ELEMENTS OF STATISTICS AND MATHEMATICS
Academic year and teacher
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- Versione italiana
- Academic year
- 2022/2023
- Teacher
- RICCARDO IEVOLI
- Credits
- 6
- Didactic period
- Primo Semestre
- SSD
- SECS-S/01
Training objectives
- The main objective of the course is to provide mathematical foundations, concepts and models of experimental sciences to investigate natural phenomena.
The course has the further objective of introducing some elements of descriptive statistics and probability theory, which represent the prerequisites for introducing statistical inference. The joint use of techniques from the two disciplines, mathematics and statistics, finds application in the interpretation and resolution of various problems from the most diverse fields.
At the end of the course the student will acquire:
- knowledge of the main mathematical functions and their properties;
- the ability to use the concepts of limit and continuity;
- knowledge of the derivative of relevant functions and their geometric meaning;
- the ability to calculate and interpret the integral of functions and their simple compositions;
- knowledge of probability measures and related properties
- the ability to summarize the information from the data through graphs and descriptive statistics
- knowledge of inferential techniques such as point estimation, interval estimation and hypothesis testing
- the modeling of real problems in the language of mathematics, probability and statistics
- the application of statistical (and mathematical) techniques to support decision-making processes.
The main skills will be:
- Knowledge of the concepts of the analysis of elementary functions, and differential and integral calculus;
- Identification of appropriate strategies for solving problems;
- Analysis and interpretation of the data also using techniques related to descriptive and inferential statistics. Prerequisites
- Symbolic computations, math symbols, set operations, fundamentals number sets and their properties, mention on equations and inequalities, systems of coordinate, Cartesian geometry. This course does not require any prerequisites.
Course programme
- Mathematics module (24 hours)
- review of the prerequisites, percentage, sets, polynomial, equations, inequalities, analytical geometry;
- definition and properties of real functions, notable functions, piecewise functions and graphs;
-exponential growth and decay models
- the concept of limit of a real function, property of limits, calculation of limits and indeterminate forms;
- Continuity of functions, points of discontinuity;
- The concept of derivative and its geometric meaning, calculation of derivatives, rate of growth, function study;
- indefinite integrals (calculus of primitives) and definite integrals;
Statistical module (24 hours)
- Descriptive statistics
- Basic Excel features and data entry and manipulation features, histograms, pie charts, line and scatter charts
- Axioms of probability and combinatorial calculation
- Conditional probability and independence
- Discrete random variables.
- Sample distributions.
-Basics of Measurement Theory and evaluation of uncertainty.
- Statistical tests Didactic methods
- The course is organized as follow:
- frontal lectures,
- practice exercise. At the end of particular topic, we take time to show the solution of problems and exercises. Learning assessment procedures
- The test consists of multiple-choice questions (of which only one is exact) on IT platform or OCM forms. The topics of the questions are on all topics of the course.
Reference texts
- - M. Abate, McGraw-Hill Education, 3° ed, Matematica e statistica. Le basi per le scienze della vita.
