Elements of Basic Mathematics
A.Y. 2025/2026
Learning objectives
The aim of this course is to provide students with the basic language and the essential tools, which are the fundamentals to face the BSc program in Mathematics.
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.
Lesson period: First semester
Assessment methods: Giudizio di approvazione
Assessment result: superato/non superato
Single course
This course cannot be attended as a single course. Please check our list of single courses to find the ones available for enrolment.
Course syllabus and organization
Elementi di matematica di base (ediz.1)
Responsible
Lesson period
First semester
Course syllabus
(1) Basics of Logic: propositional calculus, logical connectors. Logical implication and equivalence, necessary and/or sufficient conditions. First order logic, quantifiers. Proofs by contrapositive and by contradiction.
(2) Basics of set theory: elements and subsets of a set; inclusion, union, intersection; power set and Cartesian product; relations and functions. Equivalence relations and ordered sets. The induction principle.
(3) Elements of combinatorics: cardinality of unions, products, function sets, power sets. Decimal expansion of rational numbers.
(2) Basics of set theory: elements and subsets of a set; inclusion, union, intersection; power set and Cartesian product; relations and functions. Equivalence relations and ordered sets. The induction principle.
(3) Elements of combinatorics: cardinality of unions, products, function sets, power sets. Decimal expansion of rational numbers.
Prerequisites for admission
No specific preliminary knowledge is required
Teaching methods
Teaching methods
Teaching methods
Frontal lessons. Meetings on request, for students who need extra explanations.
Teaching Resources
Materials will be posted on the official web site of the teaching
Useful books:
1) Matematica zero- ROMA Casa Editrice Aracne (1984)
2) M.Bramanti-G.Travaglini: Matematica. Questione di Metodo -Zanichelli (2009
Useful books:
1) Matematica zero- ROMA Casa Editrice Aracne (1984)
2) M.Bramanti-G.Travaglini: Matematica. Questione di Metodo -Zanichelli (2009
Assessment methods and Criteria
The written exam consists of two parts (to be done on the same day):
Part A: exercises on the Syllabus course topics;
Part B: exercises on the EMB course topics.
The final examination is positive if both part A and part B of the written exam are. Final marks are Approved/Not approved.
Part A: exercises on the Syllabus course topics;
Part B: exercises on the EMB course topics.
The final examination is positive if both part A and part B of the written exam are. Final marks are Approved/Not approved.
MAT/01 - MATHEMATICAL LOGIC - University credits: 1
MAT/02 - ALGEBRA - University credits: 1
MAT/03 - GEOMETRY - University credits: 1
MAT/02 - ALGEBRA - University credits: 1
MAT/03 - GEOMETRY - University credits: 1
Lessons: 27 hours
Professor:
Garbagnati Alice
Elementi di matematica di base (ediz.2)
Responsible
Lesson period
First semester
MAT/01 - MATHEMATICAL LOGIC - University credits: 1
MAT/02 - ALGEBRA - University credits: 1
MAT/03 - GEOMETRY - University credits: 1
MAT/02 - ALGEBRA - University credits: 1
MAT/03 - GEOMETRY - University credits: 1
Lessons: 27 hours
Professor:
Vezzani Alberto
Professor(s)