# Unit MATHEMATICS AND STATISTICS

Course
Biological sciences
Study-unit Code
GP004012
Curriculum
In all curricula
Teacher
Laura Angeloni
Teachers
• Laura Angeloni
Hours
• 56 ore - Laura Angeloni
CFU
8
Course Regulation
Coorte 2021
Offered
2021/22
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
E.N. Bodine - S. Lenhart - L.J. Gross, Matematica per le scienze della vita, UTET
D.Benedetto-M.degli Esposti-C.Maffei, Matematica per le scienze della vita, Casa Ed. Ambrosiana
M.M. Triola - M.F. Triola, Fondamenti di Statistica. Per le discipline biomediche, Pearson
C.Sbordone-F. Sbordone, Matematica per le scienze della vita, Edises
C.Vinti, Lezioni di Analisi Matematica, Vol I, Galeno Ed.
M.Abate, Matematica e Statistica, McGraw-Hill
Slides and Lecture notes by the teacher.
Educational objectives
The aim of the course is to present the main concepts of mathematical analysis and some basic elements of 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, followed by optional oral exam.
The verification of the objectives of the course includes a written test with open questions followed by optional oral exam. The written tests will be on the dates fixed in the examination calendar of the CdS.
The written exam lasts 3 hours and consists in the resolution of some exercises in order to check the level of knowledge and understanding achieved by the student on the program's issues. The oral exam, optional, is however recommended since it will give the opportunity to improve the results obtained in the written test, verifying also the exhibition and communication skills of the student, with a particular focus on properties of language and on the ability of self-organization of the exposition on the theoretical contents of the course.
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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