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 in Matematica applicata - 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.

1° Year

ModulesCreditsTAFSSD
12
A
MAT/02 ,MAT/03
12
A
MAT/05
12
A
FIS/01
6
B
MAT/01
12
A
INF/01
6
E
-

2° Year  activated in the A.Y. 2015/2016

ModulesCreditsTAFSSD
6
A
MAT/02
12
B
MAT/05
12
B
MAT/08
6
B
MAT/03
6
B
MAT/06
6
B
MAT/05
Uno tra i seguenti insegnamenti
6
C
SECS-P/01
6
C
FIS/01
Uno tra i seguenti insegnamenti
6
C
MAT/05
6
C
SECS-P/01

3° Year  activated in the A.Y. 2016/2017

ModulesCreditsTAFSSD
6
C
SECS-P/05
6
B
MAT/08
6
B
MAT/09
6
B
MAT/06
Uno o due insegnamenti tra i seguenti per un totale di 12 cfu
12
C
SECS-S/06
6
C
MAT/07
6
C
MAT/05
Prova finale
6
E
-
activated in the A.Y. 2015/2016
ModulesCreditsTAFSSD
6
A
MAT/02
12
B
MAT/05
12
B
MAT/08
6
B
MAT/03
6
B
MAT/06
6
B
MAT/05
Uno tra i seguenti insegnamenti
6
C
SECS-P/01
6
C
FIS/01
Uno tra i seguenti insegnamenti
6
C
MAT/05
6
C
SECS-P/01
activated in the A.Y. 2016/2017
ModulesCreditsTAFSSD
6
C
SECS-P/05
6
B
MAT/08
6
B
MAT/09
6
B
MAT/06
Uno o due insegnamenti tra i seguenti per un totale di 12 cfu
12
C
SECS-S/06
6
C
MAT/07
6
C
MAT/05
Prova finale
6
E
-
Modules Credits TAF SSD
Between the years: 1°- 2°- 3°
12
D
-
Between the years: 1°- 2°- 3°
Altre attività formative
6
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

Geometry  (2015/2016)

Teaching code

4S00247

Teacher

Coordinator

Credits

6

Language

Italian

Scientific Disciplinary Sector (SSD)

MAT/03 - GEOMETRY

Period

II semestre dal Mar 1, 2016 al Jun 10, 2016.

Seminars 0

Learning outcomes

-General Topology.
-Differential geometry of curves.
-Differential geometry of surfaces.

Program

-General Topology.

Topological space, definition. Examples: trivial topology, discrete topology, discrete topology, cofinite topology. Comparison of topologies. Basis. Neighbourhoods. Closure. Contnuos applications. Homeomorphisms. Limit points and isolated points. Dense set. Topological subspace, induced topology. Product spaces.
Separation axioms. Hausdorff spaces, Normal spaces, Regular spaces.
Countability axioms. Quotient space. Open and closed applications.
Relevant examples: sphere, projective space, Moebius strip...
Compactness. Heine-Borel Theorem. Tychonoff Theorem. Bolzano-Weierstrass Theorem.
Connectivity, local connectivity. Path connectivity. Examples and counterexamples. Simply connected, homotopy and fundamental group. Jordan curve Theorem.

-Differential geometry of curves.

Curves in the plane:
Examples. Regular points and singular points. Embedding and immersion. Vector fields along a curve. Tangent vector and line. Length of an arc. Parametrization by arc-length. Inflection points. Curvature and radius of curvature. Center of curvature. Frenet-Serret formula. Asymptotes. Contact points of curves. Osculator circle. Main facts about algebraic curves.
Curves in the space:
Tangent line. Normal plane. Inflection points. Osculator plane. Curvatures. Principal frame. Frenet-Serret formula. Torsion.

-Differential geometry of surfaces.

Definitions. Differentiable atlas. Oriented atlas, Tangent plane, Normal versor.
First fundamental quadratic form: metric and area. Tangential curvature and normal curvature of a curve on a surface. Curvatures, normal sections, Meusnier Theorem. Principal curvatures, Gaussian curvature and mean curvature: Theorem Egregium. Geodetics.

Examination Methods

Written test (2 hours).

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