- Docente: Massimo Campanino
- Credits: 6
- SSD: MAT/06
- Language: Italian
- Teaching Mode: In-person learning (entirely or partially)
- Campus: Bologna
-
Corso:
Second cycle degree programme (LM) in
Computer Science (cod. 8028)
Also valid for Second cycle degree programme (LM) in Mathematics (cod. 8208)
Learning outcomes
At the end of the course the student knows some advanced
probability theories with application to computer science, such as
Markov chains with discrete and continuous time. He is able to
analyze some simple stochastic systems such some with application
to biology.
Course contents
Denumerable additivity. One-dimensional random walk. Generating
function. Gamblers' ruin problem. Galton Watson processes. Markov
chains. Recurrent and transient states. Stationary distributions.
Markov chains with continuous time. Poisson process. Pure birth
processes. Semi-Markov processes. Queueing processes. Queueing
Markov processes.. Open and closed systems of queues. Jackson's
property.
Readings/Bibliography
S. Ross. Introduction to Probability Models. Academic Press.
W. Feller. An Introduction to Probability Theory and its
Applications. I Volume. Wiley.
Teaching methods
Lectures.
Assessment methods
Final verification consists in an oral test.
Oral test consists in an talk, starting from three questions, with the goal of testing the understanding of the basic concepts ofvthe course, the ability of solving simple exercises and of developing simple logical arguments.
Teaching tools
Lectures.
The course is based on lectures in which a series of probability models that arevrelevant for applications to computer science will be illustrated withnexamples of their applications and the development of simple exercises in order to familiarize students with concrete application of the introduced Mathematical models.
Office hours
See the website of Massimo Campanino