Elements of Basic Mathematics

A.Y. 2016/2017
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 mathematic 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 theory of sets and functions, and of combinatorics.
Course syllabus and organization

Elementi di matematica di base (ediz.1)

Responsible
Lesson period
First semester
Course syllabus
1. Elements of logic: implications, negations, logical equivalences, necessary and/or sufficient conditions, quantifiers, counter-nominal proofs and proofs by contradiction.
2. Elements of set theory: inclusion, union, intersection, complement; power set, Cartesian product; functions (injective, surjective), relations, function graphs (some examples of elementary functions). Equivalence relations and quotient set. Natural numbers and the Principle of induction. Cardinality of the set of subsets of a finite set. An overview of integer and rational numbers.
3. Combinatorics: finite sets, number of functions between finite sets (dispositions with repetition); number of injective functions between finite sets (simple dispositions); permutations; simple combinations and binomial coefficients.
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: Mantovani Sandra

Elementi di matematica di base (ediz.2)

Responsible
Lesson period
First semester
Course syllabus
1. Elements of logic: implications, negations, logical equivalences, necessary and/or sufficient conditions, quantifiers, counter-nominal proofs and proofs by contradiction.
2. Elements of set theory: inclusion, union, intersection, complement; power set, Cartesian product; functions (injective, surjective), relations, function graphs (some examples of elementary functions). Equivalence relations and quotient set. Natural numbers and the Principle of induction. Cardinality of the set of subsets of a finite set. An overview of integer and rational numbers.
3. Combinatorics: finite sets, number of functions between finite sets (dispositions with repetition); number of injective functions between finite sets (simple dispositions); permutations; simple combinations and binomial coefficients.
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: Zampieri Elena
Professor(s)
Reception:
Thursday 12.45-14.15, by appointment
Studio 1019, I Floor, Dipartimento di Matematica, Via Saldini, 50