## 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 technical-administrative 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, 2018 | Jan 31, 2019 |

II semestre | Mar 4, 2019 | Jun 14, 2019 |

Session | From | To |
---|---|---|

Sessione invernale d'esame | Feb 1, 2019 | Feb 28, 2019 |

Sessione estiva d'esame | Jun 17, 2019 | Jul 31, 2019 |

Sessione autunnale d'esame | Sep 2, 2019 | Sep 30, 2019 |

Session | From | To |
---|---|---|

Sessione estiva | Jul 16, 2019 | Jul 16, 2019 |

Sessione autunnale | Nov 19, 2019 | Nov 19, 2019 |

Sessione invernale | Mar 11, 2020 | Mar 11, 2020 |

Period | From | To |
---|---|---|

Sospensione attività didattica | Nov 2, 2018 | Nov 3, 2018 |

Vacanze di Natale | Dec 24, 2018 | Jan 6, 2019 |

Vacanze di Pasqua | Apr 19, 2019 | Apr 28, 2019 |

Vacanze estive | Aug 5, 2019 | Aug 18, 2019 |

## 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

Vallini Giovanni

giovanni.vallini@univr.it 045 802 7098; studio dottorandi: 045 802 7095## 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 enrolment year.

Modules | Credits | TAF | SSD |
---|

Modules | Credits | TAF | SSD |
---|

Modules | Credits | TAF | SSD |
---|

1° Year

Modules | Credits | TAF | SSD |
---|

2° Year activated in the A.Y. 2019/2020

Modules | Credits | TAF | SSD |
---|

3° Year activated in the A.Y. 2020/2021

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 (2018/2019)

Teaching code

4S02690

Credits

12

Coordinatore

Language

Italian

Scientific Disciplinary Sector (SSD)

MAT/05 - MATHEMATICAL ANALYSIS

The teaching is organized as follows:

##### matematica

##### statistica

## Learning outcomes

Mathematics: This course aims at providing the students with the mathematical tools (set-theoretic 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 methods and their ap-plications in the correct planning of experiments, data sampling, analysis, and presentation. The course conjugates con-cepts of basic statistics and probability theory 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 real-life 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.

## Program

------------------------

MM: matematica

------------------------

1. PRELIMINARY. a) Sets and operations on sets. b) Natural numbers N, integers Z and rational Q c) Real numbers. Operations and arrangement in R. Sets of limited or unlimited real numbers. Upper extremity and lower extremity of sets of real numbers. Intervals. Distance. d) Polinomial and irrational equations and inequalities, with modules and systems e) Analytical geometry in the Cartesian plane: distances between points, line, circumference, parabola, ellipse and hyperbola. Mutual positions and geometric problems 2. ELEMENTARY FUNCTIONS. a) Real functions of real variable, graph, domain, image. Composition of functions. Inverse function. Monotone functions. Limited functions and unlimited functions. Maxima and minima. Upper and lower extremes of functions. Sign and zeros of a function. Diagram operations: translations, symmetries. b) Absolute values. Powers with natural, rational and real exponent. The polynomial functions x ^ a, irrational, exponential a ^ x, logarithmic. The trigonometric functions. c) Algebric, exponential and logarithmic inequalities, systems of inequalities. 3. CONTINUOUS LIMITS AND FUNCTIONS. a) Distance and surroundings, right and left surroundings. Function limits. Continuity in one point. Elementary limits. Algebra of limits. Limits of compound functions. Comparison theorem. Some indeterminate forms. Comparison between infinites and infinitesimal. Horizontal, vertical, oblique asymptotes. b) Continuous functions and their fundamental properties. Theorem of the zeros. Weierstrass theorem. . 4. DERIVATIVES AND APPLICATIONS. a) Definition of derivative in a point. Right derivative and left derivative. Straight tangent to the graph. Derived function. Derivatives of elementary functions. Rules of derivation of sum, product, quotient, compound function, inverse function. Derivability and continuity. Relative maximum and minimum points. Fermat, Rolle and Lagrange theorems. Consequences of the Lagrange theorem: derivable functions with null derivative, derivable functions with the same derivative, sign of the first derivative and intervals of monotony of the function. Search for points of maximum or minimum relative through the sign of the derivative. Second derivative, its sign and convexity. b) Qualitative study of the graph of a function. c) Subsequent derivatives. Local approximation of functions with polynomials. Theorems of De l'Hospital. Taylor's polynomial and Taylor's theorem. Use of the theorem for determining limits. 5. INTEGRAL. a) Primitive functions (indefinite integrals). Elemental integrals. Definition of definite integral. Fundamental theorem of integral calculus. b) Calculation of areas through the use of integrals. c) Overview of improper integrals on unlimited intervals. 6. DIFFERENTIAL EQUATIONS. Definitions of differential equation (in normal and non-normal form) and of order of a differential equation. Solution and general solution of a differential equation. Examples of differential equations. Cauchy problem. 7. LINEAR ALGEBRA. a) Geometric vectors. Vectors in R ^ n. Matrixes with real coefficients. Produced between matrices and its property. Linear systems in matrix form Ax = b. Systems resolution with the Gauss method. b) Rank (or characteristic of A). Determinant of square matrices. Rouché-Capelli theorem. Cramer's theorem. Inverse of a square matrix. c) The scalar product and its properties. Standard (or form) of a vector. Orthogonal vectors. Elements of analytical geometry. Vector product in R ^ 3.

