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.
Type D and Type F activities
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 2025/2026The educational activities of type D are the student's choice, those of type F are additional knowledge useful for entering the world of work (internships, transversal skills, project works, etc.). According to the Didactic Regulations of the Course, some activities can be chosen and entered independently in the booklet, others must be approved by a special committee to verify their consistency with the study plan.
The following activities can cover type D or F training activities.
1. Teachings delivered at the University of Verona.
Include the teachings listed below and/or in the Catalog of Teachings (which can also be filtered by language of delivery through Advanced Search).
Booklet entry mode: if the teaching is included among those listed below, the student can enter it independently during the period in which the curriculum is open; otherwise, the student must make a request to the Secretariat, sending to carriere.scienze@ateneo.univr.it the form in the period indicated.
2. CLA certificate or language equivalency.
In addition to those required by the curriculum, the following are recognized for those matriculated from A.Y. 2021/2022:
English language: 3 CFU are recognized for each level of proficiency above that required by the course of study (if not already recognized in the previous course of study).
Other languages and Italian for foreigners: 3 cfu are recognized for each proficiency level starting from A2 (if not already recognized in the previous study cycle).
These cfu will be recognized, up to a maximum of 6 cfu in total, of type F if the teaching plan allows it, or of type D. Additional elective credits for language knowledge may be recognized only if consistent with the student's educational project and if adequately motivated. Those enrolled until A.Y. 2020/2021 should consult the information found here.
Way of inclusion in the booklet: request the certificate or equivalence from CLA and send it to the Student Secretariat - Careers for the inclusion of the exam in the career, by email: carriere.scienze@ateneo.univr.it
3. Soft skills
Discover the training paths promoted by the University's TALC - Teaching and learning center, intended for students regularly enrolled in the academic year of course delivery https://talc.univr.it/it/competenze-trasversali Booklet entry mode: the teaching is not expected to be included in the curriculum. Only upon obtaining theOpen Badge will the booklet CFUs be automatically validated. The registration of CFUs in career is not instantaneous, but there will be some technical time to wait.
4. Contamination lab
The Contamination Lab Verona (CLab Verona) is an experiential pathway with modules dedicated to innovation and business culture that offers the opportunity to work in teams with students from all courses of study to solve challenges launched by companies and institutions. The pathway allows students to receive 6 CFUs in the D or F area. Find out about the challenges: https://www.univr.it/clabverona
PLEASE NOTE: To be eligible to take any teaching activity, including electives, you must be enrolled in the course year in which it is offered. Therefore, it is recommended that undergraduates in the December and April sessions DO NOT undertake extracurricular activities of the new academic year, in which they are not enrolled, since these degree sessions are valid concerning the previous academic year. Therefore, for activities carried out in an academic year in which they are not enrolled, no recognition of CFU can be given.
5. Internship/internship period
In addition to the CFU stipulated in the curriculum (check carefully what is indicated on the Academic Regulations) here you can find information on how to activate the internship. Check in the regulations which activities can be Type D and which can be Type F.
Please also note that for internships activated from October 1, 2024, it will be possible to recognize excess hours in terms of Type D credits, limited only to internship experiences carried out at host institutions outside the University.
PROCEDURE FOR RECOGNIZING WORK ACTIVITY AS INTERNSHIP CREDITS
As per the resolution of the Teaching College of Mathematics and Data Science No. 4 -24/25, the student who intends to have hours of work activity recognized as internship credits, before the start of the activity, is required to send to the e-mail address of the student secretariat and in copy knowledge to the student practices committee (paolo.daipra@univr.it, luca.dipersio@univr.it, barbara.gaudenzi@univr.it) explicit request.
The request should specify the type of activity, name of the company and place of work, and hours/credits for which recognition is being sought. The activity must have taken place during the years of enrollment in the course of study to be recognizable. Once the student practices committee has ascertained that the current work activity is consistent with the course objectives, the student will be promptly notified, with the secretary's office as a copy.
At the end of the stipulated work period, the student sends the following documentation to the student secretariat: a detailed final report that is forwarded to the committee for final approval (signed by the student and a company contact person); a statement from the legal representative of the company/entity and/or documentation demonstrating the type of professional activity and the hourly commitment to it.
The student secretary's office will forward the documentation received to the student practices committee and record the CFUs (taf F and any additional taf D credits) decided by the committee.
