Mathematics and Statistics

A.Y. 2020/2021
10
Max ECTS
96
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
To present the methods, as well as the mathematical and statistical basic tools that should be part of the knowledge base of any graduate with a scientific degree
Expected learning outcomes
By the end of the course, the students will:
- know how to use calculus tools and represent functions;
- understand certain demonstration and representation processes;
- analyze, interpret and reprocess statistical data.
Course syllabus and organization

Single session

Responsible
Lesson period
First semester
The lessons will be held on the Microsoft Teams platform and can be followed both in sync on the base of the first semester schedule and asynchronously because they will be recorded and left available to students on the same platform. Some lessons and PDF files may be available on the Ariel platform.
Course syllabus
Mathematics
· Number sets;
· Set operations;
· Direct and reverse proportionality;
· Percentages;
· Radicals;
· Logarithms;
· Exponential;
· Integer and fractional first-degree equations;
· Integer and fractional second-degree equations;
· Equations above the second degree;
· Systems of integer and fractional first degree equations;
· Systems of integer and fractional second-degree equations;
· Whole and fractional first-degree inequalities;
· Whole and fractional second degree inequalities;
· Whole and fractional systems of first-degree inequalities;
· Whole and fractional systems of second-degree inequalities;
· Trigonometry elements;
· Limits;
· Derivatives;
· Elements of mathematical logic;
· Algorithms

Statistics

Samples and populations. Types of variables: qualitative, quantitative. Absolute and relative frequency
Diagrams and histograms, frequency distribution, cumulative frequencies, quantiles and percentiles. Box-plot.
Measures of central tendency: mean, median, mode. Measures of dispersion: range of variation, deviance, variance, standard deviation, coefficient of variation
Probability. Basic rules of probability. Discrete and continue probability distribution
Binomial distribution. Poisson distribution
Normal distribution. Standardization of a variable. Normalized standard distribution. Asymmetry and kurtosis
The central limit theorem. The sampling distribution of an estimate: the standard error. The confidence interval. Student's t-distribution
Verifying hypotheses. Null hypothesis and alternative statistical significance and P-value Error types I and II
Comparison between a sample mean and a population mean. Comparison between two sample means
The chi-square test. The chi-square distribution. The 2x2 contingency table
Relationship between variables: covariance. Correlation and linear regression. Regression analysis
Analysis of variance: the comparison between means of several groups:. The F-distribution
Prerequisites for admission
Basic knowledge of math at high school level
Teaching methods
Lectures and theoretical exercises
Teaching Resources
Mathematics: material produced by the teacher and available on the Ariel page of the course.

Statistics: 1) material produced by the teacher and available on the Ariel page of the course.
2) Whitlock M.C., Schulter D. - Analisi statistica dei dati biologici - Ed. Zanichelli, 2010-
3)Triola M.M., Triola M. F. - Fondamenti di statistica per le discipline biomediche- Pearson Italia, 2013
4)Pagano M., Gauvreau K.: "Biostatistica", Ed. Idelson-Gnocchi, Milano, 2003.
Assessment methods and Criteria
The exam consists of a written test with questions related to the Mathematics module and a written test with questions related to the Statistics module. The two parts are carried out on the same day in separate times. The final evaluation is the arithmetic mean of the evaluations of the 2 tests.
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: 16 hours
Lessons: 32 hours
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: 16 hours
Lessons: 32 hours
Professor: Rizzi Rita Maria