First cycle
degree courses
Second cycle
degree courses
Single cycle
degree courses
School of Engineering
Course unit
INP5070357, A.A. 2019/20

Information concerning the students who enrolled in A.Y. 2019/20

Information on the course unit
Degree course Second cycle degree in
IN2191, Degree course structure A.Y. 2017/18, A.Y. 2019/20
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Degree course track Common track
Number of ECTS credits allocated 12.0
Type of assessment Mark
Department of reference Department of Civil, Environmental and Architectural Engineering
Mandatory attendance No
Language of instruction English
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 PAOLO GUIOTTO MAT/05
Other lecturers MICHELE PAVON ING-INF/04

ECTS: details
Type Scientific-Disciplinary Sector Credits allocated
Core courses MAT/05 Mathematical Analysis 6.0
Core courses MAT/06 Probability and Mathematical Statistics 6.0

Course unit organization
Period First semester
Year 1st Year
Teaching method frontal

Type of hours Credits Teaching
Hours of
Individual study
Lecture 12.0 96 204.0 No turn

Start of activities 30/09/2019
End of activities 18/01/2020
Show course schedule 2019/20 Reg.2017 course timetable

Prerequisites: Differential and Integral Calculus, Basic Linear Algebra.
Target skills and knowledge: The goal of the course is to introduce analytical and probabilistic tools and methods of paramount relevance in applied engineering modeling.

The student is expected to solve complex problems involving advanced analytical and probabilistic mathematical tools, including the ability to determine the appropriate setting for applied problems.

The course is preparatory for all successive courses.
Examination methods: Exam is written, it consists in a set of applied problems and simple abstract or theoretical questions.
Assessment criteria: - Proper application of tools and methods presented in the course
- Precision and care in arguing
- Ability in abstract arguments
Course unit contents: Analytical Methods

1. Lebesgue Measure and Integral
2. Elements of Abstract Measure and Integral
3. Normed Spaces and Banach spaces
4. Inner product spaces, Hilbert spaces
5. Elements of Harmonic Analysis: Fourier series and integrals.

Probabilistic Methods

6. Introduction to probability — probability spaces, axioms of probability, conditional probabilities, independence of events.
7. Random variables (discrete and continuous) — definition, expectation and moments. Examples of random variables and applications, with a focus on Gaussian random variables.
8. Random vectors.
9. Characteristic function.
10. Convergence of random variables: weak, in probability, in L^p, almost sure.
11. The law of large numbers and the central limit theorem with applications.
12. Conditional expectation.
13. Martingales in discrete time.
Planned learning activities and teaching methods: Lectures supported by exercises.
Additional notes about suggested reading: All teacher lecture notes are made available to the students through the moodle platform. Further material such as journal articles or lecture notes are also made available in the same fashion. Finally, indications are provided on URL sites where supplementary interesting material is available.

Sheldon Ross, A first course in Probability, Pearson, 1976. Ninth edition

Erhan Cinlar, Probability and Stochastics, Springer, 2011.
Textbooks (and optional supplementary readings)

Innovative teaching methods: Teaching and learning strategies
  • Lecturing
  • Problem based learning
  • Interactive lecturing
  • Questioning
  • Problem solving
  • Loading of files and pages (web pages, Moodle, ...)

Innovative teaching methods: Software or applications used
  • Moodle (files, quizzes, workshops, ...)
  • One Note (digital ink)
  • Camtasia (video editing)
  • Latex
  • Mathematica
  • Matlab