Unit MATHEMATICS AND STATISTICS
- Course
- Biological sciences
- Study-unit Code
- GP004012
- Curriculum
- In all curricula
- Teacher
- Marco Cantarini
- Teachers
-
- Marco Cantarini
- Hours
- 56 ore - Marco Cantarini
- CFU
- 8
- Course Regulation
- Coorte 2025
- Offered
- 2025/26
- Learning activities
- Base
- Area
- Discipline matematiche, fisiche, statistiche e informatiche
- Academic discipline
- MAT/05
- Type of study-unit
- Obbligatorio (Required)
- Type of learning activities
- Attività formativa monodisciplinare
- Language of instruction
- Italian
- Contents
- The course aims to present the main topics of basic mathematical analysis and an overview of probability calculus with applications to statistics.
- Reference texts
- 1) C. Vinti, Lezioni di Analisi Matematica - Volume 1. Com Publishing. 2) S. M. Ross, Probabilità e Statistica per l'ingegneria e le scienze. Apogeo. Additional teaching material (such as the pdf of the lessons) will be uploaded on the unistudium platform.
- Educational objectives
- The aim of the course is to present the main notions of basic mathematical analysis and some elements of probability and statistics, so as to provide students with the essential mathematical tools to be able to face and analyze applicative problems related to biological sciences. The main knowledge acquired (Dublin Descriptor 1) will be: •knowledge of the concept of function, of the main elementary functions and of the calculation of the limits of functions; •knowledge of the derivability of functions of one variable and of all those notions that allow the student to carry out a study of a function; •knowledge of the notion of Riemann integral, of the main results and of some methods of calculating integrals; •knowledge of the basic notions of Probability and Statistics. The main skills acquired (ability to apply the knowledge acquired, Dublin Descriptor 2, and to adopt with autonomy of judgment the appropriate approach, Dublin Descriptor 3) will be: •ability to solve equations, inequalities, limits, derivatives, integrals and to deal with some simple problems of Statistics; •ability to elaborate a reasoning that leads the student to identify the methods of solving the problem posed.
- Prerequisites
- Basic elements of mathematics: sets, elementary operations, equations and inequalities, elementary functions, basic concepts of Euclidean geometry.
- Teaching methods
- Frontal lessons. Afternoon exercises are also planned to be agreed with the students.
- Learning verification modality
- Written test with exercises and theory questions. The written test will last 90 minutes. For information on support services for students with disabilities and/or DSA, visit the page http://www.unipg.it/disabilita-e-dsa.
- Extended program
- 1) Mathematics Basic mathematics recall: sets, numerical sets, equations and inequalities, trigonometric functions and main elementary functions. Functions: main definitions, injective, surjective and bijective functions, composition of functions, inverse functions, graphs and main functions of population dynamics (exponential, logarithmic, periodic, trigonometric functions). Limits and continuity: definition of limit of functions, algebra of limits and notable limits, sequences and limits of sequences, definition of continuity and points of discontinuity, properties of continuous functions. Derivatives: definition, geometric meaning, calculation and main results on differentiable functions, study of the graph of a function of a real variable. Integrals: definition, geometric meaning, calculation rules and main results. 2) Statistics Notes on Probability Calculus: random events, definition of probability, conditional probability, independence; random variables, Gaussian distribution and main properties. Elements of descriptive and inferential statistics: populations and samples, absolute and relative frequencies, graphical representation of statistical phenomena, means and variability indices, confidence intervals for the mean, testing hypotheses on the mean, regression and correlation.
- Obiettivi Agenda 2030 per lo sviluppo sostenibile
- Quality education