First cycle
degree courses
Second cycle
degree courses
Single cycle
degree courses
School of Engineering
Course unit
INL1000875, A.A. 2017/18

Information concerning the students who enrolled in A.Y. 2016/17

Information on the course unit
Degree course First cycle degree in
IN0508, Degree course structure A.Y. 2011/12, A.Y. 2017/18
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with you
Number of ECTS credits allocated 9.0
Type of assessment Mark
Department of reference Department of Information Engineering
E-Learning website
Mandatory attendance No
Language of instruction Italian
Single Course unit The Course unit can be attended under the option Single Course unit attendance
Optional Course unit The Course unit can be chosen as Optional Course unit

Teacher in charge ALBERTO TONOLO MAT/02

ECTS: details
Type Scientific-Disciplinary Sector Credits allocated
Basic courses MAT/02 Algebra 6.0
Basic courses MAT/06 Probability and Mathematical Statistics 3.0

Mode of delivery (when and how)
Period First semester
Year 2nd Year
Teaching method frontal

Organisation of didactics
Type of hours Credits Hours of
Hours of
Individual study
Lecture 9.0 72 153.0 No turn

Start of activities 25/09/2017
End of activities 19/01/2018

Examination board
Board From To Members of the board
10 A.A. 2017/2018 01/10/2017 15/03/2019 TONOLO ALBERTO (Presidente)
MARICONDA CARLO (Membro Effettivo)
9 A.A. 2016/2017 01/10/2016 15/03/2018 TONOLO ALBERTO (Presidente)
MARICONDA CARLO (Membro Effettivo)
FIOROT LUISA (Supplente)

Prerequisites: Good knowledge of differential and integral calculus (Analisi 1)
Target skills and knowledge: Combinatorics. Generating series. Basic Probability theory
Examination methods: Oral and written test.
Assessment criteria: Knowledge and understanding. This criterion expects students to use their knowledge and to demonstrate their understanding of the concepts and skills of the prescribed framework in order to be able to prove the main results, make deductions and solve problems in different situations.
Course unit contents: Discrete Mathematics.
Operations on sets. Sequences, collections, sharings, compositions, and partition.
Fundamental principles. Sample spaces and uniform probability. Occupancy constraints: sequences, sharings, collections and compositions with prescribed occupancy.
Inclusion/Exclusion principle: the cardinality of a union and of an intersection of sets. Derangements.
Stirling numbers: arbitrary partitions and partizione with prescribed occupancy.
Formal power series: definition, infinite sums and composition of formal power series, closed forms of a formal power series.
Generating series: OGF, EGF of sequences.

Multiple integral: double integrals over rectangles and normal domains. Change of variables: polar coordinates.
Axioms of probability. Conditional probability and independence. Uniform probability, Bayes formula, independent events.
Discrete random variable: Bernoulli, binomial, geometric, Poisson random variables. Expected value and its properties. Variance and covariance.
Continuous random variables: uniform, exponential, normal variables.
Markov and Chebychev disequalities. Law of large numbers. Central limit theorem.
Joint discrete random variables. Joint discrete continuous variables. Conditional density. Conditional expected value.
Planned learning activities and teaching methods: Tests are scheduled along the course. They are useful in order to verify the adequacy of oneself preparation. At the end of each lesson, the notes will be made available on the web page dedicated to the course.
Additional notes about suggested reading: It is strongly recommended to attend the course and use the suggested textbooks.
Textbooks (and optional supplementary readings)
  • Mariconda, Tonolo, Discrete Calculus. --: Springer, 2016. Unitext, Vol. 103 Cerca nel catalogo
  • Ross, Calcolo delle probabilit√†. --: Apogeo, 2013. Terza Edizione Cerca nel catalogo