The course aims to investigate notions and results of basic algebra and to elaborate on them in order to approach more advanced topics that may have an educational value.
The selected topics have a central place in the teaching of algebra in the secondary school. There will also be an attention to the applicative aspects of the chosen themes.
The selected topics have a central place in the teaching of algebra in the secondary school. There will also be an attention to the applicative aspects of the chosen themes.
scheda docente
materiale didattico
• Theory of continued fractions
• Sequences defined by recurrence, Fibonacci numbers
• Constructions with ruler and compass.
• Cardinality theory, Cantor's theorems
• Congruences, diophantine equations, applications
• Solvability of third and fourth degree equations
• Arithmetic functions
Autori: W.M. Baldoni, C. Ciliberto, G.M. Piacentini Cattaneo
Unitext Springer
Programma
• Divisibility, Euclid's algorithm• Theory of continued fractions
• Sequences defined by recurrence, Fibonacci numbers
• Constructions with ruler and compass.
• Cardinality theory, Cantor's theorems
• Congruences, diophantine equations, applications
• Solvability of third and fourth degree equations
• Arithmetic functions
Testi Adottati
Aritmetica, crittografia e codiciAutori: W.M. Baldoni, C. Ciliberto, G.M. Piacentini Cattaneo
Unitext Springer
Modalità Erogazione
Lectures by the teacher with sessions of exercises only. In any case, the instructions of the University regarding the possibility of transmitting the lessons on Microsoft Teams will be followed if this becomes necessary for the Covid emergency.Modalità Frequenza
Attending is not mandatory but strongly recommendedModalità Valutazione
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. It will be evaluated whether to take seminars instead of the oral exam. The written test (including the partial tests) consists of 5/6 practical / theoretical exercises to be carried out in 2.30 / 3 hours.