Axioms of set theory. Relation and function. Integer. Divisibility, division algorithm and greatest common visitor. Linear diophantine equation. Congruence. Operations. Rings. Homomorphism and ideals. Kernel of a homomorphism. Quotient ring. Theorem of ring homomorphism. Polynomial ring and formal series. Factorization. Principali deal domain and euclidean domain. Unique factorization domain. Chinese remainder theorem. Fermat’s little theorem.
Knowledge acquired:
The course aims to provide some basic concepts of mathematics, which are important for all the courses of the Laurea Degree Course in Mathematics.
Competence acquired:
Basic concepts on set theory. Study of algebraic structures.
Skills acquired (at the end of the course):
The student acquires basic concepts of mathematics.
Prerequisites
None
Teaching Methods
Total hours of the course (including the time spent in attending lectures, seminars, private study, examinations, etc...): 225
Hours reserved to private study and other indivual formative activities: 129
Contact hours for: Lectures (hours): 45
Intermediate examinations: 6
Further information
Frequency of lectures, practice and lab: Recommended
Teaching Tools UniFi E-Learning: http://e-l.unifi.it
Type of Assessment
Written and Oral.
Course program
Axioms of set theory. Relation and function. Integer. Divisibility, division algorithm and greatest common visitor. Linear diophantine equation. Congruence. Operations. Rings. Homomorphism and ideals. Kernel of a homomorphism. Quotient ring. Theorem of ring homomorphism. Polynomial ring and formal series. Factorization. Principali deal domain and euclidean domain. Unique factorization domain. Chinese remainder theorem. Fermat’s little theorem.