Mathematical modelling and problem solving

General Instructions

The problems are intended to practice your ability to reach as far as possible with your own thinking. It is common to assume that if you don't know how to solve a problem, you must collect more knowledge by asking or reading. However, it may equally well be that you can find the solution by spending some more time thinking and working with the problem.

Many of the problems are quite challenging, and you may encounter difficulties that you are not used to. Problems may be difficult to understand and interpret, may not always have a single right answer and be open-ended. To proceed, you will need to clarify by making your own assumptions, investigate, try things out, and yourself decide when you are satisfied with the solution. All of this is intentional, to make sure that you learn the relevant complex skills.

For this to work, you may not search for answers in books, on the Web or anywhere else, unless specifically indicated in the problem.

On the other hand, we fully accept that you may not be able to solve a problem completely. Even if you don't, you will develop your skills by trying.

You work in groups of two. Both members must actively participate in solving every problem. If you cannot find a group member yourself, contact us.

In all problem solving, time management is very important, and you must control how much time you spend on each problem. Officially, you have 20 hours per person per week (problems and lectures), and we do not require of you to work more than that. Do not spend time on unnecessarily long answers - short and clear answers are usually best and handwritten formulas and figures are fine. Save time by learning the basics of Mathematica first.

The pedagogy of this course is based on trust. We consider it as a serious breach of the rules to hand in answers that are not entirely your own. If you run into trouble, come and talk to us and we will consider reasonable ways to help.

Supervision and (weekly) meeting

The supervision is a very important part of the course, and we expect you to be present at most supervision sessions. Here, we you can discuss your ideas with us, we can share how to think in specific problem solving situations, and you avoid spending a lot of time without getting anywhere!

We give advice interactively and incrementally, so you are encouraged to come back and discuss the same exercise several times. You will then get more help every time.

Once for every module, you are required to take the initiative to have a short meeting with a supervisor. Both members of the group should be present. This is a checkpoint to resolve any misunderstandings, to help you with any general difficulties you may have with the course, and to ensure that both group members are making the expected effort. You can request this meeting anytime during the week (it is highly preferable if not all groups come at the end of the week), normally within the scheduled supervision times.

We recommend you to take a look at the whole module in the beginning of the week so that you can ask the most basic questions for several exercises during the first session.

There is a waiting list where you can add your name to see a supervisor (link). You can request to see somebody in particular, or anybody. This option is intended for when a supervisor asks to discuss your solutions in their feedback. Usually, you will ask to see anybody.

Two-step submission

Because of the importance of reflection, we employ a two-step system for the modules.

In the main submission you submit your solutions to all the problems of the module.

Then, in the compulsory follow-up lecture you receive collective feedback. Given that you know what you did yourself, the follow-up lecture will clarify most individual issues. As needed, you may also receive some individual feedback on your submission. You are also welcome to ask us for further individual feedback.

Finally, you submit your reflection, which also includes a self-assessment.

Passing requirements and grading

The course is designed so that you should not need to worry about passing if you have the right background and do the submissions in time with the expected effort. So engage in the problem solving because you want to learn!

The main submission of a module will pass unless it is clear that you have not made a best effort in solving the problems.

The reflection will pass if you have made a careful reflection. If you found the problems challenging, you have even more to learn in the reflection - in fact reflecting on your own problem solving is the key method to learn in this situation.

For your own practice, you are also asked to make self-assessments of your work. However, while we will read your self-assessments, the final grade for each module and for the course as a whole will be set by the teachers.

The final grade is based on an overall assessment at the end of the course. If you are not satisfied with the result, you will afterwards have the opportunity to discuss this with the main teacher(s). If you are close to a grade boundary, you will have the opportunity to improve your effort in the course.