Elements of Basic Mathematics

A.Y. 2018/2019
3
Max ECTS
27
Overall hours
SSD
MAT/01 MAT/02 MAT/03 MAT/04 MAT/05 MAT/06 MAT/07 MAT/08 MAT/09
Language
Italian
Learning objectives
The aim of this course is to provide students with the basic language and the essential tools of mathematics which are the fundamentals to face the first level graduation program.
Expected learning outcomes
After this course, the students should be able to manage independently elementary concepts of logic, of elementary set theory and functions, and of real numbers.
Course syllabus and organization

Elementi di matematica di base (ediz. 1)

Responsible
Lesson period
First semester
Course syllabus
(1) Basics of Logic: Compound propositions and logical connectives: conjuction, disjunction, negation, implication, biconditional. Truth tables. Logical implication and equivalence, necessary and/or sufficient conditions, universal quantifier, existential quantifier and their negation. Proofs by contrapositive and by contradiction.

(2) Basics of set theory: Relation of membership. Elements and subsets of a set. Inclusion, union, intersection, complement; power set and Cartesian product; relations and functions (injective, surjective, bijective), graphs of functions (several examples, among them elementary functions and piecewise functions). Partition of a set. Equivalence relations and quotient sets. Natural numbers and mathematical induction principle. Cardinality of the power set of a finite set.

(3) Rational numbers and their representation; real numbers. Rational numbers as fractions, this representation is not unique, fraction in its lowest terms. Representation of the rational numbers as points on an oriented line. Representation of the rational numbers as finite decimal or infinite periodic sequences. Non-existence of a rational number with square 2. Real numbers as infinite decimal sequences. Bounded and unbounded subsets in R. Sup/Inf, maximum and minimum of a set in R. Intervals in R and their notation.


EXAM
It consists of two parts (to be done in the same day), successfulness in part A is a necessary condition for the correction of part B:

Part A (1 hour, handled by Syllabus Course teachers ): check of knowledge of Syllabus
course subjects
Part B (2 hours, handled by EMB teachers): check of knowledge of EMB course subjects.

The exam is only for first year students.
MAT/01 - MATHEMATICAL LOGIC - University credits: 0
MAT/02 - ALGEBRA - University credits: 0
MAT/03 - GEOMETRY - University credits: 0
MAT/04 - MATHEMATICS EDUCATION AND HISTORY OF MATHEMATICS - University credits: 0
MAT/05 - MATHEMATICAL ANALYSIS - University credits: 0
MAT/06 - PROBABILITY AND STATISTICS - University credits: 0
MAT/07 - MATHEMATICAL PHYSICS - University credits: 0
MAT/08 - NUMERICAL ANALYSIS - University credits: 0
MAT/09 - OPERATIONS RESEARCH - University credits: 0
Lessons: 27 hours
Professor: Marra Vincenzo

Elementi di matematica di base (ediz. 2)

Responsible
Lesson period
First semester
Course syllabus
(1) Basics of Logic: Compound propositions and logical connectives: conjuction, disjunction, negation, implication, biconditional. Truth tables. Logical implication and equivalence, necessary and/or sufficient conditions, universal quantifier, existential quantifier and their negation. Proofs by contrapositive and by contradiction.

(2) Basics of set theory: Relation of membership. Elements and subsets of a set. Inclusion, union, intersection, complement; power set and Cartesian product; relations and functions (injective, surjective, bijective), graphs of functions (several examples, among them elementary functions and piecewise functions). Partition of a set. Equivalence relations and quotient sets. Natural numbers and mathematical induction principle. Cardinality of the power set of a finite set.

(3) Rational numbers and their representation; real numbers. Rational numbers as fractions, this representation is not unique, fraction in its lowest terms. Representation of the rational numbers as points on an oriented line. Representation of the rational numbers as finite decimal or infinite periodic sequences. Non-existence of a rational number with square 2. Real numbers as infinite decimal sequences. Bounded and unbounded subsets in R. Sup/Inf, maximum and minimum of a set in R. Intervals in R and their notation.


EXAM
It consists of two parts (to be done in the same day), successfulness in part A is a necessary condition for the correction of part B:

Part A (1 hour, handled by Syllabus Course teachers ): check of knowledge of Syllabus
course subjects
Part B (2 hours, handled by EMB teachers): check of knowledge of EMB course subjects.

The exam is only for first year students.
MAT/01 - MATHEMATICAL LOGIC - University credits: 0
MAT/02 - ALGEBRA - University credits: 0
MAT/03 - GEOMETRY - University credits: 0
MAT/04 - MATHEMATICS EDUCATION AND HISTORY OF MATHEMATICS - University credits: 0
MAT/05 - MATHEMATICAL ANALYSIS - University credits: 0
MAT/06 - PROBABILITY AND STATISTICS - University credits: 0
MAT/07 - MATHEMATICAL PHYSICS - University credits: 0
MAT/08 - NUMERICAL ANALYSIS - University credits: 0
MAT/09 - OPERATIONS RESEARCH - University credits: 0
Lessons: 27 hours