Kaisa_2012_3_photo by Veikko Somerpuro

A 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 hands-on experience.

The full course consists of four parts (each can be taken separately):

(1) Fundamentals (construction of simple models and basic calculus)
(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. All you need is to use Excel or any other software capable of simple calculations and plotting. Both undergraduates and graduate students are welcome.

Ilmoittaudu
30.9.2019 klo 12:00 - 29.10.2019 klo 23:59

Aikataulu

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

PäivämääräAikaOpetuspaikka
Ti 29.10.2019
08:15 - 09:45
To 31.10.2019
08:15 - 09:45
Ti 5.11.2019
08:15 - 09:45
To 7.11.2019
08:15 - 09:45
Ti 12.11.2019
08:15 - 09:45
To 14.11.2019
08:15 - 09:45
Ti 19.11.2019
08:15 - 09:45
To 21.11.2019
08:15 - 09:45
Ti 26.11.2019
08:15 - 09:45
To 28.11.2019
08:15 - 09:45
Ti 3.12.2019
08:15 - 09:45
To 5.12.2019
08:15 - 09:45
Ti 10.12.2019
08:15 - 09:45
To 12.12.2019
08:15 - 09:45
Ke 18.12.2019
08:15 - 09:45
To 16.1.2020
10:15 - 11:45
Ma 27.1.2020
10:15 - 11:45

Materiaalit

Tehtävät

Homework exercises

Weekly homework assignments from the file "Exercises and solutions" (you find the file under "Materials"). Exercises marked with *: write down the solution as carefully as in an exam. This will be read by a fellow student. The marked exercises are not more difficult than the others.

Set 1: 1, 2, (4/5), 6, 9* discussed on 7 November. Choose one of 4 and 5.
Set 2: 8, 12*, 13, 14, 15 discussed on 14 November.
Set 3: 10, 16, A1, 21,22 discussed on 21 November. A1 is newly added (after 16) to the pdf Exercises and solutions.
Set 4: 7, 20, 23*, 26, 30 discussed on 28 November.
Set 5: 11*, 24, 29, 31 discussed on 5 December. You can ignore the remark after 24 because you know how to do the correction. If you have not had Part 1 of this course, here is a hint to 31: in equilibrium, on average as many enzyme molecules bind the inhibitor as many release it, so that alpha*z*x (number binding per unit of time, alpha*z is the speed of binding, proportional to z, i.e., to how easy it is to find an inhibitor molecule) equals beta*y (number releasing per unit of time, beta is the speed of releasing). Here x+y is the total enzyme concentration (free plus inhibited), which is N divided with the volume of the test tube. x/(x+y) is the fraction of free enzyme molecules, i.e., for large N, this is the probability of being free.

Set 6: 34, 35*, 36, 37, discussed on 12 December. These exercises are best done after the last lecture.

Kurssin suorittaminen

Homework exercises: see the weekly assignments under Tasks.

Exam: problem-solving (in writing), the problems are similar to the homework exercises. Everything may be used (books, notes, etc) but may not be shared during the exam. There is no need for laptops; nevertheless you can use your laptop if you want, but the internet connection must be switched off (download necessary files in advance). Exercise class activity decides marginal grades. This part of the course gives 3 credits (3 op)

EXAM TIMES:
First exam: Wed 18 December 8.15-10.00 in the lecture room (BK3, room 4617).
Second exam: Thu 16 January 10.15-12.00 in BK3, room 6602 (6th floor)
BRING A CALCULATOR TO THE EXAM!

Kuvaus

none

Basic probability theory; modelling probabilistic phenomena; the concept of hypothesis testing and the Bayesian approach

Period II of the academic year 2017-2018. If attendance is satisfactory, offered in period II every other year (2019 etc)

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 hands-on experience. The course is specifically tailored for biology students and assumes no background in mathematics. Part 2 contains the fundamentals of probability theory, providing tools for probabilistic models and future studies in statistics (hypothesis testing and Bayesian statistics).

Contact teaching; exercise classes; completion by written exam

0-5, exam only

Teaching in English

Eva Kisdi

Replaces the former course 57382 Mathematical methods in biology, part 2, 3 cr.