Elements of Basic Mathematics
A.Y. 2024/2025
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 can be attended as a single course.
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
Frontal lessons. Meetings on request, for students who need extra explanations.
Teaching Resources
1) Matematica zero- ROMA Casa Editrice Aracne (1984)
2) M.Bramanti-G.Travaglini: Matematica. Questione di Metodo -Zanichelli (2009)
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
MAT/02 - ALGEBRA
MAT/03 - GEOMETRY
MAT/04 - MATHEMATICS EDUCATION AND HISTORY OF MATHEMATICS
MAT/05 - MATHEMATICAL ANALYSIS
MAT/06 - PROBABILITY AND STATISTICS
MAT/07 - MATHEMATICAL PHYSICS
MAT/08 - NUMERICAL ANALYSIS
MAT/09 - OPERATIONS RESEARCH
MAT/02 - ALGEBRA
MAT/03 - GEOMETRY
MAT/04 - MATHEMATICS EDUCATION AND HISTORY OF MATHEMATICS
MAT/05 - MATHEMATICAL ANALYSIS
MAT/06 - PROBABILITY AND STATISTICS
MAT/07 - MATHEMATICAL PHYSICS
MAT/08 - NUMERICAL ANALYSIS
MAT/09 - OPERATIONS RESEARCH
Lessons: 27 hours
Professor:
Bertolini Marina
Shifts:
Turno
Professor:
Bertolini MarinaElementi di matematica di base (ediz.2)
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. Meetings on request, for students who need extra explanations.
Teaching Resources
1) Matematica zero- ROMA Casa Editrice Aracne (1984)
2) M.Bramanti-G.Travaglini: Matematica. Questione di Metodo -Zanichelli (2009)
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 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.
MAT/01 - MATHEMATICAL LOGIC
MAT/02 - ALGEBRA
MAT/03 - GEOMETRY
MAT/04 - MATHEMATICS EDUCATION AND HISTORY OF MATHEMATICS
MAT/05 - MATHEMATICAL ANALYSIS
MAT/06 - PROBABILITY AND STATISTICS
MAT/07 - MATHEMATICAL PHYSICS
MAT/08 - NUMERICAL ANALYSIS
MAT/09 - OPERATIONS RESEARCH
MAT/02 - ALGEBRA
MAT/03 - GEOMETRY
MAT/04 - MATHEMATICS EDUCATION AND HISTORY OF MATHEMATICS
MAT/05 - MATHEMATICAL ANALYSIS
MAT/06 - PROBABILITY AND STATISTICS
MAT/07 - MATHEMATICAL PHYSICS
MAT/08 - NUMERICAL ANALYSIS
MAT/09 - OPERATIONS RESEARCH
Lessons: 27 hours
Professor:
Vezzani Alberto
Shifts:
Turno
Professor:
Vezzani AlbertoElementi di matematica di base (ediz.3)
Lesson period
First semester
MAT/01 - MATHEMATICAL LOGIC
MAT/02 - ALGEBRA
MAT/03 - GEOMETRY
MAT/04 - MATHEMATICS EDUCATION AND HISTORY OF MATHEMATICS
MAT/05 - MATHEMATICAL ANALYSIS
MAT/06 - PROBABILITY AND STATISTICS
MAT/07 - MATHEMATICAL PHYSICS
MAT/08 - NUMERICAL ANALYSIS
MAT/09 - OPERATIONS RESEARCH
MAT/02 - ALGEBRA
MAT/03 - GEOMETRY
MAT/04 - MATHEMATICS EDUCATION AND HISTORY OF MATHEMATICS
MAT/05 - MATHEMATICAL ANALYSIS
MAT/06 - PROBABILITY AND STATISTICS
MAT/07 - MATHEMATICAL PHYSICS
MAT/08 - NUMERICAL ANALYSIS
MAT/09 - OPERATIONS RESEARCH
Lessons: 27 hours
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