# Unit MATHEMATICS AND BASIC STATISTICS

Course
Industrial pharmacy
Study-unit Code
A001966
Curriculum
In all curricula
Teacher
Fernanda Pambianco
Teachers
• Fernanda Pambianco
Hours
• 48 ore - Fernanda Pambianco
CFU
6
Course Regulation
Coorte 2023
Offered
2023/24
Learning activities
Base
Area
Discipline matematiche, fisiche, informatiche e statistiche
MAT/03
Type of study-unit
Obbligatorio (Required)
Type of learning activities
Attività formativa monodisciplinare
Language of instruction
Italian
Contents
Sets Theory. Real and complex numbers. Functions, limits, continuity, derivation, integration. Numerical series. Vector spaces, matrices, linear systems.
Basic elements of Descriptive and Inferential Statistics.
Reference texts
Paolo Marcellini, Carlo Sbordone, CALCOLO. Ed. Liguori.

Vinicio Villani, Graziano Gentili, MATEMATICA. Comprendere e interpretare fenomeni delle scienze della vita. Ed Mcgraw-hill.
Educational objectives
Knowledge of mathematical language and a suitable mastery of foundamental concepts of differential calculus and linear algebra. Basic knowledge for a correct comprehension and application of statistics to bio-medical sciences.
Prerequisites
No prerequisites except the basic knowledge of arithmetic and algebra.
Teaching methods
The course is organized as follows:

-lectures on all subjects of the course

-exercises in classroom.
Learning verification modality
The method of verifying the learning outcomes consists of an oral test initially consisting in the setting and discussion of some exercises that are the application of the theory addressed in teaching.
Then we move on to questions relating to theoretical aspects inherent to the issues addressed and aimed at ascertaining their knowledge and understanding by the student, as well as the ability to present their content.
Extended program
Elements of logic. Sets Theory. Real and complex numbers. Equivalence relations and partitions. Modular arithmetic.
Functions of real variable. Exponential. Logarithm.
Combinatorial analysis: samples.
Limits. Theorems of unicity, of sign permanence, of confront.
Continuity: theorems of Weierstrass and midway values.
Derivation. Theorems of Rolle and Lagrange. Applications.
Integration. Foundamental theorem of calculus. Indefinite integrals. Principal technics of integration.
Numerical series. Examples. Technics for series with positive terms.
Vector spaces, matrices, linear systems. Autovectors.
Geometric vectors. Scalar product, vector product.
Descriptive Statistics: Averages. Fashion, median. Variance and standard deviation. Normal distribution. Two-character distributions. Covariance. Regression line.
Inferential Statistics: Probability from a classical, frequentist and subjectivist point of view. Conditional probability and Bayes' theorem. The predictive value of a diagnostic test. Applications to genetics.
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