Kaisa_2012_3_photo by Veikko Somerpuro

This course focuses on how to construct and analyse mathematical models of population behavior, rigorously derived from the mechanics of the underlying processes on the level of the individuals, and the analysis of these models to obtain results relevant to the application field. Many examples are taken from ecology but provide methods that are transferable to other fields as well. Topics include mono- and bimolecular reactions, reaction networks, the principle of mass action, predator-prey models, competition models, diffusion and taxis, pattern formation, structured populations and developmental delays.

RECOMMENDED TO
Students of the master programs MAST (mathematical modeling) and LSI (biomathematics)

PREREQUISITE
Familiarity with differential equations and probability theory

TIMETABLE
Lectures on Mondays 10-12 room CK107 and on Tuesdays 10-12 room B121
Exercise classes on Tuesdays 14-16 room B119

EXAM
Monday 11 December from 10 to 12 in room CK107

Ilmoittaudu
14.8.2017 klo 09:00 - 12.12.2017 klo 23:59

Viestit

Stefan Geritz

Julkaistu, 16.1.2018 klo 14:48

RE-EXAM :
I could organize a re-exam Mathematical Modelling during the general exam on Wednesday 7 February from 16-20. Alternatively I could try to book a room for the exam on 25 (Thursday) or 26 (Friday) January.
If you are interested in a (re-)exam, please give me feedback via email with subject line "Re-exam Mathematical Modelling".

Stefan Geritz

Julkaistu, 28.11.2017 klo 8:10

- Today's lecture is cancelled.
- Next week I will be available for questions in the usual lecture rooms during the usual lecture times.
- During the exam on Monday 11 December you are allowed to use one "cheat sheet", i.e., one A4 page (one-side only) with handwritten notes. What exactly you put on the cheat sheet is entirely up to yourself.

Stefan Geritz

Julkaistu, 27.11.2017 klo 15:41

Next week I will be available for questions in the usual lecture rooms during the usual lecture times.

During the exam on Monday 11 December you are allowed to use one "cheat sheet", i.e., one A4 page (one-side only) of handwritten notes.

Stefan Geritz

Julkaistu, 27.11.2017 klo 15:37

Lecture notes L-21-11-2017 now available in Materials.

N.B., there are no lecture notes of 20-11-2017, because on that lecture we went a bit slower again over material that we already covered.

Stefan Geritz

Julkaistu, 22.11.2017 klo 16:45

Exercises E-28-11-2017
are now available in Materials

Stefan Geritz

Julkaistu, 9.11.2017 klo 9:22

Erratum:
In condition 5 on page 162 of the lecture notes of 07-11-2017, the "D>r" is not needed and should be removed.

Stefan Geritz

Julkaistu, 15.10.2017 klo 9:49

There are two exam dates:
- Monday 11 December from 10 to 12
- Tuesday 12 December from14 to 16
You can choose one and only one.
There will be a possibility of a re-exam in January 2018.

Stefan Geritz

Julkaistu, 30.8.2017 klo 9:00

Neither the lectures nor the exercise classes are mandatory. However, participation in 12/14 exercise classes will gain you the equivalent of halve a credit point on top of the raw score of the exam. That means, e.g., that a 4.1 will be rounded off to a full 5 instead of to a 4.

There are many books on mathematical modeling of populations. These books are useful as far as model analysis is concerned, but they tend to be very disappointing when it comes to the modeling itself. The emphasis of my course is on modeling techniques and principles for the derivation of population models from a model of the behavior of the individuals. The course material will consist of handouts of copies of my own notes. However, the handwritten lecture notes and exercises of the previous courses (see link below) are still useful, but I probably will deviate from its contents, present things in a different order, introduce new things, omit old things. It is the lectures that define the material of the exam.

Link to the previous course:
https://wiki.helsinki.fi/display/mathstatKurssit/Mathematical+modelling%...

Aikataulu

Tästä osiosta löydät kurssin opetusaikataulun. Tarkista mahdolliset muut aikataulut kuvauksesta.

PäivämääräAikaOpetuspaikka
Ma 4.9.2017
10:15 - 12:00
Ti 5.9.2017
10:15 - 12:00
Ma 11.9.2017
10:15 - 12:00
Ti 12.9.2017
10:15 - 12:00
Ma 18.9.2017
10:15 - 12:00
Ti 19.9.2017
10:15 - 12:00
Ma 25.9.2017
10:15 - 12:00
Ti 26.9.2017
10:15 - 12:00
Ma 2.10.2017
10:15 - 12:00
Ti 3.10.2017
10:15 - 12:00
Ma 9.10.2017
10:15 - 12:00
Ti 10.10.2017
10:15 - 12:00
Ma 16.10.2017
10:15 - 12:00
Ti 17.10.2017
10:15 - 12:00
Ma 30.10.2017
10:15 - 12:00
Ti 31.10.2017
10:15 - 12:00
Ma 6.11.2017
10:15 - 12:00
Ti 7.11.2017
10:15 - 12:00
Ma 13.11.2017
10:15 - 12:00
Ti 14.11.2017
10:15 - 12:00
Ma 20.11.2017
10:15 - 12:00
Ti 21.11.2017
10:15 - 12:00
Ma 27.11.2017
10:15 - 12:00
Ti 28.11.2017
10:15 - 12:00
Ma 4.12.2017
10:15 - 12:00
Ti 5.12.2017
10:15 - 12:00
Ma 11.12.2017
10:15 - 12:00
Ti 12.12.2017
10:15 - 12:00

Muu opetus

05.09. - 17.10.2017 Ti 14.15-16.00
31.10. - 12.12.2017 Ti 14.15-16.00
Stefanus Geritz
Opetuskieli: englanti

Materiaalit

Kuvaus

Optional course.

Master's Programme in Mathematics and Statistics is responsible for the course.

The course belongs to the Mathematics and Applied mathematics module.

The course is available to students from other degree programmes.

BSc courses on differential equations, linear algebra, probability theory

Constructing mathematical models of biological phenomena, with emphasis on the derivation of the models from the underlying processes on the level of individual behavior. Analysing the models using the qualitative theory of ordinary differential equations, multiple time-scales, and numerical methods.

Recommended time/stage of studies for completion: 1. year

Term/teaching period when the course will be offered: varying

This course focuses on how to construct and analyse mathematical models of population behavior, rigorously derived from the mechanics of the underlying processes on the level of the individuals, and the analysis of these models to obtain results relevant to the application field. Many examples are taken from ecology but provide methods that are transferable to other fields as well. Topics include mono- and bimolecular reactions, reaction networks, the principle of mass action, predator-prey models, competition models, diffusion and taxis, pattern formation, structured populations and developmental delays.

Lectures and exercise classes

Exam and excercises, Course will be graded with grades 1-5

Exam, other methods will be described later