Ecobiology

General goals. This course is devoted to mathematical modeling of biological phenomena. Starting from discrete models (as logistic map, fractals, cellular automata), passing through the development of simple differential population models (as Malthusian model, predator-prey, evolutionary games) up to stochastic models (genetics), the course will provide mathematical fundamentals to understand the bases of modeling in biology. Moreover, at the same time, students are supposed to learn not only general facts but also to appreciate to what extent correct models of phenomena can give information to laws that govern them. Specific goals. The main goal of the course is to acquire, in practice, the "scientific method" (observation and data collection, theoretical description of phenomena main characteristics, predictions). Starting, in particular, from a certain number of biological examples, the course aims to show how to describe mathematically the most relevant aspects of each phenomenon and how to make predictions by using this description. An interesting consequece of this approach is that a deeper analysis of the model can often generate new questions on biological phenomena. By using this method the student undestand, often for the first time, that mathematics (calculus, statistics and probability) can be used for very interesting purposes. These results can be obtained not only by means of lessons and seminars, but also by reading selected papers that can be discussed in the classroom. These papers, with the slides of lessons and notes, can be downloaded from elearning website. In the final exam students can also submit a short seminar whose subject is not included in the program: this allows the teacher to verify student autonomy and skill. A) Knowledge and understanding - knowing and understanding a mathematical model, through its predictive properties - comprehension of the "scientific method" (observation and data collection, theoretical description of phenomena main characteristics, predictions) - comprehension of the descriptive and interpretative power of mathematics - comprehension of the main mathematical methods useful in biological sciences B) Applying knowledge and understanding - be able to use the specific terminology - be able to identify the right methods to comprehend the problem under examination - be able to extract the information of biological interest from a mathematical C) Making judgements - critical thinking through the study of a mathematical model, in order to understand its applicability limits - learning by questioning D) Communication skills -be able to communicate what has been learned during the oral exam E) Learning skills - learning the specific terminology - be able to make the logical connections between the topics covered - be able to identify the most relevant topics