# Unit MATHEMATICS AND STATISTICS

Course
Biological sciences
Study-unit Code
GP004012
Curriculum
In all curricula
Teacher
Danilo Costarelli
Teachers
• Danilo Costarelli
Hours
• 56 ore - Danilo Costarelli
CFU
8
Course Regulation
Coorte 2022
Offered
2022/23
Learning activities
Base
Area
Discipline matematiche, fisiche e informatiche
MAT/05
Type of study-unit
Obbligatorio (Required)
Type of learning activities
Attività formativa monodisciplinare
Language of instruction
Italian
Contents
The course covers the main topics of mathematical analysis and basic outlines of probability theory 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 materials (as the pdf files of the lessons) will be uploaded on unistudium.
Educational objectives
The aim of the course is to present the main concepts of mathematical analysis and some basic elements of probability and statistics, in order to provide students with the essential mathematical tools to address and analyze application problems related to biological sciences.

The main acquired knowledge (Dublin Descriptor 1) will be:
• knowledge of the concept of function, of the properties of the main elementary functions and of limits;
• knowledge of the differentiability of functions of one variable and of all the notions that allow the student to develop a function study;
• knowledge of the Riemann integral notion, of the main results and of some methods of integral resolution;
• knowledge of some basic issues of Probability and Statistics.

The main skills acquired (ability to apply the acquired knowledge, Dublin Descriptor 2, and to adopt with appropriate judgment the appropriate approach, Dublin Descriptor 3) will be:
• ability to solve equations, inequalities, limits, derivatives, integrals and to address some simple Statistics problems;
• ability to elaborate an autonomous reasoning that leads the student to identify the suitable methods to solve the posed problems.
Prerequisites
Basic elements of Mathematics: sets, arithmetic operations, equations and inequalities, elementary functions, basic concepts of euclidean geometry.
Teaching methods
Frontal lessons. Also afternoon exercises sessions will be organized.
Other information
Supplementary material available on the e-learning platform: www.unistudium.unipg.it.
Learning verification modality
Written examination with open questions/exercises, followed by optional oral exam. The written exam will have a duration of 90 minutes (3 practical exercises and 1 theoretical exercise). During the examination, the student should show that he achieved a sufficient degree of knowledge concerning the topics studied during the course.
The written exams will be on the dates given in the exams calendar.
Extended program
1) Mathematics
Hints about basic notions of mathematics: sets, sets of numbers, equations and inequalities, trigonometric functions and properties of the main basic functions.
Functions: key definitions, injective, surjective and bijective functions, composition of functions, inverse functions, graphics and main functions of population dynamics (exponential, logarithmic, periodic, trigonometric functions). Limits and continuity: definition of limit of functions, algebra of limits and examples, sequences and limits of sequences, definition of continuity and discontinuity points, 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 key results.
2) Statistics
Elements of Probability: random events, definition of probability, conditional probability, independence; random variables, gaussian distribution and its main properties.
Elements of descriptive and inferential Statistics: populations and samples, absolute and relative frequencies, graphical representation of statistical phenomena, averages and variability indices, confidence intervals for a mean, hypothesis test on a mean, regression and correlation
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