
Course unit
DISCRETE MATHEMATICS AND PROBABILITY
INL1000875, A.A. 2017/18
Information concerning the students who enrolled in A.Y. 2016/17
ECTS: details
Type 
ScientificDisciplinary 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 teaching 
Hours of Individual study 
Shifts 
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)
COLPI
RICCARDO
(Supplente)

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.
Probability.
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

Ross, Calcolo delle probabilità. : Apogeo, 2013. Terza Edizione


