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

A.A. 2024/2025 A.A. 2023/2024 A.A. 2022/2023 A.A. 2021/2022 A.A. 2020/2021 A.A. 2019/2020 A.A. 2018/2019 A.A. 2017/2018 A.A. 2016/2017 A.A. 2015/2016 A.A. 2014/2015 A.A. 2013/2014 A.A. 2012/2013 A.A. 2011/2012 A.A. 2010/2011 A.A. 2009/2010

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 2025/2026

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 enrollment year.

CURRICULUM TIPO:

1° Year 

ModulesCreditsTAFSSD
6
B
MAT/07
6
B
MAT/06
6
B
MAT/03
6
B
MAT/05
12
B
MAT/05

2° Year   activated in the A.Y. 2023/2024

ModulesCreditsTAFSSD
6
B
MAT/05
Final exam
32
E
-
activated in the A.Y. 2023/2024
ModulesCreditsTAFSSD
6
B
MAT/05
Final exam
32
E
-
Modules Credits TAF SSD
Between the years: 1°- 2°
1 module between the following (a.a. 2022/23 Computational Algebra not activated; a.a. 2023/24 Homological Algebra not activated)
6
B
MAT/02
6
B
MAT/02
Between the years: 1°- 2°
1 module between the following
6
C
MAT/08
6
C
MAT/08
Between the years: 1°- 2°
3 modules among the following
6
C
MAT/03
6
C
MAT/02 ,MAT/03
6
C
MAT/02
6
C
MAT/08
6
C
MAT/08
6
C
MAT/02
6
C
MAT/06
6
C
INF/01
6
C
MAT/05
6
C
MAT/09
6
C
MAT/02
6
C
MAT/08
6
C
MAT/08
6
C
MAT/07
6
C
INF/01 ,MAT/06
Between the years: 1°- 2°
12
D
-
Between the years: 1°- 2°
Further activities
4
F
-

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.

A Basic activities
B Characterizing activities
C Related or complementary activities
D Activities to be chosen by the student
E Final examination
F Other training activities
S Placements in companies, public or private institutions and professional associations

Advanced geometry  (2022/2023)

Teaching code

4S003197

Teacher

Coordinator

Credits

6

Language

English en

Scientific Disciplinary Sector (SSD)

MAT/03 - GEOMETRY

Period

Semester 2 dal Mar 6, 2023 al Jun 16, 2023.

Lessons timetable MoodleMoodle Seminars 0

Learning objectives

This course provides students with the basic concepts of Graph Theory and the basics of Discrete and Computational Geometry. At the end of the course, the student will know the main classical theorems of graph theory, in particular about structural properties, colorings, matchings, embeddings and flow problems. He/she will also be familiar with basic Discrete Geometry results and with some classical algorithms of Computational Geometry. He/she will have the perception of links with some problems in non mathematical contexts. he/she will be able to produce rigorous proofs on all these topics and he/she will be able to read articles and texts of Graph Theory and Discrete Geometry.

Prerequisites and basic notions

Fundamental idea of general topology, affine and euclidean geometry.

Program

GRAPH THEORY
-Definitions and basic properties.
-Matching in bipartite graphs: Konig Theorem and Hall Theorem. Matching in general graphs: Tutte Theorem. Petersen Theorem.
-Connectivity: Menger's theorems.
-Planar Graphs: Euler's Formula, Kuratowski's Theorem.
-Colorings Maps: Four Colours Theorem, Five Colours Theorem, Brooks Theorem, Vizing Theorem.

DISCRETE GEOMETRY
-Convexity, convex sets convex combinations, separation. Radon's lemma. Helly's Theorem.
-Lattices, Minkowski's Theorem, General Lattices.
-Convex independent subsets, Erdos-Szekeres Theorem.
-Intersection patterns of Convex Sets, the fractional Helly Theorem, the colorful Caratheodory theorem.
-Discrete surfaces and discrete curvatures.

COMPUTATIONAL GEOMETRY
-General overview: reporting vs counting.
-Convex-hull problem: Graham's scan and other algorithms.
-Polygons and Art Gallery problem. Art Gallery Theorem, polygon triangulation.
- Voronoi diagram and Fortune's algorithm.
- Delaunay triangulation properties and Minimum spanning tree.

Bibliography

Vai alla bibliografia
Visualizza la bibliografia con Leganto, strumento che il Sistema Bibliotecario mette a disposizione per recuperare i testi in programma d'esame in modo semplice e innovativo.

Didactic methods

Lectures and exercise sessions.

Learning assessment procedures

Written test (2 hours).
The written exam on Graph Theory consists of three/four exercises and two questions (1 on general definition / concepts and 1 with a proof of a theorem presented during the lectures).

Oral Test (Mandatory)
It is a discussion with the lecturer on definitions and proofs discussed during the lectures about Discrete and Computational Geometry.

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

Evaluation criteria

To pass the exam, students must show that:
- they know and understand the fundamental concepts of graph theory
- they know and understand the fundamental concepts of Discrete and Computational Geometry
- they have analysis and abstraction abilities
- they can apply this knowledge in order to solve problems and exercises and they can rigorously support their arguments.

Criteria for the composition of the final grade

Written exam maximum 30/30. Oral part, if positive, could add at most 5 points.

Exam language

English