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.
Academic calendar
The academic calendar shows the deadlines and scheduled events that are relevant to students, teaching and technicaladministrative staff of the University. Public holidays and University closures are also indicated. The academic year normally begins on 1 October each year and ends on 30 September of the following year.
Course calendar
The Academic Calendar sets out the degree programme lecture and exam timetables, as well as the relevant university closure dates..
Period  From  To 

I semestre  Oct 1, 2020  Jan 29, 2021 
II semestre  Mar 1, 2021  Jun 11, 2021 
Session  From  To 

Sessione invernale d'esame  Feb 1, 2021  Feb 26, 2021 
Sessione estiva d'esame  Jun 14, 2021  Jul 30, 2021 
Sessione autunnale d'esame  Sep 1, 2021  Sep 30, 2021 
Session  From  To 

Sessione estiva di laurea  Jul 16, 2021  Jul 16, 2021 
Sessione autunnale di laurea  Oct 11, 2021  Oct 11, 2021 
Sessione autunnale di laurea  Dicembre  Dec 6, 2021  Dec 6, 2021 
Sessione invernale di laurea  Mar 9, 2022  Mar 9, 2022 
Period  From  To 

Festa dell'Immacolata  Dec 8, 2020  Dec 8, 2020 
Vacanze Natalizie  Dec 24, 2020  Jan 3, 2021 
Epifania  Jan 6, 2021  Jan 6, 2021 
Vacanze Pasquali  Apr 2, 2021  Apr 5, 2021 
Festa del Santo Patrono  May 21, 2021  May 21, 2021 
Festa della Repubblica  Jun 2, 2021  Jun 2, 2021 
Vacanze estive  Aug 9, 2021  Aug 15, 2021 
Exam calendar
Exam dates and rounds are managed by the relevant Science and Engineering Teaching and Student Services Unit.
To view all the exam sessions available, please use the Exam dashboard on ESSE3.
If you forgot your login details or have problems logging in, please contact the relevant IT HelpDesk, or check the login details recovery web page.
Academic staff
Study Plan
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
Modules  Credits  TAF  SSD 

2° Year activated in the A.Y. 2021/2022
Modules  Credits  TAF  SSD 

3° Year activated in the A.Y. 2022/2023
Modules  Credits  TAF  SSD 

Modules  Credits  TAF  SSD 

Modules  Credits  TAF  SSD 

Modules  Credits  TAF  SSD 

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.
Mathematics and statistics (2020/2021)
Teaching code
4S02690
Credits
12
Language
Italian
Scientific Disciplinary Sector (SSD)
MAT/05  MATHEMATICAL ANALYSIS
The teaching is organized as follows:
Matematica Mod. 1
Statistica
Matematica Mod. 2
Learning outcomes
Mathematics: This course aims at providing the students with the mathematical tools (settheoretic and algebraic structures, differential and integral calculus in one or several real variables, ordinary differential equations) whose knowledge is indispensable for the achievement of the degree. A particular attention is paid to the concrete application of the learned notions. At the end of the course students should be able to use appropriately the mathematical language and the notions of the syllabus and furnish valid arguments in support of the solution of the proposed problems. Statistics: The aim of the course is to make the students acquainted with basic statistical ideas and mathematical methods and their applications in the correct planning of experiments, data sampling, analysis, and presentation. The course conjugates concepts of basic statistics and probability theory as well as applied mathematics with real situations as they emerge in a standard biotechnology laboratory. The students acquire appropriate skills to understand how biological systems work and more generally to cope with reallife problems in different applied scientific fields. At the end of the course the students are able to:  analyse experimental observations and prepare professional reports  appropriately plan experiments  autonomously acquire new skills in specific fields of applied statistics and mathematics.
Program

