## MATHEMATICS FOR STATISTICS

General Mathematics Knowledge, as provided by a reasonably good High School diploma. Elements of differential and integral calculus.

The evaluation is determined by one or more written tests, aimed at verifying the acquisition of knowledge and skills as reported by the European descriptor system (Dublin Descriptors) for three-year college degrees. In particular, with regard to the Knowledge and Understanding, to become familiar with some basic probability and statistics techniques; with regard to the Applied Knowledge and Understanding, to develop and support reasoning on statistical and mathematical issues relevant to the scope of study; with regard to Judgment Making, to be able to perform simple statistical analysis; with regard to Communication Skills, to know how to communicate the ideas behind the solution/s to a sampling and data analysis problem; with regard to Learning Skills, to have developed the mathematical skills needed to undertake with a high degree of autonomy further studies. At the student’s or teacher's request, evaluation may be supplemented by an oral test.

One of the (many) challenges science is required to answer today is the ability to make predictions. That is, to elaborate and validate models that, starting from a set of initial data, allow to predict the temporal evolution of a system, whatever it is, and formulate the probability with which an event might occur or not.

Therefore, the course aims to develop the fundamental mathematical skills to approach Inferential Statistics, the particular area of Statistic which studies the application of mathematical models capable of inducing the characteristics of a population from the observation of a part of it (sample), randomly chosen.

Review of Mathematics: Functions of one and two real variables. Partial derivatives and applications of differentiation rules. Maxima and minima of differentiable functions with continuous second partial derivatives. The Riemann integral and the Fundamental Theorem of Integral Calculus for functions of one real variable. The Riemann improper integral. Fubini-Tonelli's Theorem for integrable functions of two real variables.

Elements of Probability Theory: Finite and infinite probability spaces. Probability of the logical sum of events. Conditional probability. Probability of the logical product of events. The Bayes Theorem. Random variables. Indices of central tendency for random variables. The moment generating function: the case of the Gaussian distribution. Chebychev's inequality. The Law of Large Numbers. The Central Limit Theorem. Functions of random variables. New types of distributions: The distribution of χ ^ 2 (or of Pearson). A particular χ ^ 2 variable. Student's T distribution. A particular T variable. The Fisher distribution F. Bivariate probability distributions.

Elements of Inference Theory: The maximum likelihood method for estimating the parameters of a distribution: the case of the Gaussian distribution. Confidence intervals. Estimate of the regression curves of a bivariate population with the least squares and maximum likelihood methods: the case of linear regression. Statistical significance of a sample regression line. Confidence intervals of intercept and slope.

Notes and exercises prepared by teacher.

Web pages related to the course topics, (such as: https://www.statlect.com/)

Lessons will be held twice a week and organized in two sessions of 45 minutes each. With particular reference to issues related to the management of potential long distance students, there will be set up adequate teaching support and online communication tools.

Contacts:

Department of Chemistry and Pharmacy

Via Piandanna 4, Sassari

Tel. 079 229486; Cell. 347 116 1591; Fax 079 229482;

e-mail: pensa@uniss.it

Supervision hours: Please contact the teacher by @mail.

Available to offer individual assistance in a foreign language to incoming students (English): YES

Materials prepared by the teacher will be made available to students in the online Moodle platform and in a dedicated DropBox file. Available to accept examination of incoming students also in foreign language (English): YES

In order to acquire greater skills in the topics considered as basics and improve understanding of the arguments

presented in the course, the use of the following website is recommended: https://www.khanacademy.org/