
Course unit
INSTITUTIONS OF MATHEMATICS
PSP4063395, A.A. 2019/20
Information concerning the students who enrolled in A.Y. 2017/18
ECTS: details
Type 
ScientificDisciplinary Sector 
Credits allocated 
Educational activities in elective or integrative disciplines 
MAT/07 
Mathematical Physics 
9.0 
Course unit organization
Period 
First semester 
Year 
3rd Year 
Teaching method 
frontal 
Type of hours 
Credits 
Teaching hours 
Hours of Individual study 
Shifts 
Lecture 
9.0 
63 
162.0 
No turn 
Prerequisites:

Basic notions of mathematics necessary for the access to the Bachelor Degree in "Scienze psicologiche, cognitive, e psicobiologiche". Basic notions of probability from the course Psicometria. 
Target skills and knowledge:

This course provides basics notions on mathematical topics useful for health and mental health care disciplines. (a) Basic notions of linear algebra (vectors and matrices), and some of its main applications; (b) Basic notions on conditional probabilities and Bayes' Theorem, with particular attention to its applications for risk assessment, especially in healthcare.
(a) Linear algebra is part of the mathematical and methodological background for understanding most contemporary sciences, for which it provides a main languages and a basic investigation, understanding, and communication tool.
(b) Conditional probabilities are ubiquitous when it is necessary to evaluate the relative impact of events which are not independent, as in medical or psychological tests. "The probability that a woman in the age bracket 4060 has breast cancer is 0.8 percent. If a woman has breast cancer, the probability is 90 percent that she will have a positive mammogram. If a woman does not have breast cancer, the probability is 7 percent that she will still have a positive mammogram. Imagine a woman who has a positive mammogram. What is the probability that she actually has breast cancer?"
The second part of the course provides the basic knowledge for the analysis of uncertainty inherent in statistical information, mainly in the form of conditional probabilities, in order to obtain a correct evaluation and communication of risk. Basic notions of elementary and Bayesian probabilities are introduced and commented, and their use is explained in problems related to healthcare, as well as formats and strategies for the (rap)presentation and communication of risk to nonprofessionals (patients). Recent legislation explicitly imposes to all health care professionals a correct risk assessment and the adequate communication of it to patients. In Italy, see for instance Art.1 of Law 219 of 22122017 on informed consent (published on GU n. 12, date 1612018):
http://www.trovanorme.salute.gov.it/norme/dettaglioAtto?id=62663 
Examination methods:

Written exam with open questions. A supplementary oral examination is also possible. The written exam (duration two hours, containing one or two theoretical questions plus 45 exercises, each involving a few specific questions) aims at verifying that the expected learning goals have been reached by the student. The optional oral test focuses first on the discussion of the salient points in the written test, and goes on to a more indepth discussion of some of the topics covered in the course. 
Assessment criteria:

Evaluation based on the result of the written exam (theoretical questions and exercises), and on the oral questions (discussion of the written exam and theoretical questions). 
Course unit contents:

(a) Linear algebra. Vector spaces, vectors, generators, bases, dimension, direct sum. Matrices; rank and determinant. Systems of linear equations; Rouche'Capelli theorem and explicit description of the set of solutions to a linear system. Matrices and linear maps; eigenvalues and eigenvectors.
(b) Conditional probabilities and risk evaluation. Uncertainty in statistical information. Problems related to the evaluation of risk and communication of risk. Realworld examples. Bayesian inferences through the use of probabilities, and by means of natural frequencies. Suitability of the latter for a more intuitive and direct insight in both risk estimation and in a transparent representation of risk. Examples focussing on the correct judgement of the probabilistic predictive value of medical diagnostic tests, and aiming at avoiding misleading risk information. Evaluation of the effect of interventions: Relative risk and Absolute Risk, and Relative and Absolute Risk Reduction (or Increase); Number Needed to Treat or to Harm [ARR, RR, RRR, NNT, NNH]. 
Planned learning activities and teaching methods:

Class lectures, with presentation of the main points indicated above. Some theory and many examples. Recitations and exercises to complement the theoretical parts, also directly involving students in both individual and group work. The main focus is on realworld applications of the topics treated during the coursework. 
Additional notes about suggested reading:

A textbook is indicated below. Further material is made available by the instructor through moodle during the course. See also the extra reading material indicated in the references below. 
Textbooks (and optional supplementary readings) 

E. Bodine et al., Matematica per le scienze della vita. Milano: UTET, 2014.

Materiale aggiuntivo  Auxiliary reading material  Stephanie Kurzenhäuser, Natural frequencies in medical risk communication: improving statistical thinking in physicians and patients. Dissertation: FU Berlin: 2003, . http://www.diss.fuberlin.de/diss/servlets/MCRFileNodeServlet/FUDISS_derivat e_000000001633/00_kurzenhaeuser.pdf

Innovative teaching methods: Teaching and learning strategies
 Lecturing
 Problem based learning
 Working in group
 Questioning
 Problem solving
 Loading of files and pages (web pages, Moodle, ...)
Innovative teaching methods: Software or applications used
 Moodle (files, quizzes, workshops, ...)
Sustainable Development Goals (SDGs)