MM: mathematics

1. PRELIMINARIES.
a) Sets and operations with sets.
b) Numerical sets. Bounded and unbounded sets. Minimum, maximum, infimum and supremum of numerical sets.
c) Natural numbers N, integers Z, rationals Q, and reals R. Intervals. Distance.
d) Monomials, polynomials and polynomial decomposition.
e) Absolute values. Powers with natural, rational and real exponent. The polynomial functions x^a, irrational, exponential a^x, logarithmic.
f) Trigonometry.
g) Entire, rational, irrational, with absolute values and systems of equalities and inequalities.
h) Exponential, logarithmic and systems of inequalities.
i) Analytical geometry in the Cartesian plane: distances between points, lines, circumference, parabola, ellipse and hyperbola. Mutual positions and geometric problems.
2. FUNCTIONS.
a) Functions of real variable, plot, domain and image.
b) Compounded functions.
c) Inverse functions.
d) Monotonic functions.
e) Bounded and unbounded functions.
f) Maxima and minima, suprema and infima of functions.
g) Signs and zeros of a function.
h) Operations with plots, translations and symmetries.
3. LIMITS.
a) Distance and neighborhoods, right and left neighborhoods. Limit with functions. Continuity at one point. Elementary limits. Limits algebra. Limits of composed functions. Squeeze theorem. Indeterminate forms. Comparison between infinites and between infinitesimals. Horizontal, vertical, and obliquos asymptotes.
b) Continuous functions and their fundamental properties. Weierstrass theorem.
4. DERIVATIVES.
a) Definition of derivative at one points. Left and right derivative. Tangent line to a plot. Derivative function.
b) Derivatives of elementary functions. Derivation rules.
c) Derivability and continuity.
d) Critical points. Fermat theorem, Rolle theorem and Lagrange theorem. Implications of Lagrange theorem: derivable functions with null derivative, derivable functions with equal derivative, sign of first derivative and monotonicity intervals of a function. Detection and classification of relative maxima and minima through derivative's sign.
e) Second derivative, its sign and convexity.
f) Higher order derivatives. Local approximation of functions with polynomials. De l’Hopital theorem. Taylor's series and Taylor's theorem. Determine limits by using Taylor's theorem.
5. INTEGRALS.
a) Primitive functions (indefinite integrals). Elementary integrals. Definition of definite integral. Fundamental theorem of integral calculus.
b) Computing areas using integrals.
c) Overview of improper integrals on unlimited intervals.
6. DIFFERENTIAL EQUATIONS.
a) Definitions of differential equations (in normal and nonnormal form) and of order of a differential equation.
b) Solution and general solution of a differential equation. Examples of differential equations. Cauchy problem.
7. ALGEBRA LINEARE.
a) Vectors and vectors in R^n. Real valued matrices. Product between matrices.
and its properties. Linear systems in matrix form Ax = b. Solving linear systems with Gauss method.
b) Rank of a matrix. Determinant of square matrices. RouchéCapelli's theorem. Cramer Teorema. Inverse of a square matrix.
c) Scalar product and its properties. Norm of a vector. Orthogonal vectors.
8. COMPLEMENTS
a) Bivariate functions, domain, detection and classification of critical points.
b) Complex numbers, operations with complex numbers, Euler formula.

MM: statistics

Each class introduces basic concepts of probability theory and applied statistics through combination of lectures and exercises. The exercises focus on the analysis of real experimental data collected in the teacher's lab or in other biotechnology labs. Lectures • brief introduction on the scientific method: the philosophical approach of Popper, Khun, and Lakatos and the concept of validation/falsification of hypotheses • variables and measurements, frequency distribution of data sampled from discrete and continuous variables, displaying data • elements of probability theory: definition, a brief history of probability, the different approaches to probability, the rules for adding and multiplying probabilities, Bayes' theorem • discrete probability distributions: the Binomial and the Poisson distributions and the limiting dilution assay with animal cells • continuous probability distributions: the concept of probability density, the Normal distribution and the Z statistics • statistical inference: the problem of deducing the properties of an underlying distribution by data analysis; populations vs. samples. The central limit theorem • the Student distribution and the t statistics. Confidence intervals for the mean. Comparing sample means of two related or independent samples • mathematical properties of the variance and error propagation theory • planning experiments and the power of a statistical test • the χ2 distribution and confidence intervals of the variance • goodnessoffit test and χ2 test for contingency tables • problems of data dredging and the ANOVA test • correlation and linear regression The program follows the topics listed in the textbook up to chapter 17 (included) with the following extras: key aspects in probability theory, probability distributions in the biotechnology lab (practical examples), error propagation theory Reference textbook: Michael C. Whitlock, Dolph Schluter. Analisi Statistica dei dati biologici. Zanichelli, 2010. ISBN: 9788808062970 Lecture slides are available at: http://profs.scienze.univr.it/~chignola/teaching.html
Bibliography
Activity  Author  Title  Publishing house  Year  ISBN  Notes 

Matematica Mod. 1  M.Bramanti,C.D.Pagani,S.Salsa  Analisi Matematica 1  Zanichelli  2009  9788808064851  
Matematica Mod. 1  Walter Dambrosio  Analisi matematica Fare e comprendere Con elementi di probabilità e statistica  Zanichelli  2018  9788808220745  
Matematica Mod. 1  Dario Benedetto Mirko Degli Esposti Carlotta Maffei  Matematica per scienze della vita  Casa Editrice Ambrosiana. Distribuzione esclusiva Zanichelli  2015  9788808184849 
Examination Methods

MM: mathematics

The final exam is written and must be completed in 3 hours. Neither midterm tests nor oral exams will take place. The exam paper consists of 6 exercises. The total of the marks of the exam paper is 30. Any topic dealt with during the lectures can be examined. Students are not allowed to use books, notes or electronic devices during the exam. The evaluation of any exercise will take into consideration not only the correctness of the results, but also the method adopted for the solution and the precise references to theoretical results (e.g. theorems) taught during the lectures. The pass mark for the exam of the Mathematics module is 18.

