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.
Curriculum
teacher profile teaching materials
- M. FONTANA E S. GABELLI: INSIEMI, NUMERI E POLINOMI, CISU, (1989)
- R.B.J.T. ALLENBY: RINGS, FIELDS AND GROUPS, EDWARD ARNOLD, (1991)
- M. ARTIN: ALGEBRA, PRENTICE-HALL, (1991)
Programme
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.Core Documentation
- G.M. PIACENTINI CATTANEO: ALGEBRA, UN APPROCCIO ALGORITMICO, DECIBEL-ZANICHELLI, (1996)- M. FONTANA E S. GABELLI: INSIEMI, NUMERI E POLINOMI, CISU, (1989)
- R.B.J.T. ALLENBY: RINGS, FIELDS AND GROUPS, EDWARD ARNOLD, (1991)
- M. ARTIN: ALGEBRA, PRENTICE-HALL, (1991)
Attendance
Attending is not mandatory but strongly recommendedType of evaluation
The exam will consist of a written and an oral test at the end of the course. During the course there will be two partial written tests that will be evaluated as a written exam. To those who pass both tests during the course with a vote higher than 18/30 (for each test) the teacher will propose a vote to verbalize the exam without the need to take an oral test. This proposal may also be refused by students if they wish to take an oral test to try to improve the final result. The oral is however necessary for those who want to aspire to praise. The written test (including the partial tests) consists of 5/6 practical / theoretical exercises to be carried out in 2.30 / 3 hours. teacher profile teaching materials
- M. FONTANA E S. GABELLI: INSIEMI, NUMERI E POLINOMI, CISU, (1989)
- R.B.J.T. ALLENBY: RINGS, FIELDS AND GROUPS, EDWARD ARNOLD, (1991)
- M. ARTIN: ALGEBRA, PRENTICE-HALL, (1991)
Programme
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.Core Documentation
- G.M. PIACENTINI CATTANEO: ALGEBRA, UN APPROCCIO ALGORITMICO, DECIBEL-ZANICHELLI, (1996)- M. FONTANA E S. GABELLI: INSIEMI, NUMERI E POLINOMI, CISU, (1989)
- R.B.J.T. ALLENBY: RINGS, FIELDS AND GROUPS, EDWARD ARNOLD, (1991)
- M. ARTIN: ALGEBRA, PRENTICE-HALL, (1991)
Attendance
Attending is not mandatory but strongly recommendedType of evaluation
The exam will consist of a written and an oral test at the end of the course. During the course there will be two partial written tests that will be evaluated as a written exam. To those who pass both tests during the course with a vote higher than 18/30 (for each test) the teacher will propose a vote to verbalize the exam without the need to take an oral test. This proposal may also be refused by students if they wish to take an oral test to try to improve the final result. The oral is however necessary for those who want to aspire to praise. The written test (including the partial tests) consists of 5/6 practical / theoretical exercises to be carried out in 2.30 / 3 hours.