|
| Udgave: |
Forår 2013 NAT |
| Point: |
7,5 |
| Blokstruktur: |
4. blok |
| Skemagruppe: |
A |
| Fagområde: |
mat |
Semester: |
Forår |
| Varighed: |
9 uger |
| Institutter: |
Institut for Matematiske Fag |
| Uddannelsesdel: |
Bachelor niveau |
| Kontaktpersoner: |
Postdoc Steven Deprez, rum 04.01.12 email: sdeprez@math.ku.dk og
Postdoc Elisenda Feliu, rum 04.3.10, email: efeliu@math.ku.dk |
| Skema- oplysninger: |
 Vis skema for kurset
Samlet oversigt over tid og sted for alle kurser inden for Lektionsplan for Det Naturvidenskabelige Fakultet Forår 2013 NAT |
| Undervisnings- periode: |
22. april – 23. juni 2013
|
| Undervisnings- form: |
One double lecture per week. 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. |
| Indhold: |
We proceed systematically; to begin with, we introduce relevant parts of Maple and we look at ‘half finished’ models: you will practice being able to comprehend the extent to which a given mathematical model mirrors a real life problem, and to identify chosen, as well as potential, assumptions and simplifications. 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). 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. 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. |
| Kompetence- beskrivelse: |
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.
In the course we proceed systematically; to begin with, we don’t train independent formulation of models, but the student should comprehend the extent to which a given mathematical model mirrors a real life problem, and should be able to identify chosen, as well as potential, assumptions and simplifications. We then proceed rapidly to more independent modelling. Similarly, initially phase two is approached with modest insistence on formalism/rigour, but rather on computational techniques (involving computers, and the competency of handling them); this will progress to increasing use of mathematically sophisticated methods. Finally, the course will encompass discussions of realism and useability of models – striving towards ever higher levels of sophistication.
|
| Målbeskrivelse: |
At the end of this module
the student is expected to be able to build, analyze, and describe mathematical models.
The student is expected to be able to identify mathematizable problem areas from the real world, including other scholarly disciplines, to translate these into a mathematically formulated problem, to solve this problem, and to translate the solution obtained back to the relevant part of the real world.
Moreover, the student is expected to be able to analyze the basis for and the properties of an existing model and to be capable of judging its scope and validity, including ”de-mathematizing“ (features of) this model, i.e. to interpret elements of it and its conclusions in relation to the situation that it models.
|
| Lærebøger: |
Recommended text: Edwards and Hamson: Guide to Mathematical
Modelling, 2nd edition, Palgrave Mathematical Guides, Houndsmill, 2001 or Industrial Press Inc 2007.
|
| Tilmelding: |
Kursus- og eksamenstilmelding og afmelding sker på
www.kunet.dk
Tilmelding skal ske i perioden den 15. november – 1. december 2012.
|
| Faglige forudsætninger: |
An1 or similar. |
| Eksamensform: |
Continuous assessment with internal censor and with grade given for a total evaluation of 2 problem sets, 2 mini-projects, an abstract for and a report of a final project. Each homework assignment must be separately evaluated as passed. In the overall grade the problem sets and mini-projects are weighed equally, and the abstract for and report on the final project are together weighed as equivalent to two mini-projects.
Reexam:
Resubmission of the homework assignments that are evaluated with internal censor and graded. It is a requirement that the homework assignments separately are evaluated as passed. In the overall grade the problem sets and mini-projects are weighed equally, and the abstract for and report on the final project are together weighed as equivalent to two mini-projects.
|
| Eksamen: |
Løbende evaluering.
Reeksamen: Genaflevering af opgaver d. 22. august 2013. |
| Kursus hjemmeside: |
 |
| Pensum: |
Will be specified during the course. |
| Undervisnings- sprog: |
Engelsk
|
| Sidst redigeret: |
30/10-2012 |