Mathematics and statistics

A.Y. 2018/2019
10
Max ECTS
108
Overall hours
SSD
MAT/02 SECS-S/01
Language
Italian
Learning objectives
Knowledge of the basics of Maths, in particular, of
elementary Calculus (real functions in one variable, limits,
derivatives, integrals). Knowledge of descriptive
statistics. Position and variability indices. Acquisition of
the principles and the techniques of regression and
correlation between variables. Knowledge of inferential
statisticsKnowledge of the basics of Maths, in particular, of elementary Calculus (real functions in one variable, limits, derivatives, integrals). Knowledge of descriptive statistics. Position and variability indices. Acquisition of the principles and the techniques of regression and correlation between variables. Knowledge of inferential statistics.
Expected learning outcomes
Possibility of exploiting the basic tools of Maths in any
context. Describe phenomena using main statistical
indicators. Plan sampling surveys. Using the one and two-
ways analysis of variance. Objective assessment of
statistical surveys resultsPossibility of exploiting the basic tools of Maths in any context. Describe phenomena using main statistical indicators. Plan sampling surveys. Using the one and two-ways analysis of variance. Objective assessment of statistical surveys results.
Course syllabus and organization

Single session

Lesson period
First semester
Unit 1
Course syllabus
Numerical sets.: N, Z, Q e R. The coordinate plane: straight lines, parabolas, circles. Outline of Trigonometry. Elementary functions and their graph. Equations, inequalities and system of algebraic and irrational inequalities. Generalities about real funcion: domain, range, injective and surjective functions, composed functions, inverse functions, geometric transforms of elementary functions. Limits: computing limits, comparison of infinites and infinitesimals, indeterminate forms. Continuity. Asymptotes: vertical, horizontal and slant. Differential calculus: first derivative, tangent line, monotonicity, global and local maxima and minima. Second derivative: convexity and concavity, inflection points. Integral calculus. Integrals of rational functions, some integration techniques. Computation of plane areas.
Teaching methods
agrimat and matematica assistita: free download at http://ariel.ctu.unimi.it/corsi/mateassistita
Unit 2
Course syllabus
1- The language of statistics. 2- Organization of data end graphical representation. 3- Position and variability indices (mean, mode, median), variance. 4- Bivariate analysis for qualitative or quantitive data. 5- Probability, probability rules. Independents events. Total probability theorem. Bayes theorem. 6-Random variables, distributions. Distributions: binomial, geometrical, Poisson, Gaussian. 7- Random samples. Confidence intervals. Estimation. Sample mean. Central Limit Theorem. Confidence interval for the mean. 8- Hypothesis tests: fundamentals, phases, simple test. 9- Hypothesis test on a single population proportion. 10- Test and confidence interval for the difference of two means using independent sample. 11- Correlation analysis. Univariate linear regression. Inference. 12- Analysis of variance.
Teaching methods
Introduzione alla Statistica, di M.K. Pelosi e T.M. Sandifer, ed. McGraw-Hill, 2009.
Unit 1
MAT/02 - ALGEBRA - University credits: 6
Practicals: 40 hours
Lessons: 28 hours
Professor: Bernardi Giulia
Unit 2
SECS-S/01 - STATISTICS - University credits: 4
Practicals: 16 hours
Lessons: 24 hours
Professor: Baldi Lucia
Professor(s)
Reception:
on appointment
Via Celoria 2, Milan, Italy, 3rd floor (or by Skype/Teams/Zoom)