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 |
---|
Modules | Credits | TAF | SSD |
---|
Modules | Credits | TAF | SSD |
---|
3 course to be chosen among the following
One course to be chosen among the following
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.
Advanced geometry (2015/2016)
Teaching code
4S003197
Teacher
Coordinator
Credits
6
Language
English
Scientific Disciplinary Sector (SSD)
MAT/03 - GEOMETRY
Period
II semestre dal Mar 1, 2016 al Jun 10, 2016.
Learning outcomes
Introduction to Graph Theory, Discrete Geometry and Computational 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.
-Embedding Finite Metric Space into Normed Spaces, the Johnson-Lindenstrauss Flattening Lemma
-Discrete surfaces and discrete curvatures.
COMPUTATIONAL GEOMETRY
-General overview: reporting vs counting, fixed-radius near neighbourhood problem.
-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.
Examination Methods
Written exam (120 minutes) and oral exam.