Mathematics and Statistics for Biologists
Syllabus, Bachelor's level, 1MA071
- Code
- 1MA071
- Education cycle
- First cycle
- Main field(s) of study and in-depth level
- Mathematics G1F
- Grading system
- Fail (U), Pass (3), Pass with credit (4), Pass with distinction (5)
- Finalised by
- The Faculty Board of Science and Technology, 23 October 2015
- Responsible department
- Department of Mathematics
Entry requirements
Chemistry 30 credit points, The Evolution and Diversity of Organism 10 credit points, Professional Qualifications in Biology and Scientific Methods 5 credits, Molecular Biology and Genetics 5 credits, Microbiology with Infection Biology 5 credits.
Learning outcomes
In order to pass the course (grade 3) the student should
Content
Powers, logarithms, allometry. The exponential function, exponential growth, difference equations. The derivative: definition, rules, derivatives of higher order, the mean value theorem, the connection between the sign of the derivative and increase/decrease of the function. Maximisation problems. Taylor's formula. Population dynamics and discrete dynamical systems, the logistic model and the Ricker model. Matrices, vectors and linear systems of equations, determinants, eigenvalues and eigenvectors with demographic models as application. Differential equations: separable, linear and systems of linear equations. Briefly about partial differential equations.
Population, sample, natural variation. Ideas behind hypothesis-testing. Replicated experiments. Descriptive statistics. Discrete and continuous data. General ideas on sampling. Statistical tests, the binomial distribution and the sign test. The normal distribution. Estimation of mean, variance and deviation. The t-distribution, briefly about Poisson, exponential and chi2 distributions. Tests for one and two normal distributions. Paired observations. One-way and two-way analysis of variance, randomized blocks. Multiple comparisons. Correlation. Simple linear regression. Chi2 test. Wilcoxon's rank sum test.
Instruction
Lectures and problem solving sessions.
Assessment
Written and oral presentation of a project and/or a written examination at the end of the course. Compulsory assignments during the course.