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

FIRST LECTURE
Thursdays 5 September, time 14-16 in room CK107

FIRST EXERCISE CLASS
Thursday 12 September, time 10-12 in room C129

GENERAL TIMETABLE
Lectures on Mondays, time 14-16, room B222, Exactum Building, Kumpula Campus.
Lectures on Thursdays, time 14-16 in room CK107, Exactum Building, Kumpula Campus.
Exercises on Thursdays, time 10-12, room C129, Exactum Building, Kumpula Campus.

EXAMS
There will be two dates for the exam. You can go only to one, so you have to choose. Let me know by email (Stefan.geritz@helsinki.fi) which exam you will take. Both are written exams. Use of notes is not allowed. The dates and places are:
(1) Mon 9.12.2019 at 14:15 - 17:00 in Physicum, D104
(2) Thu 12.12.2019 at 14:15 - 17:00 in Exactum, B121
If the exam result disappoints you, we can always make an appointment for a re-exam.

Ilmoittaudu

Viestit

Käyttäjän Cecilia Berardo kuva

Cecilia Berardo

Julkaistu, 7.12.2019 klo 12:43

Solutions for the sets of exercise Z-Exercise and ZZ-Sample Exam are now available at the end of the section Material.

Stefan Geritz

Julkaistu, 2.12.2019 klo 16:23

* I uploaded another sample exam in materials for practice: "ZZ-Sample Exam".

* The exam will be about the lecture notes The exam will be about lectures L1, ... L10, L11(new), L12,L13, L14a, L14b, L14c, and L17supplement plus corresponding exercises. This is the same list as before (see below) but with the L11-supplement removed.

Käyttäjän Cecilia Berardo kuva

Cecilia Berardo

Julkaistu, 2.12.2019 klo 11:26

Solutions for the set of exercises Z-Sample Exam are now available at the end of the section Material.

Stefan Geritz

Julkaistu, 2.12.2019 klo 9:41

* Extra exercise for Thursday 5 Dec on the translation of a "life-history story" into a mathematical model. The file is in materials at the bottom of the (alphabetic) list and has the name Z-Exercise.

* Also see the previous two messages.

Stefan Geritz

Julkaistu, 2.12.2019 klo 9:06

Oh, I forgot to mention (see previous message) that the exercises corresponding to the lectures L1, L2, ... , L13, L14a, L14b, L14c, and L17supplement are also part of the exam.

Stefan Geritz

Julkaistu, 2.12.2019 klo 8:58

* Today (2 Dec) and on Thursday (5 Dec) no lectures. Instead of giving lectures I will be present on the classroom to answer questions about the course material.

* The exam will be about lectures L1, L2, ... , L13, L14a, L14b, L14c, and L17supplement.

Stefan Geritz

Julkaistu, 28.11.2019 klo 12:39

New file "L17supplement" has been uploaded

Käyttäjän Cecilia Berardo kuva

Cecilia Berardo

Julkaistu, 26.11.2019 klo 12:03

Solutions for the set of exercises E9 are now available in the section Material.

Stefan Geritz

Julkaistu, 25.11.2019 klo 13:25

The exercises for Thursday 28 November are in the file "Z-Sample Exam" at the bottom of the list in the section Material.

Stefan Geritz

Julkaistu, 22.11.2019 klo 15:22

Two messages ...

>> The lecture of Monday 25 November has been cancelled because of a bus strike.

>> There will be two dates for the exam. You can go only to one, so you have to choose. Let me know by email (Stefan.geritz@helsinki.fi) which exam you will take. Both are written exams. Use of notes is not allowed. The dates and places are:
(1) Mon 9.12.2019 at 14:15 - 17:00 in Physicum, D104
(2) Thu 12.12.2019 at 14:15 - 17:00 in Exactum, B121
If the exam result disappoints you, we can always make an appointment for a re-exam.

Sivut

Aikataulu

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

PäivämääräAikaOpetuspaikka
Ma 2.9.2019
14:15 - 16:00
To 5.9.2019
14:15 - 16:00
Ma 9.9.2019
14:15 - 16:00
To 12.9.2019
14:15 - 16:00
Ma 16.9.2019
14:15 - 16:00
To 19.9.2019
14:15 - 16:00
Ma 23.9.2019
14:15 - 16:00
To 26.9.2019
14:15 - 16:00
Ma 30.9.2019
14:15 - 16:00
To 3.10.2019
14:15 - 16:00
Ma 7.10.2019
14:15 - 16:00
To 10.10.2019
14:15 - 16:00
Ma 14.10.2019
14:15 - 16:00
To 17.10.2019
14:15 - 16:00
Ma 28.10.2019
14:15 - 16:00
To 31.10.2019
14:15 - 16:00
Ma 4.11.2019
14:15 - 16:00
To 7.11.2019
14:15 - 16:00
Ma 11.11.2019
14:15 - 16:00
To 14.11.2019
14:15 - 16:00
Ma 18.11.2019
14:15 - 16:00
To 21.11.2019
14:15 - 16:00
Ma 25.11.2019
14:15 - 16:00
To 28.11.2019
14:15 - 16:00
Ma 2.12.2019
14:15 - 16:00
To 5.12.2019
14:15 - 16:00
Ma 9.12.2019
14:15 - 17:00
To 12.12.2019
14:15 - 17:00

Muu opetus

05.09. - 17.10.2019 To 10.15-12.00
31.10. - 12.12.2019 To 10.15-12.00
Stefanus Geritz
Opetuskieli: englanti

Materiaalit

Tehtävät

Exercise class Thursday 12 September

For the exercise class of Tuesday 12 September, study the lecture notes L01 and L02 and make exercises1 and 2a of the exercise set E1.

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