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Course unit
STOCHASTIC METHODS
SCP7079197, A.A. 2017/18

Information on the course unit
Degree course Second cycle degree in DATA SCIENCE SC2377, Regulation 2017/18, A.Y. 2017/18 6.0 STOCHASTIC METHODS http://datascience.scienze.unipd.it/2017/laurea_magistrale Department of Mathematics No English PADOVA

Lecturers
 Teacher in charge PAOLO DAI PRA MAT/06

ECTS: details
Type Scientific-Disciplinary Sector Credits allocated
Educational activities in elective or integrative disciplines MAT/06 Probability and Mathematical Statistics 6.0

Mode of delivery (when and how)
Period First semester 1st Year frontal

Organisation of didactics
Type of hours Credits Hours of
teaching
Hours Individual
study
Shifts
Lecture 6.0 48 102.0 No turn

Calendar
Start of activities 02/10/2017 19/01/2018

Examination board
Board From To Members of the board
1 Stochastic Methods - 2017/2018 01/10/2017 30/09/2018 DAI PRA PAOLO (Presidente)
VARGIOLU TIZIANO (Membro Effettivo)
BIANCHI ALESSANDRA (Supplente)
CALLEGARO GIORGIA (Supplente)
FORMENTIN MARCO (Supplente)

Syllabus
 Prerequisites: Basic notions of differential and integral calculus, linear algebra and probability. Target skills and knowledge: The aim of this course in to introduce tools from the theory of Probability and Stochastic Processes that have high impact in the study of networks as well as algorithmic and computational tools. Using the software R (R development Core Team, 2006), specific problems will be dealt with via computer simulation. Examination methods: Written exam Assessment criteria: The final grade is based on the results in the written exam. In the exam student are asked to implement in specific applications the tools learned in the course. Correctness and efficiency will be particularly valued. Course unit contents: 1. Probability reviews. • discrete and continuous distributions • random variables, expectation and conditional expectation • approximation of probability distributions. 2. Markov chains and random walks • Markov Chain and their stationary distribution • Monte Carlo (MCMC), convergence of MCMC-based algorithms • Electrical networks. 3. Random graphs • Erdos-Renyi graphs: connectivity, giant component. • Random regular graphs • Dynamic graphs. Preferential attachment. Planned learning activities and teaching methods: Frontal lessons. Some problems will be solved in classroom via computer simulation Additional notes about suggested reading: The teacher in charge will provide lecture notes, exercises and scientific papers. Textbooks (and optional supplementary readings) P. Dai Pra, Stochastic Methods for Data Science. --: --, 2017. Lecture notes