MM: statistics

At the end of the course students are expected to master the basic concepts of probability theory and of validation/falsification of hypotheses, and to apply these concepts to the analysis of experimental data collected in a generic biotechnology laboratory. To pass the final written test, students are asked to solve 4 exercises within a maximum of 2 hours. The exercises concern the analysis of problems as they are found in a biotechnology laboratory. During the test, students are allowed to use learning resources such as books, lecture slides, handouts, but the use of personal computers or any other electronic device with an internet connection is not allowed. Eight points are assigned to the solution of each exercise and all points are then summed up. To pass their test students must reach a minimum score of 18 points.
The final score of the whole course in Mathematics and Statistics is calculated as the mean of the marks obtained by students in both tests.
Type D and Type F activities
Le attività formative in ambito D o F comprendono gli insegnamenti impartiti presso l'Università di Verona o periodi di stage/tirocinio professionale.
Nella scelta delle attività di tipo D, gli studenti dovranno tener presente che in sede di approvazione si terrà conto della coerenza delle loro scelte con il progetto formativo del loro piano di studio e dell'adeguatezza delle motivazioni eventualmente fornite.
years  Modules  TAF  Teacher 

3°  Model organism in biotechnology research  D 
Andrea Vettori
(Coordinator)

years  Modules  TAF  Teacher 

3°  Python programming language  D 
Vittoria Cozza
(Coordinator)

years  Modules  TAF  Teacher  

1°  Subject requirements: chemistry and biology  D  Not yet assigned  
1°  Subject requirements: basic mathematics and physics  D  Not yet assigned  
3°  LaTeX Language  D 
Enrico Gregorio
(Coordinator)

Career prospects
Module/Programme news
News for students
There you will find information, resources and services useful during your time at the University (Student’s exam record, your study plan on ESSE3, Distance Learning courses, university email account, office forms, administrative procedures, etc.). You can log into MyUnivr with your GIA login details: only in this way will you be able to receive notification of all the notices from your teachers and your secretariat via email and also via the Univr app.
Graduation
List of thesis proposals
theses proposals  Research area 

Studio delle proprietà di luminescenza di lantanidi in matrici proteiche  Synthetic Chemistry and Materials: Materials synthesis, structureproperties relations, functional and advanced materials, molecular architecture, organic chemistry  Colloid chemistry 
Multifunctional organicinorganic hybrid nanomaterials for applications in Biotechnology and Green Chemistry  Synthetic Chemistry and Materials: Materials synthesis, structureproperties relations, functional and advanced materials, molecular architecture, organic chemistry  New materials: oxides, alloys, composite, organicinorganic hybrid, nanoparticles 
Dinamiche della metilazione del DNA e loro contributo durante il processo di maturazione della bacca di vite.  Various topics 
Il problema della donazione degli organi  Various topics 
Risposte trascrittomiche a sollecitazioni ambientali in vite  Various topics 
Studio delle basi genomicofunzionali del processo di embriogenesi somatica in vite  Various topics 
Attendance modes and venues
As stated in the Didactic Regulations, there is no generalised obligation of attendance. Individual lecturers are, however, free to require a minimum number of hours of attendance for eligibilitỳ for the profit exam of the teaching they teach. In such cases, attendance of teaching activities is monitored in accordance with procedures communicated in advance to students.
Parttime enrolment is permitted. Find out more on the Parttime enrolment possibilities page.
The course's teaching activities take place in the Science and Engineering area, which is composed of the buildings of Ca‘ Vignal 1, Ca’ Vignal 2, Ca' Vignal 3 and Piramide, located in the Borgo Roma cluster, and Villa Lebrecht and Villa Eugenia located in the San Floriano di Valpolicella cluster.
Lectures are held in the classrooms of Ca‘ Vignal 1, Ca’ Vignal 2 and Ca' Vignal 3, while practical exercises take place in the teaching laboratories dedicated to the various activities.