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

Queste informazioni sono destinate esclusivamente agli studenti e alle studentesse già iscritti a questo corso.
Se sei un nuovo studente interessato all'immatricolazione, trovi le informazioni sul percorso di studi alla pagina del corso:

Laurea magistrale in Mathematics - Immatricolazione dal 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.

1° Year

ModulesCreditsTAFSSD
12
B
MAT/05
6
B
MAT/07
12
B
MAT/03
Un insegnamento a scelta
6
B
MAT/02
6
B
MAT/02
Un insegnamento a scelta
12
C
MAT/08
12
C
MAT/04
Un insegnamento a scelta
6
B
MAT/01
6
B
MAT/05

2° Year  activated in the A.Y. 2012/2013

ModulesCreditsTAFSSD
6
C
INF/01
Un insegnamento a scelta (insegnamenti seminariali ad esclusione di Psicologia dell'educazione e Matematica finanziaria)
6
C
MAT/03
6
C
M-PSI/04
6
C
MAT/06
6
C
MAT/01
6
C
MAT/08
6
C
MAT/06
6
C
MAT/02
6
C
MAT/08
6
C
MAT/02
6
C
MAT/09
Un insegnamento a scelta
6
C
MAT/01
6
C
MAT/09
Prova finale
32
E
-
ModulesCreditsTAFSSD
12
B
MAT/05
6
B
MAT/07
12
B
MAT/03
Un insegnamento a scelta
6
B
MAT/02
6
B
MAT/02
Un insegnamento a scelta
12
C
MAT/08
12
C
MAT/04
Un insegnamento a scelta
6
B
MAT/01
6
B
MAT/05
activated in the A.Y. 2012/2013
ModulesCreditsTAFSSD
6
C
INF/01
Un insegnamento a scelta (insegnamenti seminariali ad esclusione di Psicologia dell'educazione e Matematica finanziaria)
6
C
MAT/03
6
C
M-PSI/04
6
C
MAT/06
6
C
MAT/01
6
C
MAT/08
6
C
MAT/06
6
C
MAT/02
6
C
MAT/08
6
C
MAT/02
6
C
MAT/09
Un insegnamento a scelta
6
C
MAT/01
6
C
MAT/09
Prova finale
32
E
-
Modules Credits TAF SSD
Between the years: 1°- 2°
Altre attivita' formative
4
F
-
Between the years: 1°- 2°
12
D
-

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 (2011/2012)

Teaching code

4S02812

Credits

12

Coordinator

Mauro Spera

Language

Italian

Scientific Disciplinary Sector (SSD)

MAT/03 - GEOMETRY

Seminars 0

The teaching is organized as follows:

Teoria

Credits

10

Period

I semestre

Academic staff

Mauro Spera

Esercitazioni

Credits

2

Period

I semestre

Academic staff

Nicola Sansonetto

Learning outcomes

Educational objectives

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

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

Exam 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