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Mathematics and statistics

A.Y. 2018/2019

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.

**Lesson period:** First semester
(In case of multiple editions, please check the period, as it may vary)

**Assessment methods:** Esame

**Assessment result:** voto verbalizzato in trentesimi

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

Lessons: 28 hours

Professor:
Bernardi Giulia

Unit 2

SECS-S/01 - STATISTICS - University credits: 4

Practicals: 16 hours

Lessons: 24 hours

Lessons: 24 hours

Professor:
Baldi Lucia

Educational website(s)

Professor(s)

Reception:

on appointment

Via Celoria 2, Milan, Italy, 3rd floor (or by Skype/Teams/Zoom)