within a week the “Delftse Bedrijvendagen” will start, which is an opportunity for students to get in contact with loads of companies in order to get to know them, to find an internship, a thesis project or maybe even a job. I am planning to orient myself on the different available jobs/companies and moreover, maybe even to find a thesis project.

I will keep you informed!

Holidays!

 

It has been a long time since I last wrote my last blog, so it is about time! Last month was a busy month. I am not sure whether you (the reader) know about Sinterklaas. To make sure we understand each other correctly; this is not the Santa Claus which is worldwide known, but another, much more slimmer man. To be concise: Sinterklaas is from Spain and comes to the Netherlands each November till the 5th of December to bring presents to all children with the help of Zwarte Pieten (“black Petes”). Now, back to the story, on the 6th of December we celebrated Sinterklaas with some fellow students of Applied Mathematics. Everybody had to bring some presents (which I forgot, shame on me!) and we made up a dice game to win the presents. I did not deliver any present because of my ignorance, but I went home with three nice little presents. Fun night!

This month I also got my first master ECTS! The course System & Control finished at the end of November and 6 ECTS are ‘in the pocket’! In the photo you can see the great victory team, with whom I gave the final presentation.

Last week the holidays started to celibrate Christmas. First, I went to Köln in Germany together with my girlfriend. There were little Christmas markets (Weihnachtsmarkten) with lots of glühwein, sugared nuts and other German delicates. After the successful weekend, I went to my parents and those of my girlfriend’s. It was nice to really spend some time with family after a busy period. Unfortunately, the time for relaxing is behind and the rest of the holidays I will mostly spend time on meeting my deadlines for the beginning of January. Wish me luck!

Student assistent

Hi all,

Last weblog I told about the intensive course Systems & Control and some weeks have passed since I went to Twente for the intensive week. All students had to be in a lecture room on Monday 13.00 pm to have a lecture about some theory. I guess that about 20 students from several universities were present, for example Groningen, Eindhoven, Delft, Leiden, Amsterdam and of course Twente. After the lecture we got a ‘homework’ assignment, which actually had to be done during the following two days. That meant some serious writing and agony!

Thereafter, at the beginning of Wednesday, we got assigned a theoretical research about a certain topic on systems & control in groups of two or three students. That meant some serious working in daytime, but serious relaxing and having fun after dinner. On Wednesday night we had a Halloween party at the campus, which was especially fun because everybody came along and had a few beers. Furthermore, we played a lot of board games in the common room of our hotel at the campus. Althought the assignments were not as great as it could have been, it certainly was a great week because of the fun with everybody.

Furthermore, the past week I have especially been busy with my new ‘job’ as student assistent. In the picture you can see how many homework assignments I had to correct. A total of 76 students with about 30 pages each student on average, a whole box! I am glad I finished this one (althought the next box is already waiting for me :().

Last week I started with another mathematical elective, namely Nonlinear Differential Equations. This should become a valuable course in the future, for it has many applications. Moreover, this course will deliver 6 ECTS in one quarter of a year. I am curious!

Second blog

Hi everybody!

Some weeks have passed since my first blog and I thought it was time to update you all. A few weeks ago I had a meeting with Martin van Gijzen, the master coordinator of Applied Mathematics. We discussed my study program for this semester, and also discussed some courses of the second semester.

This semester I have three common courses, namely Functional Analysis, Stochastic Processes and Scientific Computing. Probably the most difficult courses for me are Stochastic Processes and Functional analysis. This year there are no mandatory assignments for these courses (unlike previous years), which asks for quite some discipline to keep up with the lectures. So far, so good! Furthermore, I follow the courses Systems & Control and Non-linear Differential equation (the last one has yet to start) as mathematical electives.

Systems & Control has a two-hour lecture every two weeks in Utrecht, with a total of three meetings and thereafter, we will have an intensive week in Twente. I received an e-mail one week ago about the possibilities of staying in Twente for that week, so I should have an accommodation by now. I really look forward to this week of in-depth lectures, projects with other (inter)national students and probably some free time as well!

 

First blog

Hello everybody! Since this is my first blog, let me introduce myself. I am Alex Sangers and this month I started with the master Applied Mathematics at Delft University of Technology. Before this master, I also did my bachelor’s degree in Delft. I live in Delft in a cozy student house near the centre for five years now.

The master of Applied Mathematics started three weeks ago with the master kick-off. All master students from the faculty of EEMCS went to Arnhem (east of Delft) in order to get some useful information and to get to know each other. As soon as we arrived at the hostel in Arnhem, we got an introduction to different departments within the master Applied Mathematics and worked in a group of approximately five students on a project.

Before the master kick-off I already knew some Dutch students who did the bachelor’s degree of mathematics in Delft as well, but a lot of other nationalities were also present, such as Malaysia, Mongolia, Greece and Lithuania. The group of Applied Mathematics consisted of sixteen people and it was nice to learn the different backgrounds and cultures of a various group of students. Besides the introduction information and the project there also was the opportunity to have a drink at the bar in the evening or have a walk around the nice environment of Arnhem. The master kick-off really helped me to get in touch with a lot of other (international) students and also after this week we got together at the faculty to do some homework and at the /Pub (the pub  in the basement of EEMCS) to have a beer.

It was a fun week!

Alex

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