BASIC MATHEMATICS FOR BIOMEDICAL SCIENCES
Learning outcomes of the course unit
Knowledge and understanding.
At the end of the lectures, students should have acquired knowledge and understanding of the basic elements of mathematics (sets, operations with sets, elementary Logic, real valued functions), statistics and probability.
Applying knowledge and understanding.
By means of the classroom exercises students learn how to apply the theoretical knowledges to solve concrete problems (such as e.g., the problem of dosing the elements when preparing a medicine to administer to an animal or the problem of extracting significant information from a large number of data, also using probabilistic tools).
Students must be able to evaluate coherence and correctness of results obtained by themselves or by others.
Students must be able to communicate in a clear
and precise way mathematical statements in the field of study, also in a context broader than mere calculus. Through the front lectures and the assistance of the teacher, the students acquire the specific and appropriate scientific vocabulary.
The student, who has attended the course, is able to deepen autonomously his/her knowledge in statistics and probability, starting from the basic and fundamental knowledges provided by the course. He/She will also be able to consult specialized textbook, even outside the topics illustrated during the lectures. This to facilitate the entry in the labour market as well as a second-level study in a field which requires good mathematical skills.
None, even if it is very useful to already have a good knowledge of the main properties of logarithms and exponential functions.
Course contents summary
The first lectures cover topics of general interest related to the foundations of Mathematics and mathematical logic such as operations in numerical sets and predicate calculus. The second part regards the discussion of the fundamental contents of Statistics: data collection, averages and dispersion indicators. The third part is devoted to combinatorics, probability calculus, Gauss and Bernoulli distributions.
1)Elementary theory of sets.
2) Elements of mathematocal logic.
3) Numerical sets, operations and properties. Applications: proportions, percentages, equivalences.
4) Floating point representation of real numbers; pperations in scientific notation, truncation and rounding approximations, significant digits.
5) Outline of functions. Real functions of real variable, qualitative properties, polynomial, exponential and logarithmic functions.
6) Elements of descriptive statistics. Data collection, classification and graphical representation; frequency distributions, averages, mode, median, square error, variance, standard deviation, index of variation; Gauss distribution; two characters distribution.
8) Discrete probability.Events and probability calculus; elements of probability theory; Bernoulli distribution.
M. Abate: “Matematica e Statistica, Le basi per le scienze della vita”, McGraw-Hill, (2009).
V. Villani: “Matematica per le discipline bio-mediche”, Quarta edizione, McGraw-Hill, (2007).
The course schedules 3 hours of lectures per week. The didactic activities consist of frontal lectures and exercises and are developped also with the help of a tablet PC which projects on a screen the notes the teacher is writing. At the end of the lecture, a pdf file with the notes of the lecture is uploaded on the elly website. During the didactic activities, the topics of the course will be presented and discussed in a rigorous way. Much emphasis will be given to the application of the abstract results presented. To this aim, particular importance will be given to exercises, which are the most useful way to make students understand the relevance of the results presented in the theoretical lectures and to learn how they can be applied.
Assessment methods and criteria
Written final examination. Pass mark: 18/30; Maximum score: 33. Students who gain more than 30 points pass the mathematical modulus with 30 cum laude.
Since it is an integrated teaching together with Physics and Computer Science, the final score will be the arithmetic average of the three marks, which have to be anyway all equal to or greater than 18/30.