00674 - Mathematics

Learning outcomes

At the end of the course, students: - know the basic concepts of mathematics, necessary for the following courses; - know the foundations of probability and statistics and are able to apply them to understand statistical and statistical-epidemiological techniques aimed at health planning and at the organization and management of health services.

Course contents

1. Number sets.
2. Powers and roots.
3. Proportions and percentages.
4. Proportionality.
5. Main units of measure. Multiples and submultiples. Scientific notation. Approximation.
6. Areas and volumes.
7. Definition of function. Domain and image. Image and inverse image. Monotonic functions. Invertible functions and inverse function.
8. Graphs of polynomial, rational, irrational, exponential and logarithmic functions. Related problems.
9. Degrees and radians. Trigonometric functions. Right triangles.
10. Limits and derivatives (hints).
11. Combinatorics: combinations and permutations.
12. Classical and frequentist definition of probability. Sample space. Union and intersection of events. Complementary event. Mutually exclusive and non-exclusive events. Dependent and independent events. Conditional probability. Diagnostic tests.
13. Arithmetic mean, weighted mean, median, variance and standard deviation of a data set. Regression and correlation.
14. Random variables and probability distributions. Expected value, variance and standard deviation of a random variable. Uniform, geometric and binomial distribution. Normal distribution and gaussian function. Central limit theorem. Standardization. Poisson distribution. Continuity correction.
15. Hypothesis tests.

Readings/Bibliography

V. Villani, G. Gentili, Matematica 5/ed - Comprendere e interpretare fenomeni delle scienze della vita, McGraw-Hill, 2012.

F. Cagliari, Matematica per Farmacia, McGraw-Hill Create, 2014 (special edition from Marco Abate, Matematica e Statistica - Le basi per le scienze della vita, seconda edizione, McGraw-Hill, 2013).

D. Benedetto, M. Degli Esposti, C. Maffei, Matematica per le scienze della vita, Casa Editrice Ambrosiana, 2008.

Assessment methods

Written exam.

Office hours

See the website of Luca Ferrari