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