Elements of Basic Mathematics
A.Y. 2026/2027
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
Single session
Responsible
Lesson period
First semester
MATH-01/A - Mathematical Logic - University credits: 1
MATH-02/A - Algebra - University credits: 1
MATH-02/B - Geometry - University credits: 1
MATH-02/A - Algebra - University credits: 1
MATH-02/B - Geometry - University credits: 1
Lessons: 27 hours
Professor:
Mantovani Sandra
Shifts:
Turno
Professor:
Mantovani SandraSurname A-L
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
Frontal lessons.
Teaching Resources
Daniel J. Velleman "How to Prove It"
Richard Hammack "Book of Proof"
Richard Hammack "Book of Proof"
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 time limit of each part is proportioned to the level and number of the given exercises.
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 time limit of each part is proportioned to the level and number of the given exercises.
The final examination is positive if both part A and part B of the written exam are. Final marks are Approved/Not approved.
MATH-01/A - Mathematical Logic - University credits: 1
MATH-02/A - Algebra - University credits: 1
MATH-02/B - Geometry - University credits: 1
MATH-02/A - Algebra - University credits: 1
MATH-02/B - Geometry - University credits: 1
Lessons: 27 hours
Professor:
Stellari Paolo
Shifts:
Turno
Professor:
Stellari PaoloSurname M-Z
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
Frontal lessons.
Teaching Resources
Daniel J. Velleman "How to Prove It"
Richard Hammack "Book of Proof"
Richard Hammack "Book of Proof"
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 time limit of each part is proportioned to the level and number of the given exercises.
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 time limit of each part is proportioned to the level and number of the given exercises.
The final examination is positive if both part A and part B of the written exam are. Final marks are Approved/Not approved.
MATH-01/A - Mathematical Logic - University credits: 1
MATH-02/A - Algebra - University credits: 1
MATH-02/B - Geometry - University credits: 1
MATH-02/A - Algebra - University credits: 1
MATH-02/B - Geometry - University credits: 1
Lessons: 27 hours
Professor:
Vezzani Alberto
Shifts:
Turno
Professor:
Vezzani AlbertoProfessor(s)
Reception:
Thursday 12.45-14.15, by appointment
Studio 1019, I Floor, Dipartimento di Matematica, Via Saldini, 50
Reception:
Fix an appointment by email
Dipartimento di Matematica "F. Enriques" - Room 2046