| years | Modules | TAF | Teacher |
|---|---|---|---|
| 1° 2° 3° | Algorithms | D |
Roberto Segala
(Coordinator)
|
| 1° 2° 3° | Basis of general chemistry | D |
Silvia Ruggieri
|
| 1° 2° 3° | Genetics | D |
Massimo Delledonne
(Coordinator)
|
| 1° 2° 3° | Introduction to quantum mechanics for quantum computing | D |
Claudia Daffara
(Coordinator)
|
| 1° 2° 3° | Python programming language [English edition] | D |
Carlo Combi
(Coordinator)
|
| 1° 2° 3° | APP REACT PLANNING | D |
Graziano Pravadelli
(Coordinator)
|
| years | Modules | TAF | Teacher |
|---|---|---|---|
| 1° 2° 3° | Algebraic Geometry | F |
Rosanna Davison Laking
(Coordinator)
|
| 1° 2° 3° | Algorithms | D |
Roberto Segala
(Coordinator)
|
| 1° 2° 3° | LaTeX Language | D |
Enrico Gregorio
(Coordinator)
|
| 1° 2° 3° | Python programming language [Edizione in italiano] | D |
Carlo Combi
(Coordinator)
|
| 1° 2° 3° | Organization Studies | D |
Serena Cubico
(Coordinator)
|
| 1° 2° 3° | Programming Challanges | D |
Romeo Rizzi
(Coordinator)
|
| 1° 2° 3° | Tools for development of applications of virtual reality and mixed | D |
Andrea Giachetti
(Coordinator)
|
| 1° 2° 3° | Protection of intangible assets (SW and invention)between industrial law and copyright | D |
Mila Dalla Preda
(Coordinator)
|
| years | Modules | TAF | Teacher |
|---|---|---|---|
| 1° | Subject requirements: mathematics | D |
Franco Zivcovich
(Coordinator)
|
Mathematical analysis 2 - Analysis II (2024/2025)
Teaching code
4S00031
Academic staff
Coordinator
Credits
12
Language
Italian
Scientific Disciplinary Sector (SSD)
MAT/05 - MATHEMATICAL ANALYSIS
Period
Semester 1 dal Oct 1, 2024 al Jan 31, 2025.
Courses Single
Authorized
Learning objectives
Topics treated in this course are: Calculus for functions of several variables, sequences and series of functions, ordinary differential equations, Lebesgue measure and integral. Emphasis will be given to examples and applications. At the end of the course, students must possess adequate skills of synthesis and abstraction. They must recognize and produce rigorous proofs. They must be able to formalize and solve moderately difficult problems on the arguments of the course.
Prerequisites and basic notions
Linear algebra - Calculus 1
Program
Some content will be available online in case of COVID-19 or for students with specific learning needs. In addition, a number of the lessons/all the lessons (see the course
schedule) will be held in-class.
i) Calculus in several variables. Neighborhoods in several variables, continuity in several variables, directional derivatives, differential of functions in several variables, Theorem of Total Differential, gradient of scalar functions, Jacobian matrix for vector-valued functions, level curves of scalar functions. Parametrized surfaces, tangent and normal vectors, changes of coordinates. Higher order derivatives and differentials, Hessian matrix, Schwarz's Theorem, Taylor's Series.
(ii) Optimization problems for functions in several variables. Critical points, free optimization, constrained optimization, Lagrange's Multiplier Theorem, Implicit and inverse function theorem, Contraction Principle.
(iii) Integral of functions in several variables. Fubini and Tonelli theorems, integral on curves, change of variables formula.
(iv) Integral of scalar function on surfaces, vector fields, conservatice vector fields, scalar potentials, curl and divergence of a vector fields, introduction to differential forms, closed and exact forms, Poincare lemma, Gauss-Green formulas.
(v) Flux through surfaces, Stokes' Theorem, Divergence Theorem
(vi) Introduction to metric spaces and normed spaces, spaces of functions, sequence of functions, uniform convergence, function series, total convergence, derivation and integration of a series of functions.
(vii) Introduction to Lebesgue's Measure Theory. Measurable sets and functions, stability of measurable functions, simple functions, approximation results, Lebesgue integral. Monotone Convergence Theorem, Fatou's Lemma, Dominated convergence Theorem and their consequences.
(viii) Ordinary differential equation, existence and uniqueness results, Cauchy-Lipschitz's Theorem. Extension of a solution, maximal solution, existence and uniqueness results for systems of ODE, linear ODE of order n, Variation of the constants method,
other resolutive formulas.
(ix) Fourier's series for periodic functions, convergence results, application to solutions of some PDE.
Bibliography
Didactic methods
In presence teaching. Online multimedia resources on the e-learning platform of the course.
Learning assessment procedures
The final exam consists of a written test followed, in case of a positive result, by an oral test. The written test consists of some exercises on the program: students are exonerated from the first part of the test in the winter session of February if they pass a mid-term test at the beginning of December.
Evaluation criteria
The written test evaluates the ability of students at solving problems pertaining to the syllabus of the course, and also their skills in the analysis, synthesis and abstraction of questions stated either in the natural language or in the specific language of mathematics. The written test is graded on a scale from 0 to 30 points (best), with a pass mark of 18/30..
The oral test will concentrate mainly but not exclusively on the theory. It aims at verifying the ability of students at constructing correct and rigorous proofs and their skills in analysis, synthesis and abstraction. The oral exam is graded on a scale from -5 to +5 point, which are added to the marks earned in the written test. Finally, homework exercises will be graded from 0 to 2 points.
Criteria for the composition of the final grade
final grade=mark of the written test + mark of the oral exam + mark for the homework.
Exam language
italiano
