Basic facts on sets and relations; elementary logic and language.
Numerical structures: natural numbers, integers, rational and real numbers. Hints on real and complex numbers.
Elements of probability theory and of mathematical statistics.
Course Content - Last names M-Z
The language of sets and relations; logic and language.
Algebraic structures: natural numbers, integers, rationals; mentions on real and complex numbers.
Elements of probability.
Alessandro GIMIGLIANO, Leonardo PEGGION, Elementi di matematica, UTET – De Agostini, Novara, 2018.
Notes provided by the teacher.
A complete and updated bibliography will be indicated at the beginning of the course.
Authors: Alessandro GIMIGLIANO, Leonardo PEGGION
Title: Elementi di matematica
Editor: UTET – De Agostini, Novara, 2018.
Integrative sheets given by the professor.
Learning Objectives - Last names A-L
[About the mathematical subjects addressed in the course, students must show:]
- to possess basic knowledge and understanding of mathematical concepts and to know how to use and apply them to solve exercises and to propose simple mathematical models in problematic contexts of various levels of complexity;
- to be able to organize their knowledge in a hypothetical-deductive set, in particular to be able to place hierarchically definitions, sufficient conditions, necessary conditions, characterizations, properties and to draw simple conclusions by discussing the assumed hypotheses;
- to possess communicative skills, by using correctly mathematical language, both in peer-to-peer relationships and in simulating teaching-learning sets;
- to show good skills to learn autonomously and personally and to deepen the subjects, developed in the course.
Learning Objectives - Last names M-Z
Students must show:
- to possess the basic knowledges of mathematical concepts and how to use them to solve basic exercises ant to give easy mathematical models for different kinds of problems;
- to organize their knowledge;
- to be able to communicate in correct mathematical language.
Prerequisites - Last names A-L
Fundamental prerequisites are both basic knowledge and algorithmic skills, useful to understand the arguments developed in the course, as they are normally developed in every pre-academic teaching, which is supposed to be followed with seriousness and commitment.
Strong motivations towards the teaching, a positive attitude toward mathematics and awareness of the importance of mathematical education in training to a conscious and active citizenship are indispensable.
Prerequisites - Last names M-Z
The basic knowledges (contents and algorithms) should be part of the knowledges acquired by pre-universitary schools.
Teaching Methods - Last names A-L
Lecture-style instruction. As far as possible, students may be required to expose suggestions and remarks on the various topics and to try to solve exercises and to suggest mathematical models for simple problematic contexts.
Through the student reception, topics chosen by students will be discussed and deepen in individual way and any question can be posed to the teacher.
Teaching Methods - Last names M-Z
Frontal lessons.
Further information - Last names A-L
Although not mandatory, class attendance is strongly recommended, because of the relevance of relational aspects in teaching-learning processes both with other students and with the teacher.
Teaching takes advantage of MOODLE platform, which is obligatory for all students and can be particularly useful for students having motivated difficulties in attending classes with regularity.
During the course, the student reception is encouraged for any discussion on mathematical topics and for any individual in-depth analysis.
Further information - Last names M-Z
Attending lessons is recommended (though not mandatory).
Type of Assessment - Last names A-L
Written exam, followed by an oral exam.
Although it is impossible to make a strict separation between the two types, it is possible to state that subjects of particular examination of the written exam are all the skills required between the objectives with particular regard to the basic knowledge of the topics addressed and those of the type operational and problem-solving applications and modeling of problem situations, while the subject of particular examination of the oral exam is all the skills required between the objectives with particular regard to linguistic and communicative skills and the ability to structure hierarchically the mathematical knowledge learned by enhancing the originality and autonomy of mathematical thought.
In order to pass the exam, it is necessary at all stages to demonstrate to possess all basic elementary knowledge and basic skills in the execution of standard algorithms, which are taught in primary school.
Type of Assessment - Last names M-Z
Written and oral exam.
Course program - Last names A-L
The basic facts on sets, relations and applications. Logic and language; elements of propositional calculus and quantifiers. Operastions on sets. Relations and applications. Injective and surjective applications. Equivalence and order relations. Finite and infinite sets.
Numerical structures: natural numbers, integers, rational and real numbers. The principle of mathematical induction. Numbers and operations. Divisibility and prime numbers. Fractions and rational numbers. Irrational numbers. Hints on real numbers and on complex numbers.
Elementary probability theory. Combinatorial calculus. Different meanings of probability. Basic probabilistic formulas. Conditional probability. First arguments of mathematical statistics. Representation of data. Position and dispersion indices.
Course program - Last names M-Z
Sets and relations, logic and language. Basics of propositional calculus. Quantifuers. Operations with sets. Relations and functions. Equivalence and order relations. Numerical structures: natural numbers, integers, rationals, reals. Induction. Operations with numbers. Divisibility and prime numbers. Fractions and rational numbers.