- Docente: Claudio Caprara
- Credits: 6
- SSD: MAT/03
- Language: Italian
- Moduli: Claudio Caprara (Modulo 1) Stefania Curti (Modulo 2)
- Teaching Mode: Traditional lectures (Modulo 1) Traditional lectures (Modulo 2)
- Campus: Bologna
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Corso:
First cycle degree programme (L) in
Ornamental plants and landscape protection (cod. 8523)
Also valid for First cycle degree programme (L) in Applied Pharmaceutical Sciences (cod. 8518)
First cycle degree programme (L) in Applied Pharmaceutical Sciences (cod. 8518)
Learning outcomes
At the end of the course the student knows the technical mathematical tools and their use, as well as the main methods and basic tools for the quantitative study of collective phenomena. The student is then able to set up and solve problems and to assimilate new concepts from the experience and previous knowledge, to produce and process statistical data independently, developing the ability of interpretation and critical assessment of statistical information.
Course contents
Mathematics
Elements of set theory. Definition of set. Operations between sets. Set of real numbers
Functions. Concept of relation. Functions of a variable. Continuous functions.
Theory of limits. Limits for functions.
Derivatives. Definition of incremental ratio. Derivative of a function. Properties of derivatives. Derivative rules.
Integrals. Infinitesimal and differential. Indefinite integral. Integral properties. Integration by substitution. Integration for parts. Defined integral. Improper integral.
Introduction to functions study. Asymptotes, maximum and minimum points, inflection points.
Elements of Statistics
Descriptive Statistics. Types of data, qualitative and quantitative variables, discrete and continuous variables. Data presentation: frequency tables (frequency counts, relative frequencies) and graphical representations (e.g. pie charts, bar charts, histograms, scatter plot, time series, cartograms). Measures of central tendency (mean, median, mode and percentiles). Measures of variability (range, interquartile range, deviation, variance, standard deviation, variation coefficient). Skewness and kurtosis.
Relationships between two variables. Contingency Tables. Joint frequencies and joint relative frequencies. Conditional and marginal distributions. Relationships between two variables. Chi-squared statistics. Tschuprow’s T.
Elements of Probability. Introduction to probability. Remarks on the concepts of probability. Definition of simple events and sample space. Operations on events (Venn diagrams). Axioms of probability (Kolmogorov). Rules of the probability (additive, multiplicative). Conditional probability. Bayes’ theorem.
Rates and Rate Standardization. Crude rates. Specific rates. Standardization of rates (direct and indirect methods).
Readings/Bibliography
Mathematics
The files with the lessons teaching material will be stored in AMSCampus.
Elements of Statistics
M. Pagano, K. Gauvreau. Biostatistica. Idelson-Gnocchi, Napoli, 2003.
A. Montanari, P. Agati, D.G. Calò. OPEN STATISTICA con esercizi commentati e risolti. Masson, 1998.
Teaching methods
Mathematics
The course will cover the topics of the program through classroom teaching, both for lectures and for exercises.
Elements of Statistics
Lectures
Classroom exercises
Computer exercises (using Excel)
Assessment methods
Mathematics
The exam is done through a final exam with a written test and eventually an oral examination, both with grades expressed in thirtieths.
The written test is passed with a grade between 18 and 30.
The student who fails the written examination must repeat the examination at the next session.
The student who passes the written test can choose to:
- Refuse the grade and take the examination at the next session;
- Accept the grade without the oral examination and in this case the test is passed with a grade corresponding to that of the only written test;
- Try to improve the grade of the written test with an oral examination, in the awareness that, according to the oral examination, the grade of the written test may increase or decrease.
Elements of Statistics
Lab exam using Excel: 5-6 exercises to be solved using Excel. Each exercise is composed of different questions, including the interpretation of the findings.
The exam is located in the computer room (exam duration: 1 hour and 30 minutes).
Teaching tools
Mathematics
Chalkboard and video projector.
Elements of Statistics
Computer lab
Teaching materials (accessible through AMS campus)
Office hours
See the website of Claudio Caprara
See the website of Stefania Curti