NMAA05009U Mathematical Modelling (Model)

Volume 2013/2014
Education
BSc Programme in Mathematics
Content
This course will practice the classical three-phase diagram of mathematical modeling. This diagram describes the transitions between the model and reality. The three phases are:
1. A problem from the real world is translated into a mathematical problem.
2. The mathematical problem is solved in its mathematical context.
3. This solution is then translated back to the corresponding biological, economical,... reality and interpreted in this context.

To begin with, we introduce relevant parts of Maple and we look at ‘half finished’ models. We then proceed to more independent modelling. Our first mathematical models are developed with modest insistence on formalism/rigour, rather we emphasize computational techniques, incl. simulations (involving Maple, and also Excel). Then we progress to increased use of mathematically sophisticated methods. The course will encompass discussions of realism and useability of models – striving towards ever higher levels of sophistication. The main examples are taken from economy, biology, physics, sociology and daily life situations. This way the students heading towards gymnasium teaching will develop a portfolio of models of teaching relevance, while students of e.g. pure mathematics, statistics, actuarial math, mathematical economics, biology, and physics will meet mathematical models not otherwise encountered. A number of mathematical techniques, such as difference and differential equations and simulations, will be presented and tested. Report writing techniques are also part of the course.
Learning Outcome
Knowledge: the student will learn: the three-phase diagram involved in mathematical modeling; mathematical modeling techniques such as difference and differential equations, stochastic simulation and data analysis; project report writing; basic Maple programming to apply to the analysis of the models.

Skills: by the end of the course the student will have acquired skills to: apply modeling techniques to the analysis of specific models; identify chosen, as well as potential, assumptions and simplifications in a model; identify mathematizable problem areas from the real world; translate real problems into a mathematically formulated problem and solve it; translate the solution obtained in a model back to the relevant part of the real world.

Competences: by the end of the course the student is expected to be able to build and analyze a mathematical model; comprehend the extent to which a given mathematical model mirrors a real life problem; discuss realism and useability of models; interpret the results of the model in relation to the real problem originating it;
An1 or similar.
One double lecture per week for the first 7 weeks. Maple and hand-written exercises. Project work, partly in groups. The group work will be both with and without direct teacher involvement – and with and without use of computers. The last two weeks are devoted to group work on the final project.
  • Category
  • Hours
  • Lectures
  • 28
  • Practical exercises
  • 14
  • Preparation
  • 84
  • Project work
  • 80
  • Total
  • 206
Credit
7,5 ECTS
Type of assessment
Continuous assessment, 9 weeks
Continuous assessment with grade given for a total evaluation of 2 problem sets, 2 mini-projects, an abstract for and a report of a final project. The problem sets and the mini-projects counts each 1/6 of the total grade, and the final project counts 1/3 of the total grade. The student must pass each homework assignment and the final project. If the student fails a homework assignment he/she can rsubmit it once. The final project can only be resubmitted as a reexamination.
Aid
All aids allowed
Marking scale
7-point grading scale
Censorship form
No external censorship
One internal examiner
Re-exam
Resubmission of the elements that were failed during the term. The weight is the same as in the ordinary exam.
Criteria for exam assesment

The student must in a satisfactory way demonstrate that he/she has mastered the learning outcome of the course.