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
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 Biotecnologie - Enrollment from 2025/2026The 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
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2° Year activated in the A.Y. 2011/2012
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3° Year activated in the A.Y. 2012/2013
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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 [Cognomi P-Z] (2010/2011)
Teaching code
4S02690
Credits
12
Coordinator
Ida Germana Minelli
Language
Italian
The teaching is organized as follows:
MATEMATICA
Credits
8
Period
I semestre
Academic staff
Ida Germana Minelli
Learning outcomes
Module: STATISTICA
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This course aims to provide the students with the fundamental of descriptive statistics, inferential statistics and probability theory.
Module: MATEMATICA
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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.
Program
Module: STATISTICA
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Part I) descriptive statistics.
Univariate statistics: main chart (pie chart, bar chart, histogram e box-plot), measures of location (mean, mode and median), measure of spread (range, interquartile range, variance, standard deviation), measure of asymmetry (third moment, skewness index, Pearson's skewness coefficient) measure of kurtosis (fourth moment, kurtosis, excess kurtosis).
Bivariate statistics: main representations (contingency tables e shattered plots), main measures (mean, variance and covariance), correlation analysis (linear regression and Pearson's correlation coefficient).
Part II) Probability theory
Probability: probability definition (classic and modern), event taxonomy (independent events, mutually exclusive events, complementary event, union event and intersection event). Conditional probability. Probability of notable events.
Random variables: discrete random variable (discrete probability distribution, expected value and variance), continuous random variable (probability density function, expected value and variance), main continuous distributions (uniform, gaussian, standard normal and chi-square).main discrete distributions (binomial and Bernoulli), central limit theorem, Chebyshev’s inequality, convergence in law of random variables and limit random variable.
Part III) Inferential Statistics.
Estimation theory: estimation problem, main properties of an estimator (unbiased, consistency and efficiency). point estimation (expected value and variance), interval estimation (expected value and variance).
Hypothesis test: Problem statement (first type and second type error, theoretical distribution), testing process, chi-square based independence test.
Module: MATEMATICA
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Algebra. Sets, relations and functions. Real numbers. Linear algebra (affine geometry).
Functions of one real variable. Generalities. The topology of the real line, of the extended real line and of affine spaces. Limits, continuity and local behaviour. Derivation. Drawing the graph of a function. Integration.
Functions of several real variables and differential equations. Functions of two or more real variables: generalities, partial derivatives, differential. Ordinary differential equations: the linear case, the separable variables case.
Bibliography
Author | Title | Publishing house | Year | ISBN | Notes |
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D. OLIVIERI | Istituzioni di statistica | CEDAM | 2005 | Testo adatto a chi intende approfondire l'uso della statistica in ambito applicativo. | |
Navidi | Probabilità e statistica per l'ingegneria e le scienze | McGraw-Hill | 2011 | 978-8-88-3866334-5 | Testo generale. Contiene più di quanto richiesto nel corso |
Bland | Statistica Medica | Apogeo | Testo adatto a chi intende approfondire l'uso della staitistica nelle discipline mediche. |
Examination Methods
Module: STATISTICA
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The exam requires two tests. The former test is composed by close questions while the latter is composed by open questions and exercises. To pass the exam, the student have to get a positive mark in both the tests.
Module: MATEMATICA
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Written test