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.
Study Plan
This information is intended exclusively for students already enrolled in this course.If you are a new student interested in enrolling, you can find information about the course of study on the course page:
Laurea magistrale in Mathematics - Enrollment from 2025/2026The 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 enrollment year.
1° 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 module between the following1 module between the following3 modules among the followingLegend | 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.
Mathematics for Decisions (seminar course) (2019/2020)
Teaching code
4S001445
Teacher
Coordinator
Credits
6
Also offered in courses:
- Mathematics for decisions of the course Master's degree in Mathematics
Language
English
Scientific Disciplinary Sector (SSD)
MAT/09 - OPERATIONS RESEARCH
Period
II semestre dal Mar 2, 2020 al Jun 12, 2020.
Learning outcomes
Mathematics for decisions is a seminar course comprising:
+ interventions by external professors (seminars, mini-courses);
+ interventions by professionals (statements of problems from the applications, description of needs and/or projects);
+ interventions by the referent of the course, collaborators of him, or colleagues by the department (both classes and proposal of problems and projects from the applications).
The aim of this offert is to provide the students with opportunities to meet and/or get involved into working or research projects, activating and developing their own interests, motivations and talents. Among the targets of this offert:
+ provide the students with opportunities to get in touch with working and/or research environments, developing motivations, interests, attitudes;
+ allow connections with professionalities and disciplines, not necessarily within mathematics but that can motivate the work of a matematician or help appreciating its possible applicability;
+ stimulate and develope the competence in designing mathematical models for the managing of production facilities, networks, and services;
+ provide the students with occasions to experiment their computational and informatics skills and to become more aware of their impact and role.
With this the aim is to lead our students to:
+ have the competence and attitude to cover technical and professional roles with an high-level modellistic-math profile;
+ have the necessary starting background and the attitude to document themselves by accessing math texts, research articles, project deliverables, technical documentation.
Program
- Problems, Instances, Models
- Constraint Programming
- Abstract modeling programming languages - AMPL/GMPL:
- Recall the basics of Linear Programming (if needed)
- Some fact from Polyhedral Combinatorics
- Polytopes, polyhedra and equivalent representations
- Basic lemmas and characterizations
- Integrality of polyhedra
- Solution approaches to NP-hard problems:
- Enumeration
- Implicit enumeration and Branch-and-Bound
- Branch-and-Cut
- Approximation algorithms
- Complete and incomplete formulations (e.g., Traveling Salesman Problem, Perfect Matching)
- Gomory's cuts and cutting planes
- Separation oracles and callbacks
- Compact formulations
- Decomposition techniques:
- Column generation
- Dantzig-Wolfe decomposition
- Isomorphism free generation
Projects will be proposed during the course, some already at the very beginning, some others from invited companies.
Depending on their interests, students are invited to choose (or even propose and tune together) projects from three categories: industrial, academic, didactics.
| Author | Title | Publishing house | Year | ISBN | Notes |
|---|---|---|---|---|---|
| Robert J. Vanderbei | Linear Programming: Foundations and Extensions (Edizione 4) | Springer | 2001 | 978-1-4614-7630-6 | |
| Robert Fourer, David M. Gay, and Brian W. Kernighan | THE AMPL BOOK. AMPL: A Modeling Language for Mathematical Programming | 0-534-38809-4 |
Examination Methods
The students are required to develop a project. This might either come from industry, from other research centers or universities, from colleagues or on research lines of interest by the department, or even from ourselves included the students themselves).
We also encourage projects that contribute to the rather technical material (TuringArena based) we strive resorting onto in offering active and interactive learning experiences to our students.
We will propose several projects on each one of these main lines, the students are also encouraged to propose and stear themself according to their interests and competences.
Most projects comprise a development phase where the student must exhibit his/her technical and informatics skills in implementing the models and the algorithms developed or adopted to solve a given problem.
Depending on the project, other phases will be required as part of the exam or might naturally follow:
study of a topic or subject, study of a technique to employ in order to solve a problem or to be illustrated, experiments, deployment, documentation, design of a didactic problem, exposition, writing of paper, stages, thesis, internship.
