Mathematics and Statistics for Biologists

10 credits

Syllabus, Bachelor's level, 1MA071

A revised version of the syllabus is available.

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, 15 March 2007
Responsible department: Department of Mathematics

Entry requirements

Chemistry 30 credit points, The Evolution and Diversity of Organism 15 credit points, Genetics and Genetic Engineering 15 credit points

Learning outcomes

In order to pass the course (grade 3) the student should

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;

be able to solve first and second order linear difference equations with constant coefficients;

be able to determine stable equilibria of simple discrete dynamical systems;

be able to solve simple separable differential equations, in particular the logistic equation;

be able to solve systems of linear equations, master matrix calculus and know how to compute eigenvalues and eigenvectors;

be able to apply the mathematical methods covered by the course on biological models;

be familiar with the foundation for statistical investigations and know some methods for descriptive statistics;

have a basic knowledge of statistical concepts and methods that are common in quantitative biology, and a general understanding of applications of statistics in some areas of biology;

be able to use simple mathematical and statistical software.

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.