08234 - Elements of Mathematics

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 (Teaching unit 1)

Sets and functions

Definition of set. Operations between sets. Sets of numbers. Concept of relation. Functions of one variable. The graph of a function. Properties of functions. Linear, quadratic, power, polynomial functions. Exponentials, logarithms, periodic functions.

Theory of limits

Continuous function. Limits for functions. Divergence and convergence speed.

Derivatives

Definition of incremental ratio. Derivative of a function. Properties of derivatives. Derivative rules.

Functions study

Asymptotes, maximum and minimum points, inflection points.

Integrals

Antiderivative of a function. Definite and indefinite integral. Computation rules: integration by substitution, integration by parts.

Linear algebra

Vector spaces. Matrices and transformations. Linear systems.

Basics of Statistics (Teaching unit 2)

The Basic of Statistics teaching unit is part of the STAAF Degree Course but not of the EMSA Degree Course.

Descriptive statistics One-dimensional variables: Absolute frequencies, relative frequencies, cumulative frequencies. Location measures. Variability measures. Graphical representation of data. Two-dimensional variables: Bivariate frequency distributions. Marginal distributions, conditional distributions. Relationships between two variables: dependence, linear regression, linear correlation

Readings/Bibliography

Mathematics (Teaching unit 1)

Matematica per le scienze della vita, D. Benedetto, M. Degli Esposti, C. Maffei

Casa Editrice Ambrosiana (C.E.A.), 2012

Moreover, slides of the lessons will be stored, time by time, on the online platform for teaching support.

 

Basics of Statistics (Teaching unit 2)

Mecatti, F. (2015), Statistica di base. Come, quando e perché. (II edizione), Milano, McGraw-Hill. (Chapters: 2, 3, 4, 5, 7, 9, 10, 12, 13)

The teaching material will be provided to the students.

Teaching methods

The course will cover the topics of the program through classroom teaching, both for lectures and exercises.

Assessment methods

The verification of the comprehension of the entire course will be proved through a final exam which includes two written tests, one for each unit. The student can take the two tests in the same call or in different calls. The number of calls is three for the winter session, three for the summer session and one in September.

For each of the two tests, the mark will be expressed out of thirty and the written test will be considered passed if this mark is between 18 and 30.

The final grade of "Mathematics with Elements of Statistics" will be given by the weighted average of the marks of the two tests: (Mathematics Score) ∙ 0.75 + (Statistical Score) ∙ 0.25

The student who passes a written test can decide to accept the grade obtained or reject it by repeating the writing of that unit at a subsequent exam.

The student who fails one of the two tests must repeat only the written part of the associated unit.

Mathematics (Teaching unit 1)

For the written test of mathematics no notebooks, tablets, smartphones or pocket calculators are allowed.

The written exam includes 4 exercises: a function study, the calculation of a limit, the calculation of an integral, and an exercise of linear algebra.

Exercises for which only the result is provided without indicating the methodology adopted and the intermediate steps of the calculation will be considered unresolved (grade 0).

Basics of Statistics (Teaching unit 2)

As for the Statistics test, the student will be asked ten questions regarding the topics covered during the course.

Teaching tools

PC and video projector.

Office hours

See the website of Barbara Di Fabio