Mathematical methods in biologyContents:This course gives a highly practical introduction to mathematical concepts and methods applied in the life sciences. We learn mathematics through solving problems of biological interest, with emphasis on applicable skills and handson experience. The full course consists of four parts (each can be taken separately):
(2) Probability (handling stochastic phenomena, groundwork for statistics) (3) Vectors and matrices (applied to population dynamics, quantitative genetics and statistics) (4) Dynamic models (techniques to analyse models of population growth, reaction kinetics, etc.) Parts 1 & 2 are given in the fall semester, parts 3 & 4 in spring. Each part takes one study period (seven weeks), 2 h interactive lectures and 2 h exercises per week. The course is specifically tailored for biology students and assumes no background in mathematics. Both undergraduates and graduate students are welcome. Prior registration is not necessary. Prerequisites:You will need to use Excel or any other software capable of simple calculations and plotting. Time and place (spring 2016):Part 3: weeks 3  9 ( = first study period). First lecture: 19 January (Tue) 10.15. The lecture of 26 January is cancelled. Part 3 Tuesday 10.15  12.00, Biokeskus 3, room 1401; Thursday 10.15  12.00, Biokeskus 1, room 3106 Exam, course codes and credits:Each part of the course gives separate credits (3 op per part). Exam: problemsolving (in writing), the problems are similar to the homework exercises. Everything may be used (books, notes, dictionary) but may not be shared during the exam. There is no need for laptops; nevertheless laptops can be used if so desired, but the internet connection must be switched off (download necessary files in advance). Exercise class activity decides marginal grades. Exam of Part 4: Friday 6 May 14.1516.00 in Kumpula, Exactum C129. Contact me if this time is not good for you. Course codes:
Part 2: 57382 Part 3: 57383 Part 4: 57384 Lecture notes and course books:The lecture notes of Parts 1, 3 and 4 can be downloaded in pdf from the link under the respective parts below. The books listed below are useful reference books also for later use, but you need not have them to participate in this course successfully: Lecturer:Eva Kisdi (PhD in Biology). Office: Kumpula campus, EXACTUM, room A420 Further information:eva.kisdi [at] helsinki.fi Feedback:You can leave comments anonymously and at any time using this feedback form. These comments will be read only by Eva Kisdi. Feedback is very important for improving courses, and your time giving feedback is much appreciated! Part 1Lecture notesLecture notes can be downloaded in pdf. Homework exercisesThis pdf contains the homework exercises and their solutions. This file will be updated regularly with new exercises. Assignments (exercises marked with *: write down the solution as carefully as for an exam, these will be read by a fellow student. The marked exercises are not more difficult than others.)
Handouts and supporting files
Part 2Homework exercisesThis pdf contains the homework exercises and their solutions (UPDATED on 17 November; exercise numbers changed!). Assignments (exercises marked with *: write down the solution as carefully as for an exam, these will be read by a fellow student. The marked exercises are not more difficult than others.)
Handouts and supporting files
Part 3Lecture notesLecture notes can be downloaded in pdf. Homework exercisesThis pdf contains the homework exercises and their solutions. This file will be updated regularly with new exercises. Assignments (exercises marked with *: write down the solution as carefully as for an exam, these will be read by a fellow student. The marked exercises are not more difficult than others.)
Handouts and supporting files
Part 4Lecture notesLecture notes can be downloaded in pdf. For the missed lecture of 26 April, study the following 3 sections of the lecture notes: 4.6 (the Brusselator), 5.1 up to Figure 13 on page 52 (limit cycles and the PoincareBendixson theorem; you can skip the method of Bendixson´s negative criterion from page 53 onwards); 6.1 with Box 2 (Hopf bifurcation through the example of the Brusselator and in general). The last lecture will assume you are familiar with this material. I am sorry for not being able to lecture it. The 28 April exercise class is on! Homework exercises
The exercises are in the lecture notes, with weekly assignments below and solutions in this pdf (updated regularly). Exercises marked with *: write down the solution as carefully as for an exam, these will be read by a fellow student. The marked exercises are not more difficult than others.
Handouts and supporting files
