Course teached as: B018779 - PROBABILITA' Second Cycle Degree in MATHEMATICS Curriculum GENERALE
Teaching Language
Italian
Course Content
The course introduces the abstract theory of probability, but with
constant reference to examples and relevant applications. The main
topics are:
- Probability spaces.
- Laws of large numbers, Central Limit Theorem.
- Markov chains. Percolation.
- Conditional expectations, martingales.
- Brownian motion.
R. Durrett, Probability and Examples. 4th edition, Cambridge Univ. Press,
2010.
- Note del docente
Learning Objectives
Knowledge acquired: the successful student has a basic knowledge of
probability theory and of several examples and applications. In particular
he/she knows the foundations of probability both in the discrete (Markov
chains, percolation) and in the continuous (Brownian motion) setting.
Competence acquired: the successful student is able to rigorously solve
several problems about determining probabilities and selection models.
He/she can also rigorously operate with probability spaces, random
variables, Markov chains, martingales.
Prerequisites
Courses required: Probabilità e Statistica (Introduction to probability and
statistics 6-9 cfu). Analisi Matematica II (Mathematical Analysis II -
multivariate calculus)
Courses recommended: Analisi Matematica III (Mathematical analysis III -
Lebesgue integration)
Teaching Methods
Number of hours for personal study and other individual learning: 153
Number of hours for classroom activities: 72
Further information
Frequency of lessons and exercises: Not required
Tools for Teaching:
http://web.math.unifi.it/users/gandolfi/didindex.html
Office hours:
by appointment
address:
Viale Morgagni, 67 / A - 50134 Florence
Tel: 055 4237478
Fax: 055 4237165
E-mail: @ alberto.gandolfi unifi.it gandolfi@math.unifi.it
Web: http://web.math.unifi.it/users/gandolfi/
Type of Assessment
Oral exam
Course program
The course introduces the abstract theory of probability, but with
constant reference to examples and relevant applications. The main
topics are:
- Probability spaces.
- Laws of large numbers, Central Limit Theorem.
- Markov chains. Percolation.
- Conditional expectations, martingales.
- Brownian motion.