Graph theory, discrete mathematics and optimization

A.A. 2019/2020
Insegnamento per
12
Crediti massimi
80
Ore totali
SSD
MAT/09 SECS-S/06
Lingua
Inglese
Obiettivi formativi
This course aims at introducing modern and advanced mathematical techniques useful for understanding and modeling big data structures and algorithms.

Struttura insegnamento e programma

Edizione attiva
Responsabile
Moduli o unità didattiche
Module Graph Theory and Discrete Mathematics
SECS-S/06 - METODI MATEMATICI DELL'ECONOMIA E DELLE SCIENZE ATTUARIALI E FINANZIARIE - CFU: 6
Lezioni: 40 ore

Module Optimization
MAT/09 - RICERCA OPERATIVA - CFU: 6
Lezioni: 40 ore
Docente: Cordone Roberto

STUDENTI FREQUENTANTI
Propedeuticità
Prerequisites for this course include a good knowledge of the mathematical tools presented in Calculus I and Linear Algebra courses.
Prerequisiti e modalità di esame
DSE students are encouraged to take two separate exams, during the mid term tests: the first one will cover module 1 part a) + part b), the second one module 2. Students who will not attend or pass the mid term tests can take the whole exam, composed by both modules, during the regular tests during the year. Please
refer to the instructors (Proff. Naldi and Micheletti for module 1, Prof. Cordone for module 2) for more information about exam structure, exam rules, course attendance. The course grade is officially recorded when positive results are obtained in both exams.
Metodi didattici
Face-to-face lectures, tutorials.
Module Graph Theory and Discrete Mathematics
Programma
Review of Linear Algebra. Review of Sequences. Limits. Series. First order difference equations. Linear equations. Homogeneous and non-homogeneous.
Nonlinear autonomous linear equations. Orbits. Steady state. Stability. Periodic orbits. Chaotic behavior. Linear difference equations with constant coefficients. Systems of difference equations. Economic and financial models.
Probability, events and Combinatorics. Finite and discrete time Markov chains. Random walks. Graph theory: definitions and fundamental concepts. Directed and undirected graphs. Graph complexity. Mining social network graphs.
Metodi didattici
Face-to-face lectures, tutorials.
Materiale didattico e bibliografia
S. Salsa, A. Squellati, Dynamical Systems and Optimal Control, Egea, 2007 (Chapters 3, 5, 8)
K. Sydsaeter, P. Hammond, A. Strom, A. Carvajal, Essential Mathematics for Economic Analysis, Pearson, 2016
K. Ruohonen, Graph Theory, Course notes. http://math.tut.fi/~ruohonen/GT_English.pdf (Chapters 1,2,3)
O. Haggstrom, Finite Markov Chains and Algorithmic Applications, London Mathematical Society, 2003. (Chapters1,2,3)
J. Leskovec, A. Rajaraman, J.Ullman, Mining of Massive Datasets, Cambridge University Press, last edition (available online at http://www.mmds.org/ ) - (Chapter 10)
Lecture notes on the module 1 web site: https://gtdmo.ariel.ctu.unimi.it/v5/home/Default.aspx
Module Optimization
Programma
1.Introduction to complex decision problems: case studies; formal definitions.
2.Mathematical Programming: Karush-Kuhn-Tucker conditions.
3.Multi-objective Programming: Paretian case; Multi-Attribute Utility Theory; Analytic Hierarchy Process; ELECTRE Methods.
4.Uncertain Programming: decision making under ignorance; decision making under risk; decision theory.
5.Game theory: generalities; zero-sum games; symmetric games.
Metodi didattici
Face-to-face lectures, tutorials.
Materiale didattico e bibliografia
Lecture notes on the module 2 web site: https://homes.di.unimi.it/cordone/courses/courses.html
STUDENTI NON FREQUENTANTI
Prerequisiti e modalità di esame
DSE students are encouraged to take two separate exams, during the mid term tests: the first one will cover module 1 part a) + part b), the second one module 2. Students who will not attend or pass the mid term tests can take the whole exam, composed by both modules, during the regular tests during the year. Please
refer to the instructors (Proff. Naldi and Micheletti for module 1, Prof. Cordone for module 2) for more information about exam structure, exam rules, course attendance. The course grade is officially recorded when positive results are obtained in both exams.
Module Graph Theory and Discrete Mathematics
Programma
Review of linear algebra. Review of Sequences. Limits. Series. First order difference equations. Linear equations. Homogeneous and non-homogeneous.
Nonlinear autonomous linear equations. Orbits. Steady state. Stability. Periodic orbits. Chaotic behavior. Linear difference equations with constant coefficients. Systems of difference equations. Economic and financial models.
Probability, events and Combinatorics. Finite and discrete time Markov chains. Random walks. Graph theory: definitions and fundamental concepts. Directed and undirected graphs. Graph complexity. Mining social network graphs.
Materiale didattico e bibliografia
S. Salsa, A. Squellati, Dynamical Systems and Optimal Control, Egea, 2007 (Chapters 3, 5, 8)
K. Sydsaeter, P. Hammond, A. Strom, A. Carvajal, Essential Mathematics for Economic Analysis, Pearson, 2016
K. Ruohonen, Graph Theory, Course notes. http://math.tut.fi/~ruohonen/GT_English.pdf (Chapters 1,2,3)
O. Haggstrom, Finite Markov Chains and Algorithmic Applications, London Mathematical Society, 2003. (Chapters1,2,3)
J. Leskovec, A. Rajaraman, J.Ullman, Mining of Massive Datasets, Cambridge University Press, last edition (available online at http://www.mmds.org/ ) - (Chapter 10)
Lecture notes on the module 1 web site: https://gtdmo.ariel.ctu.unimi.it/v5/home/Default.aspx
Module Optimization
Programma
1.Introduction to complex decision problems: case studies; formal definitions.
2.Mathematical Programming: Karush-Kuhn-Tucker conditions.
3.Multi-objective Programming: Paretian case; Multi-Attribute Utility Theory; Analytic Hierarchy Process; ELECTRE Methods.
4.Uncertain Programming: decision making under ignorance; decision making under risk; decision theory.
5.Game theory: generalities; zero-sum games; symmetric games.
Materiale didattico e bibliografia
Lecture notes on the module 2 web site: https://homes.di.unimi.it/cordone/courses/courses.html
Periodo
Primo trimestre
Periodo
Primo trimestre
Modalità di valutazione
Esame
Giudizio di valutazione
voto verbalizzato in trentesimi
Docente/i
Ricevimento:
Su appuntamento
DI - Via Celoria 18, Milano
Ricevimento:
Su appuntamento per email (alessandra.micheletti@unimi.it)
studio 1022 - via Saldini 50, 1 piano
Ricevimento:
Martedi 14.30-16.30 (o su appuntamento)
Dipartimento di Matematica, via Saldini 50, 20133 Milano II piano