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
12
B
MAT/05
Un insegnamento a scelta tra i seguenti
12
B
MAT/08
12
B
MAT/06
6
B
MAT/05
6
B
MAT/07
12
B
MAT/03

2° Year   activated in the A.Y. 2010/2011

ModulesCreditsTAFSSD
Due insegnamenti da 6 cfu ciascuno tra i seguenti, oppure quello non gia' scelto tra i due del i anno a scelta da 12 cfu
12
B/C
MAT/08
6
B/C
MAT/06
6
B/C
MAT/09
6
B/C
MAT/08
12
B/C
MAT/06
6
B/C
FIS/02
6
B/C
MAT/07
6
B/C
MAT/09
6
B
MAT/05
Altre attivita' formative
4
F
-
12
D
-
32
E
-
ModulesCreditsTAFSSD
12
B
MAT/05
Un insegnamento a scelta tra i seguenti
12
B
MAT/08
12
B
MAT/06
6
B
MAT/05
6
B
MAT/07
12
B
MAT/03
activated in the A.Y. 2010/2011
ModulesCreditsTAFSSD
Due insegnamenti da 6 cfu ciascuno tra i seguenti, oppure quello non gia' scelto tra i due del i anno a scelta da 12 cfu
12
B/C
MAT/08
6
B/C
MAT/06
6
B/C
MAT/09
6
B/C
MAT/08
12
B/C
MAT/06
6
B/C
FIS/02
6
B/C
MAT/07
6
B/C
MAT/09
6
B
MAT/05
Altre attivita' formative
4
F
-
12
D
-
32
E
-
Modules Credits TAF SSD
Between the years: 1°- 2°
Uno tra i seguenti insegnamenti da 6 cfu ciascuno
6
B
MAT/04
6
B
MAT/02
6
B
MAT/01
6
B
MAT/05
6
B
MAT/03

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

Differential geometry and topology  (2009/2010)

Teaching code

4S02812

Academic staff

Mauro Spera, Nicola Sansonetto

Coordinator

Mauro Spera

Credits

12

Language

Italian

Scientific Disciplinary Sector (SSD)

MAT/03 - GEOMETRY

Period

1st Semester dal Oct 1, 2009 al Jan 31, 2010.

Seminars 0

Learning outcomes

Learning objectives

The course delves further into general topology and introduces the basic notions of algebraic
and differential topology, focussing on the concept of differentiable manifold. Furthermore, the
elements of Riemannian geometry will be introduced as well.
The course, suitable to both curricula (didactic and applied) will be quite concrete and based
on examples also coming from other areas of mathematics.

Program

Course Programme

General topology (continued). Separation. Quotients.
Fundamental group. Covering spaces.
Differentiable manifolds.
De Rham's theory.
Riemannian manifolds.
Levi-Civita connection.
Curvature tensors (Riemann, sectional, Ricci, scalar).
Geodesics and their variational aspects.
Exponential map.
Lie groups. Symmetric spaces.
Riemann surfaces and algebraic curves.
Vector bundles, Euler's class and number, Euler-Poincare' characteristic.
The Poincare'-Hopf theorem.

Examination Methods

Written test, followed by an oral exam.

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

Teaching materials e documents