Università Roma Tre

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.

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