| AL110-ALGEBRA 1
(objectives)
Provide the elements of the "mathematical language" (set theory, elementary logic, numerical sets) and the knowledge of the basic tools of modern algebra (notions of operation, group, ring, field) through the development of examples that provide the motivations.
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Code
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20410386 |
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Language
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ITA |
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Type of certificate
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Profit certificate
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Credits
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9
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Scientific Disciplinary Sector Code
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MAT/02
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Contact Hours
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48
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Exercise Hours
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42
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Type of Activity
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Basic compulsory activities
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Teacher
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TARTARONE FRANCESCA
(syllabus)
SETS AND FUNCTIONS. EQUIVALENCE RELATIONS. NATURAL NUMBERS. PEANO AXIOMS. THE PRINCIPLE OF INDUCTION. WELL ORDERING. CONSTRUCTIONS OF THE SET OF RELATIVE INTEGER NUMBERS AND OF THE SET OF RATIONAL NUMBERS. BASIC PROPERTIES OF COMPLEX NUMBERS. DIVISIBILITY IN THE INTEGERS, EUCLIDEAN ALGORITHM, GCD. DEFINITIONS AND EXAMPLES OF THE MAIN ALGEBRAIC STRUCTURES: GROUPS, RINGS, AND FIELDS. GROUP OF THE UNITS OF A RING. GROUPS OF PERMUTATIONS. THE RING OF INTEGERS MODULO N. LINEAR CONGRUENCES. EULER PHI FUNCTION. POLYNOMIAL RINGS WITH COEFFICIENTS IN RING OF NUMBERS: CONSTRUCTION, BASIC PROPERTIES, DIVISIBILITY, IRREDUCIBILITY CRITERIA, GAUSS LEMMA AND PRIMITIVE POLYNOMIALS.
(reference books)
D. Dikranjan - M.S. Lucido, Aritmetica e algebra, Liguori.
I. Herstein, Algebra - Editori Riuniti (2010)
G.M. Piacentini Cattaneo, Algebra,un approccio algoritmico, Decibel -Zanichelli.
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Dates of beginning and end of teaching activities
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From to |
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Delivery mode
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Traditional
At a distance
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Attendance
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not mandatory
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Evaluation methods
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Written test
Oral exam
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Teacher
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CAPUANO LAURA
(syllabus)
SETS AND FUNCTIONS. EQUIVALENCE RELATIONS. NATURAL NUMBERS. PEANO AXIOMS. THE PRINCIPLE OF INDUCTION. WELL ORDERING. CONSTRUCTIONS OF THE SET OF RELATIVE INTEGER NUMBERS AND OF THE SET OF RATIONAL NUMBERS. BASIC PROPERTIES OF COMPLEX NUMBERS. DIVISIBILITY IN THE INTEGERS, EUCLIDEAN ALGORITHM, GCD. DEFINITIONS AND EXAMPLES OF THE MAIN ALGEBRAIC STRUCTURES: GROUPS, RINGS, AND FIELDS. GROUP OF THE UNITS OF A RING. GROUPS OF PERMUTATIONS. THE RING OF INTEGERS MODULO N. LINEAR CONGRUENCES. EULER PHI FUNCTION. POLYNOMIAL RINGS WITH COEFFICIENTS IN RING OF NUMBERS: CONSTRUCTION, BASIC PROPERTIES, DIVISIBILITY, IRREDUCIBILITY CRITERIA, GAUSS LEMMA AND PRIMITIVE POLYNOMIALS.
(reference books)
D. Dikranjan - M.S. Lucido, Aritmetica e algebra, Liguori.
I. Herstein, Algebra - Editori Riuniti (2010)
G.M. Piacentini Cattaneo, Algebra,un approccio algoritmico, Decibel -Zanichelli.
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Dates of beginning and end of teaching activities
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From to |
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Delivery mode
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Traditional
At a distance
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Attendance
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not mandatory
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Evaluation methods
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Written test
Oral exam
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Università Roma Tre