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Fundamental of mathematics and statistics

A.Y. 2017/2018

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

**Lesson period:**
year

**Assessment methods:** Esame

**Assessment result:** voto verbalizzato in trentesimi

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.

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.

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

MAT/02 - ALGEBRA

MAT/03 - GEOMETRY

MAT/04 - MATHEMATICS EDUCATION AND HISTORY OF MATHEMATICS

MAT/05 - MATHEMATICAL ANALYSIS

MAT/06 - PROBABILITY AND STATISTICS

MAT/07 - MATHEMATICAL PHYSICS

MAT/08 - NUMERICAL ANALYSIS

MAT/09 - OPERATIONS RESEARCH

SECS-S/02 - STATISTICS FOR EXPERIMENTAL AND TECHNOLOGICAL RESEARCH

MAT/02 - ALGEBRA

MAT/03 - GEOMETRY

MAT/04 - MATHEMATICS EDUCATION AND HISTORY OF MATHEMATICS

MAT/05 - MATHEMATICAL ANALYSIS

MAT/06 - PROBABILITY AND STATISTICS

MAT/07 - MATHEMATICAL PHYSICS

MAT/08 - NUMERICAL ANALYSIS

MAT/09 - OPERATIONS RESEARCH

SECS-S/02 - STATISTICS FOR EXPERIMENTAL AND TECHNOLOGICAL RESEARCH

Practicals with elements of theory: 24 hours

Lessons: 32 hours

Lessons: 32 hours

Professors:
Mazza Carlo, Rizzo Ottavio Giulio

Unita' didattica: statistica

MAT/01 - MATHEMATICAL LOGIC

MAT/02 - ALGEBRA

MAT/03 - GEOMETRY

MAT/04 - MATHEMATICS EDUCATION AND HISTORY OF MATHEMATICS

MAT/05 - MATHEMATICAL ANALYSIS

MAT/06 - PROBABILITY AND STATISTICS

MAT/07 - MATHEMATICAL PHYSICS

MAT/08 - NUMERICAL ANALYSIS

MAT/09 - OPERATIONS RESEARCH

SECS-S/02 - STATISTICS FOR EXPERIMENTAL AND TECHNOLOGICAL RESEARCH

MAT/02 - ALGEBRA

MAT/03 - GEOMETRY

MAT/04 - MATHEMATICS EDUCATION AND HISTORY OF MATHEMATICS

MAT/05 - MATHEMATICAL ANALYSIS

MAT/06 - PROBABILITY AND STATISTICS

MAT/07 - MATHEMATICAL PHYSICS

MAT/08 - NUMERICAL ANALYSIS

MAT/09 - OPERATIONS RESEARCH

SECS-S/02 - STATISTICS FOR EXPERIMENTAL AND TECHNOLOGICAL RESEARCH

Practicals with elements of theory: 24 hours

Lessons: 16 hours

Lessons: 16 hours

Professors:
Maggis Marco, Ugolini Stefania

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