# Mathematics and statistics (2018/2019)

Course code
4S02690
Credits
9
Coordinator
Lorenzo Meneghini
Teaching is organised as follows:
STATISTICA 3 SECS-S/01-STATISTICS II semestre Marco Sandri
MATEMATICA 6 MAT/05-MATHEMATICAL ANALYSIS I semestre Lorenzo Meneghini

#### Learning outcomes

Aim of this course of Statistic is to present, both from a theoretical and an empirical point of view, the main methods of univariate and bivariate descriptive statistics for the analysis of qualitative and quantitative data in the context of viticulture and oenology. The educational objectives have been developed with reference to Dublin descriptors, they are consistent with those characterizing the 1st cycle degree program in which the course is inserted and have been defined in coordination with those of Mathematics module, with which it forms a unique course. More specifically, students who successfully complete this course will be able to: - collect, analyze and interpret statistical data, both qualitative and quantitative, and organize results in order to draw conclusions and decide in uncertain situations; - communicate, to experts and non-experts, statistical information and evaluations, also with the help of graphical devices. By means of a gradual learning process, linking the contents of this course with the educational objectives characterizing the 1st cycle degree programs in which the course is inserted, students will acquire the methodological and applied knowledge about the basic concepts of descriptive statistics (statistical ratios, means, variability, inequality/concentration, association, correlation and regression) necessary for the professional training. Aim of the course of Mathematic is to present, both from a theoretical and an empirical point of view, the main methods of calculus and linear algebra. The educational objectives have been developed with reference to Dublin descriptors, they are consistent with those characterizing the 1st cycle degree program in which the course is inserted and have been defined in coordination with those of Statistics module, with which it forms a unique course. More specifically, students who successfully complete this course will be able to: - determine the main characteristics of a function and sketch its graph; - differentiate a function and solve simple geometrical problems; - integrate a function and solve simple geometrical problems; - solve simple differential equations; - calculate matrix determinants and inverse matrix; - solve a linear system. By means of a gradual learning process, linking the contents of this course with the educational objectives characterizing the 1st cycle degree programs in which the course is inserted, students will acquire the methodological and applied knowledge about the basic concepts of Mathematics necessary to prosecute their studies.

#### Syllabus

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MM: MATEMATICA
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(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 )

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MM: STATISTICA
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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.

#### Assessment methods and criteria

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MM: MATEMATICA
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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. Students who attend lessons can decide to divide the exam in two parts, to be done before the class ends. A time of 2 hours is scheduled for each part and the grades are on a scale of 30. In that case, the mark of Mathematics will be calculated as the average of the scores obtained in the two different parts; in the case of a non-integer result, the mark is rounded upward. Rules for defining the final grade of the Mathematics and Statistics course, which 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 non-integer result, the mark is rounded upward; in the case of an average of at least 30, the final mark will be 30 cum laude.

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MM: STATISTICA
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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, which 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 non-integer 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.

 Author Title Publisher Year ISBN Note S. Bernstein and R. Bernstein Elements of Statistics - Descriptive Statistics and Probability - Schaum’s Outline Series. McGraw-Hill 1999 0-07-005023-6