OVERVIEW

The course has the aim to give basic mathematical tools ; it is developed in the first semester, with six hours of lessons each week. the students come from different types of schools and in various cases they show serious lacks as regards competences and abilities. For these reasons, the initial part of the course is devoted to recall, re–elaborate and deepen some important background concepts.

AIMS AND CONTENT

LEARNING OUTCOMES

Aim: to provide basic mathematical tools suitable to the construction of "models" for solving problems

AIMS AND LEARNING OUTCOMES

1) To give basic instruments directed to the understanding, the planning and the solution of problems, to the construction and recognition of models (especially graphics).

2) To lead towards a scientific approach to the learning.

3) To see as Mathematics gives "unifying" language and methodologies through models and structures.

TEACHING METHODS

The classroom–taught lessons consist of theoretical part and exercises,that in some cases get the students involved in the subject in an operative way

SYLLABUS/CONTENT

Introduction of the ideas of "structure" and "model", with a “short trip” in history. Sets and structures, in particular:  integer, rational and real numbers. Functions of a real variable, with examples of physical or chemical character. Cartesian coordinate systems in the plane. Recognition of certain symmetries. Overview on elementary functions: linear, quadratic, trigonometric, exponential and logarithmic, square root, absolute value, presented as the suitable models to describe the behavior of some aspects of the nature. Functions obtained as sum, product, ratio or composition of elementary ones. Problems related to inequalities. Resolution of certain types of inequalities and their graphic interpretation. Concepts of "continuity" and "limit." Derivatives: geometric interpretation, derivatives of the above considered functions. Applications to the study of the graph of a function and to optimization problems. Short notes on the integrals, in order to compute areas in the plan. Fundamentals of probability theory. sample space, probability of an event in the "discreet" case. Probability of exclusive, conditioned, independent events. Elements of descriptive statistics.

RECOMMENDED READING/BIBLIOGRAPHY

Appunti di Matematica per CTF ( G.Tamone, "appunti interni" )

MATEMATICA DI BASE Esercizi svolti, testi d'esame,richiami di teoria, di A.M.Bigatti e G.Tamone, Editrice Esculapio (2016)

Further reference

Matematica di base , di A.M.Bigatti e L.Robbiano , Editrice Ambrosiana  ( 2014 )

TEACHERS AND EXAM BOARD

Exam Board

GRAZIA TAMONE (President)

ANNA MARIA BIGATTI

ORNELLA CAVALLERI

EMANUELA DE NEGRI

ARVID PEREGO

LESSONS

Class schedule

The timetable for this course is available here: Portale EasyAcademy

EXAMS

EXAM DESCRIPTION

The examination consists of a written exam, composed of three exercises, regarding the main parts of the syllabus, that must be solved with suitable explanations, within two hours. After the correction, the papers are analysed and discussed with the students.

If the written exam has obtained a mark ≥ 18:                                                                                    

•  an oral exam is mandatory only in the following cases:

(a) one of the exercises has reached less than half of the assigned score                                        

(b) the given explanations are completely or partially very lacking and generate doubts on the real understanding                                                                                                                    

•  no oral exam is required except cases (a), (b)                                                             

•  in any case, the student can ask also an oral exam.

If the written proof has obtained an unsatisfactory mark between 13 and 17,  there are two possibilities:           

• to apply for an oral exam ( usually consisting of  "exercises" and managed by two tenured teachers).                                                                                                                            

• to apply to one of the other scheduled exam sessions

If the written exam has obtained a mark < 13 : the student must apply to another session, but not earlier than 28 days.

During the written exam it is allowed to consult a sheet of paper of notes (size A4, two sides) and the use of a calculator: other types of notes, mobil phones, smartphones, personal computers, books are not allowed.

The sheet of the notes can be handwritten, typesetted, coloured, photocopied, according to the personals choice. It is suggested to prepare it personally.

For each session, the deadline for the registration is 5 days before the date of the exam, as one can deduce from the procedure of the online registration, which is mandatory . No exception will be allowed and the not registered students will not be able to apply to the exam.

Further, as above written, the students which have obtained a mark less than 13 in one session, are not allowed to apply to another session earlier than 28 days.

ASSESSMENT METHODS

Besides the scheduled examinations, during the year there are dispensed some practice exercises, for self–evaluation.

Exam schedule