Fundamental of mathematics and statistics

A.Y. 2018/2019
12
Max ECTS
120
Overall hours
SSD
MAT/01 MAT/02 MAT/03 MAT/04 MAT/05 MAT/06 MAT/07 MAT/08 MAT/09
Language
Italian
Learning objectives
The aim of the course is to provide a basic knowledge of the mathematics needed in the natural sciences, and the tools of descriptive and inferential Statistics, together with concepts of probability on which they are based
Expected learning outcomes
At the end of the course students will be able to describe, interpret and explain simple mathematical models describing natural phenomena, also through statistical methods
Course syllabus and organization

Single session

Responsible
Lesson period
year
Unita' didattica: matematica
Course syllabus
Real numbers. Linear algebra: vectors, matrices, systems of linear equations.
Differential and integral calculus with one variable. Functions and their graphs. Limits. Derivates. Integrals. Rules of derivation and integration. Maxima and minima of functions. Convex functions. Taylor formula. Integrals.
Unita' didattica: statistica
Course syllabus
Descriptive statistics. Types of Data. Frequency tables. Pictures of Data. Position indexes: mean, median, mode, percentiles, quartiles. Variation indexes: variance, standard deviation. Probability. Axioms of a probability measure. Classical probability. Combinatorial calculus: counting the possible configurations of n elements in k places. Conditional probability. Total probability theorem. Bayes formula. Finite and continuous random variables (r.v.). R.v. law. Probability function of a finite r.v..
Density and distribution functions of a continuous r.v..
Binomial distributions. Continuous distributions: normal distribution. Mean, variance, standard deviation of a finite r.v. and of a continuous r.v. and their properties. Central limit theorem. Sums of independent random variables and normal approximation. Confidence intervals for the mean of a normal distribution, with standard deviation known and with standard deviation unknown. Binomial proportion confidence interval.Statistical inference: populations and samples, the basic idea of statistical test. Power, protection and the detection of differences: Type I and Type II error. Comparisons for enumeration data: Fisher's exact test, the χ2 test, contingency tables. Comparisons of two sample means: Student's t test. Comparisons of any number of sample means: the Analysis of Variance (ANOVA). One-way ANOVA: the completely random design, the randomised complete block design. Regression analysis: the linear regression model and equation, tests of hypotheses. ANOVA of regression.
Unita' didattica: matematica
MAT/01 - MATHEMATICAL LOGIC - University credits: 0
MAT/02 - ALGEBRA - University credits: 0
MAT/03 - GEOMETRY - University credits: 0
MAT/04 - MATHEMATICS EDUCATION AND HISTORY OF MATHEMATICS - University credits: 0
MAT/05 - MATHEMATICAL ANALYSIS - University credits: 0
MAT/06 - PROBABILITY AND STATISTICS - University credits: 0
MAT/07 - MATHEMATICAL PHYSICS - University credits: 0
MAT/08 - NUMERICAL ANALYSIS - University credits: 0
MAT/09 - OPERATIONS RESEARCH - University credits: 0
Practicals with elements of theory: 48 hours
Lessons: 32 hours
Professors: Cottone Elisabetta, Rizzo Ottavio Giulio
Unita' didattica: statistica
MAT/01 - MATHEMATICAL LOGIC - University credits: 0
MAT/02 - ALGEBRA - University credits: 0
MAT/03 - GEOMETRY - University credits: 0
MAT/04 - MATHEMATICS EDUCATION AND HISTORY OF MATHEMATICS - University credits: 0
MAT/05 - MATHEMATICAL ANALYSIS - University credits: 0
MAT/06 - PROBABILITY AND STATISTICS - University credits: 0
MAT/07 - MATHEMATICAL PHYSICS - University credits: 0
MAT/08 - NUMERICAL ANALYSIS - University credits: 0
MAT/09 - OPERATIONS RESEARCH - University credits: 0
Practicals with elements of theory: 24 hours
Lessons: 16 hours
Professor: Maggis Marco