MATHEMATICS AND FUNDAMENTALS OF STATISTICS
Academic year and teacher
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- Versione italiana
- Academic year
- 2018/2019
- Teacher
- MICHELA BRUNORI
- Credits
- 6
- Didactic period
- Primo Semestre
- SSD
- MAT/05
Training objectives
- The main goal of the course consists in providing the mathematic basis required in other course and to use model and concept of sperimental sciences to read the date and study the natural cases.
The main acquired knowledge will be:
- Knowledge of the main functions and their properties;
- ability to use the limit and continuity concepts;
- knowledge of the main functions derivative and their geometrical meaning;
- ability to compute functions integral and to understand the geometrical meaning;
- ability to work with probabilistic events, to compute discrete and continue probabilities;
- linear regression analysis to study the relationship between phenomena.
The basic acquired abilities (that are the capacity of applying the acquired knowledge) will be:
- Kwon exhaustively, the concept of: function analysis, differential and integral compute.
- Find good strategy to solve problems.
- Analize and read dates, to study natural cases, using prabability and statistic theory. 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
- - basis of 2D analytic, solving equation, solving equation system (2 h);
- Basis of analitic geometry (2 h);
- Basis of goniometry and trigonometry, (2 h);
- real function definition and properties, graph, main functions (4 h);
- Concept of limit of a real function, theorem of uniqueness, some methods for the calculation of limits, properties and fundamental results, indeterminate forms (4 h);
- the concept of continuity for a real function of one real variable, theorem about continuos functions (4 h);
- the concept of derivability for a real function, geometrical and phisic meaning (4 h);
- the methods for the calculation of derivatives, growth, decreasing, maximum and minimum (6 h);
- the main methods for the calculation of primitives, definite integrals, fundamental theorem of integral calculus (8 h);
- Combinatorial analysis, concept of probability, conditional probability and Bayes theorem (4 h);
- calculation of mean, mode and median, variation interval, variance, mean square deviation, grouping and distribution of data, calculation of absolute and relative frequencies, normal distribution and two-character distributions (8 h). Didactic methods
- The course is organized as follow:
- frontal lectures,
- practice exercise. At the end of particular topic, I take time to show the solution of problems and exercises,
- Use of mathematic software, to visualize the concept of analysis and to verify solution of some exercises. Learning assessment procedures
- The aim of the exam is to verify at which level the learning objectives previously described have been acquired. The examination wiil be a written test. Every exercise has a mark, the final mark is the sum of marks. To pass the exam it is necessary to get at least 18 point. Calculator can be used.
Reference texts
- - M. Abate, McGraw-Hill Education, 3° ed, Matematica e statistica. Le basi per le scienze della vita.
- M. C. Patria - G. Zanghirati, Mat&matica, Pitagora
In-depth text:
- V. Villani, G. Gentili, McGraw-Hill Education, 5° ed, Matematica: Comprendere e interpretare fenomeni delle scienze della vita
