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.

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 2025/2026

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.

CURRICULUM TIPO:

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

ModulesCreditsTAFSSD
6
B
BIO/18

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

ModulesCreditsTAFSSD
6
A
FIS/07
Un insegnamento a scelta 
activated in the A.Y. 2015/2016
ModulesCreditsTAFSSD
6
B
BIO/18
activated in the A.Y. 2016/2017
ModulesCreditsTAFSSD
6
A
FIS/07
Un insegnamento a scelta 

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.




S Placements in companies, public or private institutions and professional associations

Teaching code

4S02690

Credits

12

Coordinator

Language

Italian

Scientific Disciplinary Sector (SSD)

MAT/05 - MATHEMATICAL ANALYSIS

The teaching is organized as follows:

Matematica

Credits

8

Period

I sem.

Academic staff

Simone Ugolini

Statistica

Credits

4

Period

I sem.

Academic staff

Federico Di Palma

Learning outcomes

Module: 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.


Module: STATISTICS.
-------
This course aims to provide the students with the fundamental of descriptive statistics, inferential statistics and probability theory.

Program

Module: MATHEMATICS
-------
1) Some notions of set theory.
2) The complete ordered field of the real numbers.
3) Euclidean distance and induced topology on the real line. Absolute value of a real number.
4) Cartesian plane.
5) Real functions of one real variable.
6) Polynomials and polynomial functions. Power, exponential and logarithmic functions. Trigonometric functions.
7) Limit of a function of one real variable.
8) Continuity of a function of one real variable at one point. Fundamental theorems on continuos functions.
9) Derivative of a function. Derivation rules. Fundamental theorems on differentiable functions.
10) Monotonicity of a function. Local and global minima and maxima of a function.
11) Convex functions.
12) Riemann integral. Integration rules. Improper integrals.
13) Ordinary differential equations. The separable and the linear case.
14) Linear algebra. Matrices and operations on them. Determinant of a square matrix.
15) Distance between two points in the plane and geometrical loci. Conics.
16) Functions of more variables. Level curves and level sets.
17) Topology in R^2. Continuity of a function of 2 variables.
18) Differentiable functions of 2 variables. Partial derivatives.
19) Local and global minima and maxima of a function of more variables.

Module: STATISTICS
-------
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.

Bibliography

Reference texts
Activity Author Title Publishing house Year ISBN Notes
Matematica Guerraggio, A. Matematica per le scienze con MyMathlab (Edizione 2) Pearson 2014 9788871929415

Examination Methods

Module: MATHEMATICS
-------
Written exam.

Module: STATISTICS
-------
Written exam.

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

Teaching materials e documents