## Studying at the University of Verona

Here you can find information on the organisational aspects of the Programme, lecture timetables, learning activities and useful contact details for your time at the University, from enrolment to graduation.

## Academic calendar

The academic calendar shows the deadlines and scheduled events that are relevant to students, teaching and technical-administrative staff of the University. Public holidays and University closures are also indicated. The academic year normally begins on 1 October each year and ends on 30 September of the following year.

## Course calendar

The Academic Calendar sets out the degree programme lecture and exam timetables, as well as the relevant university closure dates..

Period | From | To |
---|---|---|

I semestre | Oct 1, 2018 | Jan 31, 2019 |

II semestre | Mar 4, 2019 | Jun 14, 2019 |

Session | From | To |
---|---|---|

Sessione invernale d'esame | Feb 1, 2019 | Feb 28, 2019 |

Sessione estiva d'esame | Jun 17, 2019 | Jul 31, 2019 |

Sessione autunnale d'esame | Sep 2, 2019 | Sep 30, 2019 |

Session | From | To |
---|---|---|

Sessione di laurea estiva | Jul 22, 2019 | Jul 22, 2019 |

Sessione di laurea autunnale | Oct 15, 2019 | Oct 15, 2019 |

Sessione di laurea autunnale straordinaria | Nov 21, 2019 | Nov 21, 2019 |

Sessione di laurea invernale | Mar 19, 2020 | Mar 19, 2020 |

Period | From | To |
---|---|---|

Sospensione attività didattica | Nov 2, 2018 | Nov 3, 2018 |

Vacanze di Natale | Dec 24, 2018 | Jan 6, 2019 |

Vacanze di Pasqua | Apr 19, 2019 | Apr 28, 2019 |

Vacanze estive | Aug 5, 2019 | Aug 18, 2019 |

## Exam calendar

Exam dates and rounds are managed by the relevant Science and Engineering Teaching and Student Services Unit.

To view all the exam sessions available, please use the Exam dashboard on ESSE3.

If you forgot your login details or have problems logging in, please contact the relevant IT HelpDesk, or check the login details recovery web page.

## Academic staff

Imperio Michele

## Study Plan

The Study Plan includes all modules, teaching and learning activities that each student will need to undertake during their time at the University. Please select your Study Plan based on your enrolment year.

Modules | Credits | TAF | SSD |
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Modules | Credits | TAF | SSD |
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Modules | Credits | TAF | SSD |
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1° Year

Modules | Credits | TAF | SSD |
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2° Year

Modules | Credits | TAF | SSD |
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3° Year

Modules | Credits | TAF | SSD |
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Modules | Credits | TAF | SSD |
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#### Legend | Type of training activity (TTA)

TAF (Type of Educational Activity) All courses and activities are classified into different types of educational activities, indicated by a letter.

### Operations Research (2020/2021)

Teaching code

4S00001

Teacher

Coordinatore

Credits

6

Language

Italian

Scientific Disciplinary Sector (SSD)

MAT/09 - OPERATIONS RESEARCH

Period

II semestre dal Mar 1, 2021 al Jun 11, 2021.

## Learning outcomes

The student will encounter in concrete the concepts of: problems, models, formulations of operations research, but also of instances, algorithms, reductions and mappings among problems of the computer science field. The course will propose some models of operations research, at least the following: linear programming (LP), integer linear programming (ILP), max-flows and min-cuts, bipartite matchings and node covers, minimum spanning trees, shortest paths, Eulerian paths, and some models resorting on dynamic programming among which some knapsack variants. For all these models/problems, except PLI, the student will learn the solving algorithms, the properties on which they hinge, and how to conduct their execution.

However, besides and beyond this, the course aims at building a good and active relationship, practice, and acquaintance, with general mathematical methodologies and techniques (more typical of discrete math and for this reason not yet fully assimilated from our students) and some basic underpinnings of computer science.

