Teaching is organised as follows:  
Unit  Credits  Academic sector  Period  Academic staff 
STATISTICA  3  SECSS/01STATISTICS  II semestre 
Bruno Gobbi

MATEMATICA  6  MAT/05MATHEMATICAL ANALYSIS  I semestre 
Lorenzo Meneghini

The aim of this course is to provide, across the three modules, detailed knowledge concerning
 the main methods of calculus and linear algebra, with application to modeling in natural sciences;
 the main methods of univariate and bivariate descriptive statistics for the analysis of qualitative and quantitative data in the context of viticulture and oenology.

MM: MATEMATICA

(PREREQUISITES: Algebraic, exponential and logarithmic equalities and inequalities.)
1) Functions. Limits. Continuity.
2) Derivation and differentiation of functions. Rolle's, Lagrange's and de l'Hospital's theorems and their consequences. Applications and examples.
3) Functions and their graphs. Function's graph and linear transformations. Applications to natural sciences.
4) Integration of functions of a single real variable. Applications and examples.
5) Simple examples of differential equations.
6) Linear systems and matrices: determinants, inverse matrix, Applications to natural sciences.
Each topic is discussed both from a theoretical and an empirical point of view, with special focus on applications.
(notes and slides available at link https://app.box.com/s/t2jamq852r8j93qhhxomjy4rmckmh5vy )

MM: STATISTICA

1) Introduction to statistical data analysis: approaches and main topics 2) Univariate descriptive statistics:  Dynamic analysis by means of ratios  Frequency distributions  Location indices: Mode, median, percentiles, algebraic means  Heterogeneity and variability and indices: Gini Index, Shannon entropy, range, absolute deviations, standard deviation, variance. 3) Bivariate descriptive statistics:  Joint frequency distributions  Analysis of association  Analysis of mean dependence  Analysis of linear correlation  Simple linear regression Each topic is discussed both from a theoretical and an empirical point of view, with special focus on case studies dealing with problems arising in the context of viticulture and oenology.

MM: MATEMATICA

Students are evaluated by means of a written comprehensive examination, composed of exercises and questions. A time of 2 hours is scheduled. The grades are on a scale of 30. In the event of a health emergency, the examination procedures may undergo changes which will be communicated promptly.

MM: STATISTICA

Students (regardless whether or not they attended lessons) are evaluated by means of a written comprehensive examination, composed of exercises and questions. A time of 2 hours is scheduled. The grades are on a scale of 30.

Rules for defining the final grade of the Mathematics and Statistics course

The final grade summarizes the tests carried out in the two modules: (1) A module is successfully completed if the student achieves a score of at least 15/30. (2) The examination of Mathematics and Statistics shall be passed only if both modules are successfully completed, provided that the average of the two scores, calculated as shown in (3), is not less than 18/30. (3) The final mark is calculated as the average of the scores obtained in the two modules weighted by the number of credits; in the computation of the average, at 30 cum laude obtained in a module is assigned a score of 31; in the case of a noninteger result, the mark is rounded upward; in the case of an average of at least 30, the final mark will be 30 cum laude.
The exam can be verbalized only after passing the exams related to both modules.
Reference books  
Author  Title  Publisher  Year  ISBN  Note 
S. Bernstein and R. Bernstein  Elements of Statistics  Descriptive Statistics and Probability  Schaumâ€™s Outline Series.  McGrawHill  1999  0070050236 
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