Mathematical methods in biology 3, Lectures, Lectures

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A practical introduction to mathematical concepts and methods applied in the life sciences. Part 3 covers the essential tools of vectors and matrices.

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.

The full course consists of four parts (each can be taken separately and awards 3 credits):

Mathematical methods in biology, Part 1: Fundamentals (construction of simple models and basic calculus)
Mathematical methods in biology, Part 2: Probability (handling stochastic phenomena, groundwork for statistics)
Mathematical methods in biology, Part 3: Vectors and matrices (applied to population dynamics, genetics and statistics)
Mathematical methods in biology, Part 4: Dynamic models (techniques to analyse models of ecological interactions, biochemical reactions, etc.)

In the present Part 3, we build up indispensable tools for studying models with several variables, such as the dynamics of multiple, interacting populations or biochemical reaction networks. The key to analysing such models is given by vectors and matrices. In this part, we learn what vectors and matrices are, how to perform calculations with them and how to analyse linear models in discrete time. Our leading example will be the dynamics of structured populations (age-, size-, spatial etc. structure), with further examples depending on the participants' background and interest (principal component analysis in statistics, stochastic population models and extinction probabilities, genetic drift, quantitative genetics, or a brief foray into density-dependent models of periodical cicadas and chaotic dynamics).

This part can be taken without parts 1 and 2 of Mathematical methods in biology. Together with part 1, this part (or equivalent knowledge) is needed for part 4, where we shall get to models of wide interest.

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