## 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 sem. | Oct 1, 2014 | Jan 30, 2015 |

II sem. | Mar 2, 2015 | Jun 12, 2015 |

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

Sessione straordinaria appelli d'esame | Feb 2, 2015 | Feb 27, 2015 |

Sessione estiva appelli d'esame | Jun 15, 2015 | Jul 31, 2015 |

Sessione autunnale appelli d'esame | Sep 1, 2015 | Sep 30, 2015 |

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

Sessione autunnale appello di laurea 2014 | Nov 27, 2014 | Nov 27, 2014 |

Sessione invernale appello di laurea 2015 | Mar 17, 2015 | Mar 17, 2015 |

Sessione estiva appello di laurea 2015 | Jul 21, 2015 | Jul 21, 2015 |

Sessione II autunnale appello di laurea 2015 | Oct 12, 2015 | Oct 12, 2015 |

Sessione autunnale appello di laurea 2015 | Nov 26, 2015 | Nov 26, 2015 |

Sessione invernale appello di laurea 2016 | Mar 15, 2016 | Mar 15, 2016 |

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

Vacanze di Natale | Dec 22, 2014 | Jan 6, 2015 |

Vacanze di Pasqua | Apr 2, 2015 | Apr 7, 2015 |

Ricorrenza del Santo Patrono | May 21, 2015 | May 21, 2015 |

Vacanze estive | Aug 10, 2015 | Aug 16, 2015 |

## 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

Albertini Francesca

Cordoni Francesco Giuseppe

francescogiuseppe.cordoni@univr.itRinaldi Davide

davide.rinaldi@univr.it## 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 activated in the A.Y. 2015/2016

Modules | Credits | TAF | SSD |
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3° Year activated in the A.Y. 2016/2017

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 (2016/2017)

Teaching code

4S00001

Teacher

Coordinatore

Credits

6

Language

Italian

Scientific Disciplinary Sector (SSD)

MAT/09 - OPERATIONS RESEARCH

Period

II sem. dal Mar 1, 2017 al Jun 9, 2017.

## Learning outcomes

The student of mathematics (L40, Verona) 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.

## 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, divede 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 (Hamilton 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

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

T. Cormen, C. Leiserson, R. Rivest | Introduction to algorithms (Edizione 1) | MIT Press | 1990 | 0262031418 | |

Robert J. Vanderbei | Linear Programming: Foundations and Extensions (Edizione 4) | Springer | 2001 | 978-1-4614-7630-6 | DOI: 10.1007/978-1-4614-7630-6 eBook ISBN: 978-1-4614-7630-6 Hardcover ISBN: 978-1-4614-7629-0 Softcover ISBN: 978-1-4899-7376-4 |

## 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.

In preparing yourself for this exam,

take profit of the material (text and correction for each previous exam) available at the website of the course:

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

Testing your preparation on these tasks and comparing your solutions against the ones given as reference (pay attention not only to the answers but also to the way you offer them to the examiner/verifier, to the quality of your certificates) will allow you to check your comprehension of the topics covered and of the algorithms and methodologies illustrated during the course. Furthermore, it will help

you in tuning your preparation to the exam and refine your procedures and approaches, making clear what kinds of evidences the examiner is expecting you to produce with clarity.

During the exam, be prepared to work for 4 or more hours to what I call "a paper chromatography test". I hope it serves the purpose to recognize in reasonable enough confidence the amount of work you have put in and how much you got for yourself from the course. And make a mark proposal out of it.

There are far more points available than needed to go in saturation. Indeed, your goal should be to prove the competences you have collected: what counts is what you know and/or can solve, not what you don't.

Rather, pay attention to this: only the answers given with clarity, providing the due certificates, count.

All the rest is of null measure to my correction.

In this, the spirit of the correction is in line with the methodologies from computational complexity advertised by the course.

**Students with disabilities or specific learning disorders (SLD), who intend to request the adaptation of the exam, must follow the instructions given HERE**

## 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: only in this way will you be able to receive notification of all the notices from your teachers and your secretariat via email and soon also via the Univr app.

## 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 the Teaching Regulations for the A.Y. 2022/2023, 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.