Unit MATHEMATICS AND BASIC STATISTICS
- Course
- Chemistry and technology of drugs
- Study-unit Code
- A001966
- Location
- PERUGIA
- Curriculum
- In all curricula
- Teacher
- Fernanda Pambianco
- Teachers
-
- Fernanda Pambianco
- Hours
- 56 ore - Fernanda Pambianco
- CFU
- 7
- Course Regulation
- Coorte 2022
- Offered
- 2022/23
- Learning activities
- Base
- Area
- Discipline matematiche, fisiche, informatiche e statistiche
- Academic discipline
- 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 examination is divided in two phases:
a) A written exam of one hour. The written test includes the solution of two exercises on topics covered in the program and is designed to verify the ability to correctly apply the theoretical knowledge, the understanding of the exercises proposed and the ability to communicate in writing language. The student must justify explicitly the used techniques with theoretical recalls. Valuation: from 0 to 30.
b) Oral examination of more or less 20 minutes. The oral test is designed to assess the level of knowledge and the understanding reached by the student on the contents listed in the program, this test is also used for verifying the presentation skills of the student. In this oral examination, taking into account the outcome of the previous part, it establishes the final score of the module. - 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.