------------------------

MM: statistica

------------------------

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 • goodness-of-fit 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: 978-88-08-06297-0 Lecture slides are available at: http://profs.scienze.univr.it/~chignola/teaching.html

## Bibliography

Activity | Author | Title | Publishing house | Year | ISBN | Notes |
---|---|---|---|---|---|---|

matematica | Walter Dambrosio | Analisi matematica Fare e comprendere Con elementi di probabilità e statistica | Zanichelli | 2018 | 9788808220745 | |

matematica | Guerraggio, A. | Matematica per le scienze con MyMathlab (Edizione 2) | Pearson | 2014 | 9788871929415 | |

matematica | Dario Benedetto Mirko Degli Esposti Carlotta Maffei | Matematica per scienze della vita | Casa Editrice Ambrosiana. Distribuzione esclusiva Zanichelli | 2015 | 9788808184849 | |

matematica | Sergio Invernizzi Maurizio Rinaldi Federico Comoglio | Moduli di matematica e statistica Con l'uso di R | Zanichelli | 2018 | 9788808220714 | |

statistica | Michael C. Whitlock, Dolph Schluter | Analisi Statistica dei dati biologici | Zanichelli | 2010 | 978-88-08-06297-0 |

## Examination Methods

------------------------

MM: matematica

------------------------

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 mark 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: statistica

------------------------

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 weighted mean of the marks obtained by students in both tests by taking into account the number of credits assigned to each course as weights: final grade = (2/3) x1 + (1/3) x2 where x1 and x2 are the marks obtained by students in their tests of Mathematics and Statistics, respectively.

**???AdattamentoProvaEsameDSA???**

## Type D and Type F activities

**Modules not yet included**

## 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.

## Further services

I servizi e le attività di orientamento sono pensati per fornire alle future matricole gli strumenti e le informazioni che consentano loro di compiere una scelta consapevole del corso di studi universitario.

## Graduation

## List of theses and work experience proposals

theses proposals | Research area |
---|---|

Studio delle proprietà di luminescenza di lantanidi in matrici proteiche | Synthetic Chemistry and Materials: Materials synthesis, structure-properties relations, functional and advanced materials, molecular architecture, organic chemistry - Colloid chemistry |

Multifunctional organic-inorganic hybrid nanomaterials for applications in Biotechnology and Green Chemistry | Synthetic Chemistry and Materials: Materials synthesis, structure-properties relations, functional and advanced materials, molecular architecture, organic chemistry - New materials: oxides, alloys, composite, organic-inorganic hybrid, nanoparticles |

Stampa 3D di nanocompositi polimerici luminescenti per applicazioni in Nanomedicina | Synthetic Chemistry and Materials: Materials synthesis, structure-properties relations, functional and advanced materials, molecular architecture, organic chemistry - New materials: oxides, alloys, composite, organic-inorganic hybrid, nanoparticles |

Dinamiche della metilazione del DNA e loro contributo durante il processo di maturazione della bacca di vite. | Various topics |

Risposte trascrittomiche a sollecitazioni ambientali in vite | Various topics |

Studio delle basi genomico-funzionali del processo di embriogenesi somatica in vite | Various topics |

## Attendance

As stated in the Teaching Regulations for the A.Y. 2022/2023, attendance is not mandatory. However, professors may require students to attend lectures for a minimum of hours in order to be able to take the module exam, in which case the methods that will be used to check attendance will be explained at the beginning of the module.

Please refer to the Crisis Unit's latest updates for the mode of teaching.