ELEMENTS OF STATISTICS AND MATHEMATICS
Academic year and teacher
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- Versione italiana
- Academic year
- 2019/2020
- Teacher
- GIULIA ZANIRATO
- Credits
- 6
- Curriculum
- BIOTECNOLOGIE PER L'AMBIENTE
- Didactic period
- Primo Semestre
- SSD
- SECS-S/01
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.
Another objective of the course is to introduce the first elements of descriptive statistics, the fundamental concepts of probability calculus to making statistical inference.
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; .
- know how to define probability measures and apply their properties
- know how to operate with conditional probability, in particular with the law of alternatives and the Bayes formula
- summarize the sample information through graphs and summary measures
- know how to use tests of hypotheses and interval estimates
- know how to model real problems in the language of mathematics, probability and statistics
- represent and summarize the sample information and apply inferential techniques to support decision-making processes.
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
- review of the prerequisites, solution of first and second degree equations, solution of systems of equations (2h);
- definition and properties of real functions, notable functions, piecewise functions and graphs (4 h);
- the concept of limit of a real function, property of limits, calculation of limits and indeterminate forms (4 h);
- Study of the continuity of functions, points of discontinuity, statement of the theorems of continuous functions(2 h);
- The concept of derivative and its geometric meaning, calculation of derivatives (4 h)
- growth and decrease, maximum and minimum, complete function study (4 h);
- indefinite integrals (calculus of primitives) and definite integrals (4 h);
- Descriptive statistics (6 h)
- Axioms of probability and combinatorial calculation (2 h).
- Conditional probability and independence (2 h).
- Discrete random variables (4 h).
- Sample distributions (2 hours).
- Statistical tests (8 hours).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,
- Use of mathematic software, to visualize the concept of analysis and to verify solution of some exercises. Learning assessment procedures
- Computer based test.
The test consists of 20 multiple choice questions (of which only one is exact), each of which is given a score (which can be 1 or 2 points). The final grade is given by the sum of the scores of the individual questions. An answer not given does not give any score, while an incorrect answer will lead to a penalty of -0.25. To pass the exam it is necessary to acquire a minimum score of 18. Praise is obtained with a score higher than 30 (thus making 31 or 32 points).
The use of the calculator is permitted. Reference texts
- - M. Abate, McGraw-Hill Education, 3° ed, Matematica e statistica. Le basi per le scienze della vita.
