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.

Enrol
2.10.2017 at 12:00 - 15.12.2017 at 23:59

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Eva Kisdi's picture

Eva Kisdi

Published, 10.11.2017 at 16:38

See timetable updates under "TIMETABLE"

Timetable

The 16 November (Thu) class is CANCELLED. Instead, on 17 November (Fri) we shall have a lecture. Then we continue with a lecture on Thu 23 November and we shall discuss TWO sets of exercises on Fri 24 November. TIP: start with the second set of exercises now, don't leave all exercises to the last day!

DateTimeLocation
Thu 2.11.2017
14:15 - 15:45
Fri 3.11.2017
10:15 - 11:45
Thu 9.11.2017
14:15 - 15:45
Fri 10.11.2017
10:15 - 11:45
Thu 16.11.2017
14:15 - 15:45
Fri 17.11.2017
10:15 - 11:45
Thu 23.11.2017
14:15 - 15:45
Fri 24.11.2017
10:15 - 11:45
Thu 30.11.2017
14:15 - 15:45
Fri 1.12.2017
10:15 - 11:45
Thu 7.12.2017
14:15 - 15:45
Fri 8.12.2017
10:15 - 11:45
Thu 14.12.2017
14:15 - 15:45
Fri 15.12.2017
10:15 - 11:45
Fri 15.12.2017
14:15 - 15:45

Material

Last update: 24 November (also added detailed solutions)

Weekly homework assignments from the file "homework problems and solutions". 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, 3*, 5, 6 discussed on 9 November.
Set 2: 4, 7, 9*, 12, 13 discussed on 1 December together with set 3.
Set 3: 14, A1, 15*, 18 discussed on 1 December together with set 2. Exercise A1 is a new exercise added to the updated pdf file, you find it after exercise 14. If you did not take part 1 of this course and cannot do exercise 18(a), then take the result from the solutions [probability of being open x=2/3] and do 18(b) with this extra: what is the probability that the number of open channels is "around" 12, meaning that it is at least 10 and at most 13?
Set 4: 16*, 19, 20, A2, A4, discussed on 8 December, together with set 5. A2 and A4 are new exercises added to the updated pdf file, before exercise 23. If you did not take part 1 of this course and cannot do 20(b), take exercise 22 instead.
Set 5: 10, 23, 24, 26. For 26, you need that the expectation of a binomially distributed random variable is (of course) n*p, and the variance is n*p*(1-p). If you cannot handle the differential equations in 26(a), take the equilibrium from the solution of this exercise: at equilibrium, a fraction beta/(beta+alpha*z) of the enzyme molecules are free. Exercise 24 is demanding: try your best, and we discuss it in class.
Set 6: 11, 28, 29, 30, 32, discussed on 15 December. Exercise 32 explains the basics of hypothesis testing. This we shall discuss also in the last lecture, but you can do the exercise already now.

Conduct of the course

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 laptops can be used if so desired, but using the internet is not allowed except for the normal distribution calculators linked from the Materials section of this page (download necessary files in advance). Exercise class activity decides marginal grades. This part of the course gives 3 credits (3 op).

FIRST EXAM: 15 December (Fri) 14.15-16.00 in the lecture room. Bring a calculator!

Description

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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.