In particular, we insist on the dialog with problems and with the art/technique of conjecturing, no occasion is lost to spotlight where invariants and monovariants play a role in proofs, algorithms and data structures. We build up confidence with mathematical induction as an active tool for problem solving, and introducing the dialects of induction most voted to efficiency (divide et impera, recursion with memoization, dynamic programming).

Some basic principles of informatics are underlined, like coding, algorithms, data structures, recursion as a counterpart of mathematical induction and of computability. (In some editions of the course first scratch introductions to numerability and computability have been offered). Coming to efficiency, our central perspective, the use of asymptotic notation is justified and adopted, the classes P, NP, coNP are introduced, and the concepts of good characterizations, good conjectures and good theorems are illustrated in length and complexity theory is advertised as a lively source of new methodologies in the art of facing problems and enquiry their intrinsic structural properties. Several aspects of the role and importance of the art of reducing one problem to another are discussed and clarified. The life cycle of a good conjecture, the workflow linking good conjectures and algorithms, the production and interpretation of counterexamples as a means of dialog with the problem, and the possible use of them in obtaining NP-completeness proofs, are all discussed, investigated and exemplified in action. Explicit emphasis is constantly given to the role and use of certificates.

Meanwhile these transversal and high competences of methodological interest and imprinting are delivered, the students is asked to learn and develop several concrete procedural competences, in particular within LP, and in an algorithmic treatment of graph theory, introduced as a versatile model and an intuitive and expressive language for the formulation of problems.

For a complete and detailed list of all these procedural competences delivered and requested, see the past exams and corrections over the various editions of the course.

The notions from computational complexity introduced in the course, and the attention to the languages of the certificates, will lead the student to recognize with more awareness the structure of a sound proof.

Dealing with instances, problems, models, both from the perspective of algorithms and of models and formulations, will enforce the attitude and competence in casting simple problems from the applications into mathematical models. The knowledge of the paradigmatic results of linear programming theory (duality, complementary slackness, economic interpretation, sensitivity analysis) will provide the student with important tools in obtaining non-trivial insights on the practical problem from the model.

## Program

Operations Research offers quantitative methods and models for the optimal management of resources, and optimization of profits, services, strategies, procedures.

This course of Operations Research gets to Mathematical Programming moving from Algorithmics and Computational Complexity.

After revisiting mathematical induction, recursion, divide et impera, with a curiosity driven problem solving approach, we insist on dynamic programming thinking which gets then exemplified in a few classical models of Operations Research and Computational Biology.

With emphasis on method and techniques, we get involved in formulating, encoding and modeling problems, conjecturing about them, reducing one to the other,

and well characterizing them.

The course offers an in-depth introduction to linear programming.

Following the historical path, we introduce graphs as for modeling,

and explore the basic fundamental results in combinatorial optimization and graph theory.

LIST OF TOPICS:

1. Basic Notions

problems

models

algorithms

complexity

2. Introduction to Algorithms and Complexity

analysis of a few algorithms

design techniques (recursion, divide et impera, recursion with memoization, dynamic programming, greedy)

complexity theory (P, NP, co-NP, good characterizations, good conjectures, examples of NP-completeness proofs)

3. Combinatorial Optimization Models

knapsack problems

Problems on sequences

Problems on DAGs

4. Introduction to Graph Theory

graphs and digraphs as models

a few good characterizations (bipartite, Eulerian, acyclic, planar graphs)

a few NP-hard models (Hamiltonian cycles, cliques, colorability)

shortest paths

minimum spanning trees

maximum flows

bipartite matchings

5. Linear Programming (LP)

the LP and the ILP models (definition, motivations, complexity, role)

geometric method and view (feasibility space,

pivot, duality, dual variables, degeneracy, complementary slackness)

standard and canonical form

simplex method

duality theory

complementary slackness

economic interpretation of the dual variables

sensitivity analysis

BOOKS, NOTES AND OTHER DIDACTIC MATERIALS AND RESOURCES:

At the following page you find a list of available materials (books, notes, videos) about topics covered within the course:

http://profs.sci.univr.it/~rrizzi/classes/RO/materiali

If you find out further effective material help us enlarging this list.

