Mathematics and statistics

A.Y. 2017/2018
10
Max ECTS
108
Overall hours
SSD
MAT/02 SECS-S/01
Language
Italian
Learning objectives
Knowledge of the basics of Maths, in particular, of elementary Calculus (real functions in one variable, limits, derivatives, integrals).Knowledge of descriptive statistics. Knowledge of the position and variability indicators. Knowledge of methods of inferential statistics. Acquisition of the principles and techniques of regression and correlation between various parameters.Knowledge of the basics of Maths, in particular, of elementary Calculus (real functions in one variable, limits, derivatives, integrals).Knowledge of descriptive statistics. Knowledge of the position and variability indicators. Knowledge of methods of inferential statistics. Acquisition of the principles and techniques of regression and correlation between various parameters.
Expected learning outcomes
Possibility of exploiting the basic tools of Maths in any context. Describe the phenomena by the main statistical indicators; plan sample surveys; use the methodology of the analysis of variance at 1 and 2 factors; understand the results of statistical surveys.Possibility of exploiting the basic tools of Maths in any context. Describe the phenomena by the main statistical indicators; plan sample surveys; use the methodology of the analysis of variance at 1 and 2 factors; understand the results of statistical surveys.
Course syllabus and organization

Single session

Responsible
Lesson period
First semester
Unit 1
Course syllabus
Basics of set theory. Number sets (N, Z, Q, R), real
numbers, Dedekind Axiom. Rational equations. Maps
(domain, codomain, image, definition set, composition of
maps), injective maps, invertible maps, absolute value,
powers, exponentials, logarithms, trigonometric functions
and their inverses. Exponential, logarithmic and
trigonometric equations. Basics of analytic geometry:
distance between two points in the plane, equation of a
line, parallel and orthogonal lines; second degree curves
(circle, ellipsis, hyperbole, parabola). Resolution of linear
systems with Gauss method. Limits of sequences:
definitions, operations with limits, some special limits.
Limits of functions and continuity: definitions, examples,
right and left limit, types of discontinuity, zeroes,
intermediate values, Weierstrass Theorem. Derivatives:
definition and geometrical meaning, derivatives of
elementary functions; operations with derivatives;
derivatives of composite and inverse maps. De L'Hopital
Theorem. Analysis of the graph of a function: extremal
points, Rolle and Lagrange Theorem, increasing and
decreasing functions, convex functions, asymptotes.
Integrals: geometrical meaning and basic properties.
Linearity of integral. Average Theorem. Primitives and
Fundamental Theorem of Calculus. Integrals of rational
functions, some integration techniques.
Teaching methods
Paolo Marcellini- Carlo Sbordone Elementi di calcolo
Versione semplificata per i nuovi corsi di laurea Liguori
Editore, Napoli. Paolo Marcellini- Carlo Sbordone
Esercitazioni di Matematica 1° volume parte prima e 1°
volume parte seconda Liguori Editore, Napoli.
Unit 2
Course syllabus
1- The language of statistics.
2- Organization of data end graphical representation.
3- Position and variability indices (mean, mode, median),
variance.
4- Bivariate analysis for qualitative or quantitive data.
5- Probability, probability rules. Independents events. Total
probability theorem. Bayes theorem.
6- Random variables, distributions. Distributions: binomial,
geometrical, Poisson, Gaussian.
7- Random samples. Confidence intervals. Estimation. Sample
mean. Central Limit Theorem. Confidence interval for the mean.
8- Hypothesis tests: fundamentals, phases, simple test.
9- Hypothesis test on a single population proportion.
10- Test and confidence interval for the difference of two means
using independent sample.
11- Correlation analysis. Univariate linear regression. Inference.
12- Analysis of variance.
Teaching methods
Introduzione alla Statistica, di M. K. Pelosi e T. M. Sandifer, ed.
McGraw-Hill, 2009
Unit 1
MAT/02 - ALGEBRA - University credits: 6
Practicals: 40 hours
Lessons: 28 hours
Professor: Poggioli Daniela
Unit 2
SECS-S/01 - STATISTICS - University credits: 4
Practicals: 16 hours
Lessons: 24 hours
Professor: Baldi Lucia
Professor(s)
Reception:
on appointment
Via Celoria 2, Milan, Italy, 3rd floor (or by Skype/Teams/Zoom)