Teaching - Università Roma Tre

AL110-ALGEBRA 1 (objectives)

Code

20410386

Language

ITA

Type of certificate

Profit certificate

Credits

9

Scientific Disciplinary Sector Code

MAT/02

Contact Hours

48

Exercise Hours

42

Type of Activity

Basic compulsory activities

Teacher	BARROERO FABRIZIO (syllabus) The language of sets -Sets and elements -Propositional logic -Subsets, union, intersection and complement -Power set and partitions -Cartesian product Correspondences and relations -Correspondences - Order relations - Equivalence relations Functions - Generalities on functions - Composite functions - Inverse functions Natural numbers and cardinality - The set of natural numbers and induction - The cardinality of a set The ring of integers -Construction of the set of whole numbers - Generalities about rings - The Euclidean division - The fundamental theorem of arithmetic The rings of residue classes - Definition and first properties - Linear congruences and systems of linear congruences -Morphisms -The Fermat's little Theorem and Euler's theorem The field of rational numbers -Construction of the set of rational numbers - The positional notation of rational numbers Polynomials - Generalities on polynomials - Roots, division and factorization of polynomials - Polynomials with integer and rational coefficients The fields of real numbers and complex numbers - Notions on the construction of the reals -Positional writing of real numbers - Definition of the complex field -Polinomials with real and complex coefficients - Algebraic numbers and transcendental numbers - Polar or trigonometric form of complex numbers - Roots of unity and cyclotomic polynomials (reference books) Script by the lecturer. G.M. Piacentini Cattaneo, Algebra, un approccio algoritmico, Decibel-Zanichelli, (1996) I. N. Herstein, Algebra, Editori Riuniti, (2003)
Dates of beginning and end of teaching activities	From to
Delivery mode	Traditional
Attendance	not mandatory
Evaluation methods	Written test Oral exam

Teacher	CAPUANO LAURA (syllabus) The language of sets -Sets and elements -Propositional logic -Subsets, union, intersection and complement -Power set and partitions -Cartesian product Correspondences and relations -Correspondences - Order relations - Equivalence relations Functions - Generalities on functions - Composite functions - Inverse functions Natural numbers and cardinality - The set of natural numbers and induction - The cardinality of a set The ring of integers -Construction of the set of whole numbers - Generalities about rings - The Euclidean division - The fundamental theorem of arithmetic The rings of residue classes - Definition and first properties - Linear congruences and systems of linear congruences -Morphisms -The Fermat's little Theorem and Euler's theorem The field of rational numbers -Construction of the set of rational numbers - The positional notation of rational numbers Polynomials - Generalities on polynomials - Roots, division and factorization of polynomials - Polynomials with integer and rational coefficients The fields of real numbers and complex numbers - Notions on the construction of the reals -Positional writing of real numbers - Definition of the complex field -Polinomials with real and complex coefficients - Algebraic numbers and transcendental numbers - Polar or trigonometric form of complex numbers - Roots of unity and cyclotomic polynomials (reference books) Script by the lecturer. G.M. Piacentini Cattaneo, Algebra, un approccio algoritmico, Decibel-Zanichelli, (1996) I. N. Herstein, Algebra, Editori Riuniti, (2003)
Dates of beginning and end of teaching activities	From to
Delivery mode	Traditional
Attendance	not mandatory
Evaluation methods	Written test Oral exam