TUTORING (IF AVAILABLE):

For the 2020-21 edition we are planning to introduce a tutor that will assist and guide the students in performing the exercises suggested during the class and in conducting practical experiences.

Author | Title | Publishing house | Year | ISBN | Notes |
---|---|---|---|---|---|

Garey, M. R. and Johnson, D. S. | Computers intractability: a guide to the theory of NP-completeness | Freeman | 1979 | 0-7167-1045-5 | |

T. Cormen, C. Leiserson, R. Rivest, C. Stein | Introduzione agli Algoritmi e Strutture Dati (Edizione 2) | McGraw-Hill | 2005 | 88-386-6251-7 | |

Robert J. Vanderbei | Linear Programming: Foundations and Extensions (Edizione 4) | Springer | 2001 | 978-1-4614-7630-6 |

## Examination Methods

At the end of the course, a written exam with various types of exercises and questions, and several opportunities to gather points to test and prove your preparation. You can add (in full or in part) to the mark acquired at the exam by conducting projects aiming at improving aspects and/or materials of the course in a broad sense.

Up to and included the 2018/19 edition, the exam was taking place in a room by our department in Ca' Vignal.

In the 2019/20 edition (onset of COVID-19) the exams took place from remote, followed by an oral discussion meant only as a check and also as an opportunity for direct confrontation and exchange.

Since many details concerning the exams are subject to dynamic evolution and also determined in the exchanges of ideas and proposals inside the class, and we want to make sure no student gets lost, we redirect the student directly to the reference service site that we can maintain constantly updated:

http://profs.sci.univr.it/~rrizzi/classes/RO/index.html

We warmly advise every student to subscribe to the Telegram group for the current edition of the course and for the testing of the installations, configurations, and environments set up for the exam. All these resources can be conveniently accessed from the URL here above.

We underline a peculiarity of the Operations Research course, the only one in discrete mathematics at the bachelor: the approach and spirit with which you should approach the course and the exam, and what to deliver and elaborate in your answers to the exercises, is actually related to some deep methodological messages that we decided to place at the core of the course. The more the student adopts and interprets these approaches, the more he/she will be proactive in the course and in collaborating to any verification, the more enriching the course and the more fun the exam will be. This will be important in getting the most from the course and achieve full satisfaction and recognition at the exam.

There are 4 exam sessions each academic year (June, July, September, February). The exam is the very same regardless on whether you have attended or not the course. The archives of the past exams, the relative corrections, and the videos of the classes, all can help overcoming the difficulties of the non-attending student.

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## Type D and Type F activities

**Modules not yet included**

## Career prospects

## Module/Programme news

##### News for students

There you will find information, resources and services useful during your time at the University (Student’s exam record, your study plan on ESSE3, Distance Learning courses, university email account, office forms, administrative procedures, etc.). You can log into MyUnivr with your GIA login details.

## Further services

I servizi e le attività di orientamento sono pensati per fornire alle future matricole gli strumenti e le informazioni che consentano loro di compiere una scelta consapevole del corso di studi universitario.

## Graduation

## Attachments

Title | Info File |
---|---|

1. Come scrivere una tesi | 31 KB, 29/07/21 |

2. How to write a thesis | 31 KB, 29/07/21 |

5. Regolamento tesi (valido da luglio 2022) | 171 KB, 17/02/22 |

## List of theses and work experience proposals

theses proposals | Research area |
---|---|

Formule di rappresentazione per gradienti generalizzati | Mathematics - Analysis |

Formule di rappresentazione per gradienti generalizzati | Mathematics - Mathematics |

Proposte Tesi A. Gnoatto | Various topics |

Mathematics Bachelor and Master thesis titles | Various topics |

Stage | Research area |
---|---|

Internship proposals for students in mathematics | Various topics |

## Attendance

As stated in point 25 of the Teaching Regulations for the A.Y. 2021/2022, except for specific practical or lab activities, attendance is not mandatory. Regarding these activities, please see the web page of each module for information on the number of hours that must be attended on-site.Please refer to the Crisis Unit's latest updates for the mode of teaching.