ELEMENTARY MATHEMATICS FROM AN ADVANCED STANDPOINT

Degree course: 
Corso di Second cycle degree in MATHEMATICS
Academic year when starting the degree: 
2025/2026
Year: 
1
Academic year in which the course will be held: 
2025/2026
Course type: 
Supplementary compulsory subjects
Credits: 
6
Period: 
Second semester
Standard lectures hours: 
48
Detail of lecture’s hours: 
Lesson (48 hours)
Requirements: 

bachelor degree

Final Examination: 
Orale

Take home project on a topic of the class chosen by the instructor. Final oral examination at the blackboard, including a simple exercise. There is only a final mark not parted between project and oral examination.

Assessment: 
Voto Finale

provide the student with ideas and matrials suitable for innovative teaching in high school

Selected topics from dynamical systems theory

Egyptian Fractions Inverse problem, Greedy Algorithm for determining an Egyptian fraction Special cases without the greedy algorithm Farey's sum Farey Tree Continuous Fractions Solar and lunar calendars Euclid's algorithm as a dynamical system Minkovski's ? function Toward the irrationals: Quadratic Surds Minkovski's ? Measure Orthogonality of measures, orthogonal polynomials Main properties of orthogonal polynomials Jacobi matrices and recurrence relations Iteration of polynomials in the complex field, Julia sets Systems of iterated functions, fractals and supported measures Minkovski's sums of sets and related games Hyperbolic geometry in the upper Poincare' plane Billiards in hyperbolic space Kepler's anisotropic problem And other topics that might raise our interest

Lectures at the blackboard, computer experiments.

Students may contact the instructor by e-mail to set up an appointment