## Unit MATHEMATICS AND STATISTICS

- Laura Angeloni - Didattica Ufficiale

- 56 ore - Didattica Ufficiale - Laura Angeloni

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.

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.

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.

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