Abstract: This course will give an introduction to some of the mathematical tools used by mathematicians and biologists to study the dynamics of structured populations, focusing on the modeling of populations with a discrete structure in discrete time. Although the course will be based on problems drawn from population ecology and demography, those will serve as a pretext to introduce concepts that are ubiquitous in applied mathematics (ergodic and absorbing Markov chains on a finite space, multitype branching processes, and Perron-Frobenius theory). The only prerequisites for the course are elementary probability theory (without measure theory) and basic linear algebra. In the first lesson, we will present our modeling framework, illustrate some of its properties, and establish a roadmap for the course. We will then start the formal study of the Galton-Watson branching process.

us02web.zoom.us/j/4082603129