Explore deterministic mathematical modeling in quantitative ecology through this comprehensive lecture from the Serrapilheira/ICTP-SAIFR Training Program. Delve into discrete and continuous time dynamics, population models, and various mathematical concepts crucial for ecological research. Learn about geometric production, negative population scenarios, and graphical examples to enhance understanding. Examine the logistic map, fixed points, and other essential models used in population dynamics. Gain valuable insights from Roberto Kraenkel of IFT-Unesp as he guides you through this advanced topic in the field of quantitative ecology.