Entry requirements

Alternative 1: Biology 2, Mathematics 4/Mathematics D, as well as 60 credits within the programme and participation in Evolution and Diversity of Organisms 15 credits, Molecular Biology and Genetics 10 credits, and Life and Interactions of Microorganisms 5 credits. Alternative 2: Bioscience as well as another 30 credits within the programme and participation in Evolution and Diversity of Organisms 15 credits, Molecular Biology and Genetics 10 credits, and Life and Interactions of Microorganisms 5 credits.

Learning outcomes

On completion of the course, the student should be able to:

• master the power and logarithm laws;
• know the definition of the derivative and be able to compute the derivative of simple functions and to use the derivative as a tool for determining extreme values;
• solve first and second order linear difference equations with constant coefficients;
• determine stable equilibria of simple discrete dynamical systems;
• solve simple separable differential equations, in particular the logistic equation;
• solve systems of linear equations, master matrix calculus and know how to compute eigenvalues and eigenvectors;
• apply the mathematical methods covered by the course on biological models;
• use foundations for statistical investigations and know some methods for descriptive statistics;
• use basic statistical concepts and methods that are common in quantitative biology, and have a general understanding of applications of statistics in some areas of biology;
• use simple mathematical and statistical software.

Content

The course contains both mathematics (approx. 7 credits) and statistics (approx. 3 credits).

Mathematics: 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.

Statistics: 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. Mathematical software.

Instruction

Lectures ,problem solving sessions and computerlabs.

Assessment

The mathematics and statistics content of the course is examined together in a written exam (8 credits) at the end of the course, as well as with assignments (2 credits) during the course.

If there are special reasons for doing so, an examiner may make an exception from the method of assessment indicated and allow a student to be assessed by another method. An example of special reasons might be a certificate regarding special pedagogical support from the disability coordinator of the university.