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.

Enrol

Messages

Stefan Geritz

Published, 18.11.2019 at 12:48

Sorry people,
Today's lecture (Monday 18 Nov) is cancelled.
I got sick.

Cecilia Berardo's picture

Cecilia Berardo

Published, 15.11.2019 at 10:18

Solutions for the set of exercises EX_14-11-2019 are now available in the section Material.

Stefan Geritz

Published, 15.11.2019 at 8:46

Exercises for Thursday 21 November are in file E-9

Stefan Geritz

Published, 15.11.2019 at 8:41

I have uploaded an old exam as an example of the sale of the questions. The file name is "Z-Sample exam" (to ensure that it appears at the bottom of an alphabetic listing of the uploads). The real exam will have different questions, of course, and possibly about different parts of the lecture notes.

Cecilia Berardo's picture

Cecilia Berardo

Published, 14.11.2019 at 11:50

Solutions for the set of exercises E6 are now available in the section Material.
Please check the messages in the course webpage to keep up to date with the new material:)

Stefan Geritz

Published, 14.11.2019 at 11:05

The files "L14-a Dens dep diff NEW", "L14-b Dens dep diff SIS", and "L14-c Dens dep diff SIRS" replace the older file "L14 OLD (but not wrong)". The new files contain the material we presented and discussed in the lectures. The old file is not wrong and gives even an example (predator-prey model) that is not in the new files, but concerning the exam material, the it is replaced by what is in the new files.

Stefan Geritz

Published, 7.11.2019 at 16:14

The exercises for Thursday 14-11-2019 have been uploaded as the file "Ex 14-11-2019".
Also a new version of L14 called "L14 New" has been uploaded.

Stefan Geritz

Published, 7.11.2019 at 11:59

A new version of L14 called L14 New has been uploaded

Stefan Geritz

Published, 17.10.2019 at 16:14

- The exam locations and duration (now max three hours) have been changed (see previous notice);

- On Thursday 31 October (i.e., the week after the teaching break) there will be no exercise class. The lectures on Monday and Thursday of that week continue as usual.

Stefan Geritz

Published, 17.10.2019 at 16:11

Exam dates:
(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
On both dates there will be an exam, but you have to choose. You can go only to one.
Both are written exams.
Let me know in advance by email (Stefan.geritz@helsinki.fi) which exam you will take.
If the exam result disappoints you, then we can make an appointment for a re-exam.

Pages

Timetable

Here is the course’s teaching schedule. Check the description for possible other schedules.

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

Other teaching

05.09. - 17.10.2019 Thu 10.15-12.00
31.10. - 12.12.2019 Thu 10.15-12.00
Stefanus Geritz
Teaching language: English

Material

Tasks

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.

Description

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